APPLICATION OF THE

SEQUENTIAL UNCONSTRAINED MINIMIZATIONTECHNIQUE IN A

SYSTEMATIC CONTAINERSHIP DESIGN

Robert Malcolm Fortson

DUDLEY KNOX LIBKAK1

NAVAL POSTGRADUATE SCHOUL

MONTEREY. CALIFORNIA 93940

APPLICATION OF THE

SEQUENTIAL UNCONSTRAINED MINIMIZATION

TECHNIQUE IN A

SYSTEMATIC CONTAINERSHIF DESIGN

by

ROBERT MALCOLM FORTSON, III

B. S. United States Naval Academy

- - - - " (1969)

SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF SCIENCE

MAY 10. 1974

z'i*

IWONTEREY, CAL irn-H°°'-

APPLICATION 0? THE SEQUENTIAL UNCONSTRAINED

MINIMIZATION TECHNIQUE IN A

SYSTEMATIC CCNTAINERSHIF DESIGN

by

ROBERT M. PORTSCN, III

Submitted to the Alfred P. Sloan School of Management onMay 10, 197^i in partial fulfillment of the requirementsfor the degree of Master of Science in Management.

ABSTRACT

This paper investigates the preliminary ship designprocess. The thesis begins by looking at methodologiesfor ship design and concludes that a different outlook onthe overall process could provide an improvement, In par-ticular, possible modifications were identified in theowner's requirements as traditionally given to the designer.After the new design procedure was developed, effortshifted to implementing the procedure for a containershipdesign.

A preliminary ship design model is developed. Thismodel was then used in a test design problem in which anowner desires a single ship to add to an existing traderoute. The design model was used to identify acceptableship alternatives.

The determination of attractive designs was accom-plished by a version of an optimization method known asa Sequential Unconstrained Minimization Technique. Thismethod employs a barrier penalty function to handle theproblem constraints. The search method was found to beeffective in identifying design alternatives. In parti-cular, it behaved well with the discontinuities imposedby the discrete engine selections involved with gas tur-bine power plants.

Thesis Supervisor: Thomas L. MagnantiTitle: Assistant Professor

ACKNOWLEDGEMENT

My many thank go to Professor Magnanti for the time

he spent reviewing the content and suggesting changes in

problem areas. Needless to say, a great deal of personal

appreciation goes to him for being encouraging at times

when it v/as needed most.

My thanks also to Professor Mandel for giving me the

inspiration for the thesis topic and for the time he spent

in guiding my efforts.

Thanks also to Professor Chryssostomidis for the

technical assistance and for reviewing the technical con-

tent.

Last, but not least, my appreciation and thanks to

my wife, Martha, who typed the thesis twice and for the

untimely hours she spent changing mistakes, editing and

listening to my complaints.

TABLE 0? CONTENTS

Pagetai

TITLE PAGE 1

ABSTRACT 2

ACKNOWLEDGEMENTS 3

TABLE OF CONTENTS 4

LIST OF FIGURES 7

LIST 0^ TABLES 9

INTRODUCTION 10

I. OCEAN TRANSPORTATION SYSTEM 14

1.1 Elements1.2 Subsystem Interactions

II. SHIP DESIGN PROCESS 19

2.1 General2.2 Normative Design Process2.3 Proposed Design Frocess

I I I. PROBLEM STATEMENT 31

3.1 Scenario3.2 Design Problem

IV. SHIP DESIGN CRITERIA 34

4.1 Criteria4.2 Measures of Effectiveness4.3 Measure of Economic Criteria

4.3.1 General4.3.2 Net Fresent Value4.3.3 Capital Recovery factor4.3.4 Required "reight Rate

V

.

ALTERNATIVES 48

5.1 Decision Variables5.2 Design Alternatives

Page

5.2.1 Engine Arrangements5.2.2 Ballast5.2.3 Full Load Condition5.2.4 Volume5.2.5 Containers5.2.6 Terminal Interactions5.2.7 Propeller Alternatives

VI. DECISION MODEL 56

6.1 Objective Function6.2 Constraints

VII. OPTIMIZATION TECHNIQUES 60

7.1 Basic Search Routines

7.1.1 Random Search7.1.2 Climbing Techniques

7.2 Sequential Unconstrained Minimization Technique

7.2.1 General7.2.2 Newton-Raphson Method7.2.3 Golden Section Search

7.3 SUMT Computer Frogram

VIII. DEFINITION 0? THE OBJECTIVE SURFACE 75

8.1 General8.2 Required Fropulsive Fower8.3 Discrete Fower Plant Selection8.4 Payload Configuration8.5 Input Parameters

IX. ANALYSIS 90

9.1 Program Validation9.2 Frogram Inputs9.3 Procedure9.4 SUMT Trajectories9.5 Ranking the Alternatives9.6 Discontinuities9.7 Sensitivity

X. CONCLUSIONS AND RECOMMENDATIONS HO

10.1 General10.2 Optimization in the Design Process

5

Page

10.3 Experience with SUT.T

10.4 Areas for Additional Study10.5 Applications

XI. FOOTNOTES 119

XII. BIBLIOGRAFHY 120

XIII. APPENDICES 125

APPENDIX A 126APPENDIX 3 130AFFEKDIX C 139APPENDIX D 1^0APPENDIX E 161

LIST 0? FIGURES

Figure Page

1. OCEAN TRANSPORTATION SYSTEM 15

2. SHIP DESIGN PROCESS 20

3. INFORMATION PLOWS IN A NORMATIVE DESIGN PROCESS 22

4. MODEL 0? THE PROPOSED SHIP DESIGN PROCESS 28

5. SIMPLE CAPITAL DECISION MODEL 40

6. CASH FLOW MODEL AND NPV CALCULATION 43

7. CRF AND R"R CALCULATIONS 47

8. MATHEMATICAL STATEMENT OF THE CONTAINERSHIFDESIGN PROBLEM - 59

9. PENALTY FUNCTION 64

10. NEV/TON-RAPHSON PROCEDURE 70

11. SEARCH INTERVAL 71

12. UNIMODAL FUNCTIONS 72

13. OBJECTIVE SURFACE FLOW CHART (A) 78

14. OBJECTIVE SURFACE FLOW CHART (B) 79

15. OBJECTIVE SURFACE FLOW CHART (C) 80

16. FEEDBACK LOOP DIAGRAM 81

17. OBJECTIVE SURFACE PROFILE FOR ALTERNATIVE 4 105

18. OBJECTIVE SURFACE PROFILE FOR ALTERNATIVE 3 106

19. SPEED REDUCTION FACTOR 133

20. MACHINERY WEIGHT 13^

21. COST OF MACHINERY 135

22. SPECIFIC fuel CONSUMPTION 137

Fage

23. SFC CURVES FOR MARINE GAS TURBINES 138

Zk, PROGRAM DATA DECK STRUCTURE 152

25. SAMPLE DATA CARDS FOR SUMT PROGRAM 153

26. SAMPLE DATA CARDS FOR DESIGN MODEL 15^

27. SAMPLE OUTPUT OF DETAILED DESIGN 156

28. SAMPLE OUTPUT OF SUMT PROGRAM 15?

8

LIST 0F_ TABLES

Table

1. CATALOG 0? CRITERIA

2. DECISION VARIABLES

3. A.S.A STANDARD CONTAINER DIMENSIONS AND WEIGHTS

4. PROGRAM INPUT FARAMETERS

5. PROGRAM INPUT PARAMETERS (CONT.)

6. MODEL VALIDATION

7. IDENTIFICATION OF ALTERNATIVES

8. SOLUTION TRAJECTORY FOR ALTERNATIVE 3

9. SOLUTION TRAJECTORY FOR ALTERNATIVE 4

10. SOLUTION TRAJECTORY FOR ALTERNATIVE 6

11. SOLUTION TRAJECTORY FOR ALTERNATIVE 8

12. RANKING OF ALTERNATIVES

13. SENSITIVITY ANALYSIS

14. DEFINITION OF TERMS

15. INPUT PARAMETERS FOR NNSB VALIDATION

16. INPUT PARAMETERS FOR BIW VALIDATION

17. INPUT PARAMETERS ^OR G.G. SHARP VALIDATION

18. INPUT PARAMETERS "OR SCENARIO PROBLEM

Fase

35

48

59

88

89

91. 92

95, 96

98

99

100

101

103

109

127

140, l4l

142, 143

144, 145

146, 147

INTRODUCTION

Through the years, ocean transport systems have provi-

ded a common forum in which the businessmen and engineers

could participate as a team. The complexity of the present

systems as well as the sophistication of their design has

not evolved without numerous growing pains. Over the years,

society has developed the framework in which each party

operates. The boundaries of responsibility for the two are

not always well defined nor are their liabilities. This

vagueness extends to their interaction with the rest of soc-

iety. The results of past efforts to formalize their rules

with respect to the ship design process can be found in

rules of the American Board of Shipping and of many insur-

ance companies. These rules guide the engineer/designer

in his task so that the final ship design will meet certain

minimum standards. These standards have been developed over

the years and are based on experience.

This paper does not propose a change in the traditional

roles of the businessman and the engineer as related to

ocean transport systems, nor does it develop any new innova-

tions into either of their professional areas. It does,

however, attempt to define explicitly the formal relation-

ships between the parties involved in the design process and

to indicate how these relationships can be used in actual10

ship design. The approach taken is not traditional. The

result is not a new relationship, but rather a more defined

and process oriented approach where there can be a better

agreement as to each parties role with the result of improv-

ing their joint effort.

In an attempt to demonstrate this philosophy, the the-

sis presents a sample problem. With this problem, a method

of solution is then pursued. The important aspects of this

problem are identified in the context developed earlier in

the paper which defines the roles of the participants. The

problem is approached in an objective manner and the outputs

are identified which would prove useful to a decision maker.

The paper presents the results with caution. First, because

the solution addresses only the problem outlined in the

scenario. Secondly, the design model has not yet been veri-

fied by present design practice. Finally, the optimization

method may not in itself identify the overall best alter-

native to a real life problem. For this reason, no attempt

is made to identify such a result.

One of the easiest ways to present a problem is to re-

late a scenario. From this, the assumptions and simplifi-

cations made in the analysis become more palatable and the

solution is not regarded as simply a mass of assumptions

presented for the convenience of the solution technique. The

11

scenario also identifies a clearer division of roles of the

businessman (referred to as the customer) and the engineer

(referred to as the designer) in the scenario. By restrict-

ing the problem as stated in the scenario, the real life

complications and ambiguities are minimized. However, these

will not be ignored in the development of the design process.

The information flows of the design methodology guided the

development of the design program. This program utilized

the capabilities of the computer and the solution technique.

Before the design methodology is outlined or the scenario

developed, it is important to identify the approach of the

paper.

This paper uses a systems analysis format for presenta-

tion. By this it is meant that the first issues covered

involve the problem definition and objectives of the study.

Following the problem definition, the paper proceeds to

identify criteria and measures of effectiveness for the

problem solution. This is then followed by an outline of

the different types of alternatives available. From this

position, a decision model is developed. Tools known as

optimization techniques are applied to this model. The re-

sults and the analysis are accomplished by the application

of a Sequential Unconstrained Minimisation Technique re-

ferred to as STMT. The results are then studied and pre-

sented so that a decision can be made. This decision may

12

not cover the problems originally raised in the scenario,

but should at least pave the way for the next design itera-

tion. As such, the paper demonstrates the computer's capa-

bilities. This, in turn, will demonstrate the possible role

of a computer in a computer aided design.

Definitions are imperative for a proper understanding

of any study. A list of model variables have been collected

with their definition in Table lk found in Appendix A. Their

use in context should not prove difficult for the reader.

There is one definitbn, however, that deserves explanation

before we begin. This relates to the use of the terms

'closed form' or 'explicit' as qualifiers of expressions in

the mathematical model. These will be used interchangeably

in the paper. By an explicit expression, it is meant that

the relationships between the variables involved can be

found in terms of an algebraic expression. In particular,

we will be interested in the relationships involving the de-

cision variables.

The complexity of real life design problems made it

difficult to identify and assess all the implications of

the proposed design methodology. The results of the design

model were useful in identifying the usefulness in a con-

tainer ship design. This paper should serve as a basis

from which to reanalyze the existing methods used in the

design of ship systems.

13

CHAPTER I.

OCEAN TRANSFORTATION SYSTEMS

Much has been written about transportation systems.

The important features of any transportation system are its

collection, warehousing, transport and distribution subsys-

tems as well as the associated management and human subsys-

tems. In today's economy, some transportation systems are

so large that neither a single individual nor a single cor-

poration can control and direct the action of all the ele-

ments. This is especially true of the ocean transportation

systems. Y/e will limit our discussion to the actual trans-

port by the ocean vehicle. The character of this ocean

transport subsystem which distinguishes it from other modes

of travel is the need to have a transporting vessel capable

of transisting an ocean. In this transit, a ship will ex-

perience a hostile environment. The advantage of ocean

transport as opposed to other transport methods is the abil-

ity of an ocean transport system to carry larger loads,

either in bulk or weight.

1. 1 Elements

From the following figure, the ocean transportation sys-

tem can be divided into three basic parts. The first is the

mode of ocean transport by ship. At each end of the ocean

transport is a port and terminal system. At these terminal

14

u.

EHCO>HW

oHEH

EH

OPMC/i

2!

2

oo

u

•H

facilities, the cargo is handled so that another mode of

travel can he utilized. This constitutes the second ele-

ment. In the last element, we will lump all of the remain-

ing parts of a general transportation system. These will

include the various distribution and intermediate transpor-

tation systems.

1.2 Subsystem Interactions

We want to look now at the interactions between the

three parts. As described, the elements of the transpor-

tation system function in series, thus the capacity and the

related efficiency of the total system can be affected by a

single element. Any system design will attempt to size each

of the elements so that there will be no disparity in capa-

city between single units because of the resulting ineffi-

ciencies. An exception would be the planning of excess

capacity to be utilized during a future period of growth.

Conceptually this model should prove useful and as more

ports and shipping routes are opened, the same principle

can be used to describe the larger total system. This sim-

ple model ignores the management problem of capacity utili-

zation in large networks, but the interactions should be more

easily understood.

The major purpose of the ship is to act as a mode of

containment and transportation between ports. The terminal

also serves as a location to inventory cargo so that loading

16

and unloading of the ship can be achieved without delay.

Many methods have been proposed for reducing the cargo han-

dling at the terminals and thus increasing their capacity

and efficiency. One such attempt is the containerizaticn

of cargo. Instead of handling the different cargoes indivi-

dually, containers are used, thus simplifying the loading

problems and reducing breakage and loss of cargo. Over the

last few years this method has become even more popular,

especially with customers that transport small, high value

items, such as electronic equipment. For large bulk cargoes

ship barge systems have been developed.

The interaction between the ship and terminal has many

different facets. They can be related to a time delay in

port. When a ship arrives, it awaits space next to the ter-

minal, Once along side, the crane will continuously handle

containers during the loading operation. The duration of

this evolution depends directly upon the reach, carrying

capacity and speed of the crane. After the incoming cargo

is off loaded and the outgoing cargo is on loaded, the ship

may have to v/ait for favorable navigation conditions such as

slack water at high tide so that the ship can maneuver out

of port safely. The interaction is completed in the same

way that it started, with the ship at sea proceeding between

ports at its operating speed.

The interactions betv/een the port terminal and the rest

17

of the transportation system can be defined along similar

lines. It becomes evident that there is a large management

function at the terminals. The skill developed in these

functions and the capacities of each of the elements deter-

mines the volume of cargo flow in the total system. To say

that the transportation system is capacity limited by a sin-

gle element should require that the element is operating

with maximum efficiency. Otherwise, capacity can be in-

creased without additional capital investment. The complex

problem of capcity determination will play an important role

in the total transportation system design. It should be ob-

vious that when the total system is operating at capacity,

subsystems with excess capacity are not desirable unless

there are future plans for expansion. This points out the

requirement that the design cover the whole of the transpor-

tation system. Many papers have addressed themselves to

the overall capcity balancing problem. The reader is re-

ferred to Erichsen and Hancock^.

Independent of the overall transportation system design,

there will be a stage in the total design when the capabili-

ties and costs are desired of a ship that can interact with

a given terminal configuration. This may be for an addition

of shipping capacity on an already existing route or for an

entirely new transportation system. We are interested in

this interaction between the customer and the designer.

18

CHAPTER II.

SHIP DESIGN PROCESS

2.1 General

The ship design process is that set of actions involved

from the initial desire to build a ship until the final deli-

very of the product. In some circumstances, one or both of

these events may be difficult to determine. The process

involves two groups. One is the owner or user group and the

other is the designer or builder group. The traditional pro-

cess (see Figure 2) involves the determination of the owner's

expectations and his statement as to the capabilities desired

in the ship design. Many times this v/ould be the first for-

mal step in the process. The need for the ship may result

from intuitive feelings based upon years of experience as a

ship operator. Whatever the source, a gap is identified be-

tween supply and demand for services. The owner's require-

ments have traditionally been quite explicit — the speed,

endurance, and payload of the design being specified. This

statement provides the means by which the design passed to

the engineer from the owner. As depicted in the block dia-

gram, the designer then proceeds to implement a design pro-

cedure that results in a feasible design which meets the

owner's requirements. At that point, the owner would decide

19

SHIP DESIGN PROCESS

PresentSystem

CapabilitiesGap

Analysis

Demand for Services,Opportunities in the

I'larket Flace

DesiredSystem

TerminalDesign

PotentialProfits

OtherSubsystems

r<>

x /V

Ship DesignDesign V >

Owner's Requirements

Constraintsof Nature

Constraintsof

RegulatoryAgencies

Design

Procedure

Estimatesof Profitsand Risks

FeasibleDesign

Cost Estimates

FastDesign

Experience

OWNER

DESIGNER

Figure 2

20

if the ship design should continue to a building phase.

The steps listed in Figure 2 are representative of the

process. They may either be found explicitly or implicitly

in the design effort. There are two factors which disting-

uish the process. In general, it is a single pass system.

Inside each phase there may be iteration, but there is no

provision of changing the inputs to any phase. The second

characteristic is the parallel design feature of the

other elements of the system. The decision to build does

not necessarily provide for a system wide evaluation after

the owner's requirements are fixed. Before criticizing this

form, let us investigate the nature of the system,

2.2 Normative Design Process

From the ship design process, the decisions that must be

made are identified. They are in turn associated with a

level of decision making. The following conceptual model

exemplifies the hierarchy of decision making that makes up

the ship design process (See Figure 3)« According to

M. D. Mesarovic, et. al., there is no single best model for

describing the multilevel, hierarchial system. However,

the essential characteristics are a "...vertical arrangement

of subsystems, and [a^ dependence of the higher level sub-

Li.

systems upon the actual performance of the lower levels."

In the Figure, there is no significance to the number

of levels drawn. They are used only to show possible

21

INFORMATION FLOWSIN A NORMATIVE DESIGN PROCESS

DECISION MAKER

OWNER

OWNER

NEED

±DECISION

LEVEL #1

DECISION

LEVEL #2

CRITERIA

QUALITATIVE

CRITERIA

QUALITATIVE

CRITERIA

DESIGNER DECISION

LEVEL #3

QUANTITATIVE

CRITERIA

DESIGNERDESIGN

PROCEDURE

SOLUTION

Figure 3

22

relationships. The input to the process is the result of an

analysis which identifies a need. The output of the process

is a solution (design) which hopefully meets this need to

the satisfaction of the owner. At the higher levels, the

owner plays a major role. At the lower levels, the designer

accomplishes the design procedure. From each level, require-

ments and guidelines are passed down to the next lower level,

and from each lower level the current results and unresolved

decisions are passed up for action. The levels of decision

making have been identified as different stages at which

tradeoffs between criteria are accomplished. Associated

with each level is a set of criteria which are related to

the decisions being made. The decisions concerning certain

criteria can be delegated to lower stages in the design. In

this model of the design process, the owner has responsibil-

ity over all decision levels. Those involving quantitative

critieria such as cost have been identified with the lower

stages in the process. This assumes that the owner's pre-

ferences have been identified.

In the current design practice, the designer receives

the owner's requirements and stops as soon as a good solu-

tion is reached. This means that the last two stages of

the design process are in equilibrium with each other, but

not with the rest of the system. That is, the output of the

designer is a feasible solution which satisfies the original

23

owner's requirements. The traditional process terminates

here. If, instead of the last stages being conducted inde-

pendent of the rest of the system, continuous feedback and

adjustment were possible, a more desired result may be ob-

tained. This would require more coordination of effort

between the owner and the designer throughout the design.

By setting up a formal system to handle the various

levels of decision making, the owner will help control the

whole design process by giving better direction to lower

level management. This would be most important in the de-

sign of new ship types where the final desired solution is

not obvious to the owner.

This suggests that one of the first steps in the design

process is the determination of a set of criteria and order-

ing them in a way which reflects their importance to the

owner. In the normative process, some of these criteria

are assigned to lower levels of decision making. Usually

the criteria can be categorized as either quantifiable or

non-quantifiable. The quantifiable criteria can be easily

delegated to lower levels of decision making due to the

straightforward procedures involved in the tradeoffs. This

does not prevent some or all of the nonquantif iable criteria

from also being assigned. The owner can never comfortably

remove himself from the tradeoffs required by the nonquanti-

fiable criteria. He may, however, quantify his preferences

so that lower levels can perform tradeoffs similar to those

accomplished for quantifiable criteria in the decision pro-

cess. An example of such a delegation is in the economic

criteria which identifies the owner's preferences for

changes in the timing of cash flows. By identifying a dis-

count factor consistant with the owner's time value of

money, the designer can proceed with the economic evaluation

as if the criteria were entirely quantifiable. This relieves

the owner of the need to make tradeoffs of a large number

of cases but still allows him to influence the process. An

example of this influence would be a change in the discount

rate after several iterations. This method of manipulating

the economic criteria would reflect uncertainty of the owner

in his actual preferences.

For an individual as the owner, the decision process

presents few conflicts of interest. As the number and

diversity of those in the decision group grows, internal

conflicts arise when preferences are expressed. This be-

comes a significant problem when the owner is as large as

the government. The socio-political environment may then

prevent an explicit definition of the preferences due to

the nature of the system being designed. The problems of

decision making involved in this environment are felt most

strongly by those who act as representatives for the govern-

ment. The decisions based on preferences will produce focal

25

points for conflicting interest groups. This tends to re-

duce the area in which explicit decisions are made to those

in which mutual agreement on the method of quantifying the

criteria can be achieved. This often results in the quali-

tative criteria being either ignored or being considered in-

formally.

This multilevel, hierarchial system is compatible with

the ship design process. It has the advantages of isolating

the decision maker and setting responsibilities. This then

leads to reliable subsystems. In particular, the multilevel

system offers an improvement over other systems in the uti-

lization of resources when solving large scale complex prob-

lems. It also provides more flexibility and in general can

be expected to produce better system output. This does not

suggest that the system is ideal. Some of the disadvantages

are its complex operation or behavior. As such, it is diffi-

cult to analyze or comprehend. It also is difficult for one

to control or influence its progress. However, the multi-

level, hierarchial system has proven that it's general quali-

ties are better than other systems designed to handle large

programs

.

2.3 Proposed Design Process

Any proposed system must provide a method for the flow

of information from higher authority, performance of its

design task, and the reporting of results using the developed

26

criteria to the next higher level of decision making. The

upward flow of information will be used to determine if there

is need for further iteration to achieve a better overall

design. This is done by investigating tradeoffs between

various criteria and their associated costs. The informa-

tion that would be necessary to accomplish this task would

include first, the values of the decision variable and an

estimate of the confidence limits for these values. Secon-

dly, the information should include a sensitivity analysis

that would show the decision maker the resulting effect on

the criteria measures for changes in the values of selected

variables. The proposed design process (Figure H-) attempts

to incorporate these requirements.

The best way to understand the major features of the

proposed change is to contrast this design process with the

traditional process covered earlier. First, the proposed

design process, being iterative, takes more time and effort.

Where the designers objectives are fairly clear in the

traditional process, the guidelines now provide for much

more leeway in the actual design. This in turn requires

additional effort. The process requires increased interac-

tion between the owner and designers so that the designer

can determine the preferences of the owner. The owner's

identification of the criteria and measures of effectiveness

should be given substantial attention so that this

27

MODEL OF THE PROPOSED

SHIP DESIGN PROCESS

PresentSystem

CapabilitiesDemand for Services,Opportunities in the

Market PlaceGap

Analysis

|~ Other V-iSystems'

DesiredSystem

PotentialFrofits Other

SystemsGaps

M.O.E. forShip

HardConstraints

SoftConstraints

OWNERDESIGNER

.j Otheri

^Systems 1

OWNER_DESIGNER

i Other Systemi

! Constraints [\

DESIGN

: RCCEDURE

Sensitivity

PastExperience

Figure 4

28

interaction is effective.

In both systems the owner has the responsibility of

making his desires known and making the final decision to

build the ship. In the traditional process, the owner would

use a previous ship design to communicate his desires. When

this luxury no longer exists, it becomes necessary to for-

malize the method by which such preferences were made. This

is especially true for large systems when there is no one

single decision maker who can perform the vital integration

function.

One way to rationalize the prevalence of the tradi-

tional system is to study the time history of ship design.

Over the years the design process identified successful ship

types. This meant that the individual design efforts did

not require formal iteration to achieve good designs. Ey

perpetuation and extrapolation of the ship features that

had proven themselves in actual service, sufficient success

in the ship deisng effort could be achieved. This identi-

fies a situation in which the traditional approach may be

preferred. When the changes in the need as percieved by

the owner are fairly constant over time, newer ship designs

can be based on the more successful existing ships. A

change in the traditional method would thus require that

new requirements be placed on the ocean transportation

system. These would be similar to the needs generated which

29

caused the building of liquid natural gas (LKG) ships where

no similar ship type previously existed.

In order that the additional "benefits identified by the

normative model may be incorporated in the ship design pro-

cess, a new method was proposed. The major differences were

first, the iterative nature of the process? secondly, the

change in the form of the owner's requirements entering the

design procedure. This means that the designer will no

longer identify merely a feasible solution. In turn, this

requires a change in the perspective of the designer and

the owner. No change was made in the actual design proce-

dures. The next chapter identifes a sample program which

will be used to demonstrate the proposed design process.

30

CHAPTER III.

PROBLEM STATEMENT

3.1 Scenario

A large U. S. owner, an operator of containerships,

desires to expand operations between San Diego, California,

and Yokohama, Japan. The company is interested in purchas-

ing a single ship to increase the shipping capacity of this

route. The company presently has no available ships to

transport the increased demand for cotton and leather goods

in Japan, If present rates prevail, it is assumed that each

ton of cargo transported will generate $100 in revenues for

the company. At the present time, there are no arrangements

anticipated for the backhaul of cargo. The company usually

does not consider the backhaul when making their capital in-

vestment decisions because the quantity of cargo handled on

the return voyage is so small that almost any reasonably

sized ship would be capable of providing the capacity. Each

alternative would then generate the same backhaul revenues,

and thus would not affect the decision to be made.

The trade route imposes some restrictions on the alter-

natives. First, the terminal facilities are such that a

single loading sequence will not be able to provide more

than 1200 containers without excessive delays. Secondly,

31

the pierside cranes maximum reach restricts the ships beam

to 110 feet. Finally, the harbor channel restricts the

ship's draft to be less than 37'. The ports have an average

charge associated with the pilotage and tug fees which is

incurred upon entering or departing a port. Past experience

estimates these to average $1,000 per port call, While in

port, there are additional wharfage and port fees which are

determined by the number of days in port. The port delay

times have historically averaged two days per port call.

While in port, there are additional wharfage and port fees

which are determined by the number of days in port. The

port delay times have historically averaged two days per

port call.

The container size in use is a 20' X 8' X 8' container

which meets the American Standards Association requirements.

Each full container has been estimated to v/eigh 16.7 tons.

This restricts the stacking of containers, one on top of

another without an intervening, supporting deck.

In order that all costs and prices be consistant, the

base year of 1969 was selected. The prevailing economic

conditions in the U.S. in 1969 were such that the operator

could be assured of obtaining a 55 per cent building sub-

sidy from the Maritime Administration upon request.-5 In

addition, the company was anticipating financing three quar-

ters of the unsubsidized costs by incurring a 25 year loan

32

at ten per cent v/hich would be insured by the government.

Other alternative routes have been generating a yield on

the companies original investment after tax of about twenty

per cent. The company feels that any new route should

generate a similar yield. In addition to the subsidy, the

company will be able to take a seven per cent investment

tax credit, "or comparisons between alternatives, this will

be translated into a reduction of initial otit-of -pocket

costs.

3. 2 Design Problem

The above scenario presents several questions to be

answered. Here we will attempt to identify the characteris-

tics of the design v/hich would be obtained during a preli-

minary design stage. This effort will require that design

constraints be translated so that non-feasible alternatives

can be eliminated from consideration. After a choice is

made of the ship's characteristics, its confidence must be

evaluated taking into account possible variations due to

uncertainty in the information available in the design.

This will help to measure the uniqueness of the design.

Nov/ the problem of selecting a good design must be

addressed. In the next chapter, measures will be developed

that will help to insure consistancy in our selection as

well as providing a reference from which to base our deci-

sions.

33

CHAPTER IV.

SHIP DESIGN CRITERIA

The existance of different commercial ship designs to

accomplish similar tasks can be explained by the environ-

ment and experience level of those involved in the design.

The design selection process is greatly affected by these

factors because the real-world environment will influence

individually each decision maker. Insight as to what deter-

mines the merit of a ship design thus requires investigation

of the decision maker's preferences.

The objectives of the ship system which are to be

satisfied by the decision maker's choice of alternatives

are complex, however, a simple statement would list the

commercial ship as primarily a means of improving the eco-

nomic welfare of its owners by providing a marketable service.

h.l Criteria

The difference between the worth of ships is based on

a number of criteria from which the merit of a ship is deter-

mined. Conceptually there is a single list of criteria whose

various orderings reflect the preferences of the decision

maker. The following figure attempts to give a sample cata-

log of criteria. The determination of the relative impor-

tance of these criteria is a function of the decision maker.

3^

Table 1

CATALOGUE OF CRITERIARef. [3,6,7,9,27,36,37,39]

I

.

ECONOMIC

ProfitsDurabilityAsset LifeObsolescenceSalvage Value

II. MISSION RELATED CAPABILITIES

Transport Mission

SpeedEndurance, RangeCapacity, Payload, Cargo Type

Patrol Mission

SearchInvestigatePlant and RetrieveSecure

Interaction Mission

EngagementStation-keepingAvoidance, Defense

III. OVERALL SYSTEM CAPABILITIES

MobilityViabilityFlexibilitySurvivabilityOperatabilityEffectiveness

IV. MARKETABLE QUALITIES

Aesthetic Value, Style, ColorQualityPrestigePersonal Satisfaction

V. RISKS AND UNCERTAINTIES

Investment RisksFuture UncertaintiesReliabililityMaintainabilityAvailability

The commercial ship owner, on one hand, is ultimately in-

terested in economic criteria and in particular profits,

whereas a warship's merit will be a strong function of the

ship's mission capabilities. Where the ability of providing

defense from attack may be important in the warship, this

criteria is ignored in commercial ship design. Also, the

economic criteria loses its eminence for a warship design

because profits are no longer meaningful.

Another difference between designs is reflected in the

variation of risks involved in the design and the risk pre-

ferences of the decision maker. The term 'risk' refers to

the possible outcomes associated with uncertain future events.

For a commercial ship this may be in the form of unexpected

breakdowns resulting in expenditure of funds and delays in

operation. A risk associated with warship design may be

represented by possible threats such as a surprise enemy

attack. The risk preferences relate to the utility function

of the decision maker. From this it is possible to determine

the mechanism by which the decision maker assigns weights to

criteria, taking into account the values and risks involved

for each alternative. The process of determining a decision

maker's utility function uses successive lottery choices

where the decision maker is asked to determine his preference

between only two events. It is important to note that the

decision maker is not always consistant in these choices.

36

The risks of the design are measured by many of the listed

criteria.

The multiattributed analysis of Keeney and many

others could be applicable in helping to quantify the owners

preferences. For an example, if an owner of a commercial

ship experiences a situation where a breakdown only occurred

once during the life of the ship which required assistance

to get into port, the risks may be acceptable. On the other

hand, a single weapon impact on a warship may result in a

total loss of the vessel and perhaps result in the loss of

other units which it may have been defending. The risks are

high and even though the event may be very unlikely, the

resulting risk preferences of the decision maker may cause

changes in the ordering of the design criteria.

4.2 Measures of Effectiveness

To be useful in a modeling context, each of the above

criteria must have an associated measure. For those criteria

which are basically quantitative this presents no problem.

The economic criteria can be easily measured by dollars. The

others, however, present a real problem, both to the designer

and to the owner. This becomes most evident when it is nec-

essary to make a decision based on tradeoffs between two

qualitative criteria. It is not uncommon to assign measures

to these qualifiers. The regulatory bodies have taken the

liberty to associate floodable length with the safety of the

37

7ship at sea. This is satisfactory if the proper response is

obtained by use of such indirect measures.

It is not the purpose of this paper to propose measures

for the criteria. This is a function of the individual deci-

sion maker. For the remainder of the paper, we will handle

only the more accepted measures. We will use dollars as a

measure of the economic criteria and as the measure of effec-

tiveness for judging the ship design. Other quantitative

criteria will be introduced as constraints, giving minimum

standards for the design to satisfy, the freeboard requirement

is such a constraint.

4.3 Measure of Economic Criteria

When making a capital investment decision it is impor-

tant to identify all of the interactions that can affect the

economic returns to the decision maker over the life of the

decision. These interactions may be related indirectly as

would be the case when the reputation of a ship affects

the willingness of customers to do business. For this paper,

we are restricting our interests to the direct economic

effects.

4.3.1. General

In the context of the normative process, the decision

maker attempts to tradeoff different criteria in terms of

the possible changes in profit and other qualitative aspects.

38

Once the tradeoffs are made and the owner's requirements are

identified, one economic measure of the goodness of a design

is its ability to provide profit to the owner. In ship de-

sign, this measure is subject to uncertainty because of the

lack of information about revenues over the life of the

ship. The measures in the literature assume that the reve-

nues are unknown because a good forecast cannot be obtained,

the result being that measures typically involve costs only.

For the ship design, the costs can be predicted with a fair

degree of certainty.

If one assumes that the ship will be built and we are

merely interested in determining the best designs out of

the various alternatives, then the simplified problem can

be analyzed by including revenues. A marketing study could

provide an estimate of the income expected from the cargo

transported. This would help indicate the relative earning

ability of each design. The freight rate that would be

obtained will be used to drive the solution technique in

the sample problem.

The owner's requirement for a desired cargo flow rate

would be calculated as shown in the following figure which

depicts estimates of revenues and costs for shipping a

different cargo transfer rates. The owner would select a

value of the payload transported per year that would maxi-

mize his profits. Along with this point estimate, he would

also have an estimate of costs involved if the design

39

s>toa:

oo

STAPLE CAPITAL DECISION MODEL

(SINGLE SHIP)

PROPnS

fy, (oTT. RfiuJ «ATT "\ V,C^KC»0 FLOW R4t£ (w«rrs/ye,^

Figure 5

40

fluctuates from this estimate. This cost can he associated

with a penalty cost to the designer for deviating from the

owner's original requirement. Given the flow rate of cargo

required, the owner is interested in the design that mini-

mizes the cost of this service, subject to restrictions

placed on the design. The owner would easily change his re-

quirement on the flow rate of cargo if in so doing he would

permit a design that could increase his profits. This gives

the owner two options. First, he could direct the designer

to design for a certain speed and cargo capacity, as is the

present practice, or the designer could perform the evalua-

tion to determine the new requirements. In this case the

designer would need the criteria for setting up a decision

model. This should require less work of the owner than to

determine the owner's requirements, and it would reduce the

number of iterations of the proposed design process because

the owner would not have to wait until the designer proposed

each modification to the requirements.

For the sample problem, the decision model is formulated

in terms of economic criteria. By defining the general form

of the revenue schedule, the cash flows can be determined

by the designer. The model assumes a fixed freight rate for

material transported between two specified locations. The

designer would then be able to perform the tradeoffs in the

design procedure concerned with the economic criteria once

the owner's preferences are identified. One way for the

owner to project his desires is to identify the parameters

for the calculation of the net present value of a design

alternative.

b.3.2. Net Present Value

The Net Fresent Value (NPV) calculation takes a series

of cash flows and determines an equivalent lump sum value at

a specified point in time. It is based on the premise that

there is a time value of money. The assumption is that a

person will be indifferent to receiving one dollar today or

one plus X dollars at some later time. This value is in-

ferred from the fact that the one dollar can be invested to-

day and have earned X additional dollars by the end of the

period. We define the value of X as the discount factor. In

general, the cash flows can be continuous or discrete, but

for a continuous cash flow there will be an instantaneous

discount rate. The cash flows may either be positive or

negative. Also the discount factor may be a function of

time.

For ease of computation and also because of limitations

on the projection of future cash flows, we will restrict the

discussion to discrete cash flows and a constant discount

rate. See Figure 6. Since data is available on an annual

basis, we will use annual costs directly. The horizon of

our calculations will be the expected lifetime of a ship.

K2

,i

\

o x

l'

5 4 r Y£A

^ ANNUAL CASH FLOWS

- INITIAL -OUT OF POCKET COST

1

NPV I * C (i + O - i

t(l + t)25

sv(i*0

25"

I 5

C =

sv=-

Initial Investment

Annual Cash rlows(Assumed constant)

Annual Discount ?actor

Salvage Value

Figure 6

^3

It has been standard practice to use a twenty-five year life

for ships. This has been substantiated by studies conducted

by John McMullen Associated, Inc. for the U. S. Navy in 1967.

At the end of the twenty-five years, the vessel will have a

scrap value. This is usually a fraction of the initial cost

and will be an input to the model.

Looking at the operating costs when performing our

present value calculation, we can make some important gener-

alities. First, the operating level of the ship can be

assumed constant for the duration of its life. This indicates

that the crew hours and the fuel usage per year will be cons-

tant. We can then calculate annual operating costs if the

wages and the price of fuel are known. If a current market

price is assumed, then the discount factor could adjust for

the effects of inflation. This may not be adequate if there

is a restriction in the supply of fuel oil that causes it to

increase in price faster than other expenses. One solution

would be to utilize two discount rates, one for each different

cash flow but for this problem we will assume only a single

discount factor.

Until now we have not included the maintenance and over-

haul costs. These are significant when taken over the life

of the ship. They should be estimated and included in the

NPV calculation. These costs are dependent on the policies

of the owner and data is not readily available. They will

4/+

be treated in this model as an annual cost whose value will

be a fraction of the initial ship cost.

The following list gives the major restrictions and

limitations of our use of NFV.

(1) Cash flows must be on an after tax basis.

(2) Does not account for uncertainty in cash flows.

(3) Assumes that there is no capital rationing.

(4) Gives a poor measure for liquidity or timing

preferences.

Depending on the form of the capital rationing, modifi-

cations to the straight NFV calculation can be made so that

comparisons between designs are more valid. One method in-

volves varying the discount factor and noting whether or not

the relative merit of competing designs change. Another

would impose a variable discount factor. This could model

a temporary cut-off rate. For a strict capital rationing

which limits the initial cost of the investment, the addi-

tion of cost constraints to the design model would be another

method of accounting for the rationing of capital.

The other limitations of the net present value method

indicates that it will not always serve as a good single

measure of economic worth of the different design alterna-

tives. In order to compare the results from this measure

of effectiveness or objective with some others which are

commonly used, the model calculates independently the values

45

of the capital recovery factor and the required freight rate

for each alternative. This leaves open the option of selec-

ting the objective to be used.

Jf.3.3 Capital Recovery Factor

The Capital Recovery Factor (See Figure 7 for Defini-

tion) is the resultant of dividing the value of the annual

cash flow by the initial investment. This can be used to

find an implied or yield rate. If the cash flows and the

investment base is the same as for the N.F.V. calculation,

and the annual cash flows assumed are assumed constant, the

results will be compatable with the M.P.V. measure. The

capital recovery factor calculated is based on the total in-

vestment and as such is not consistant with the net present

value measure.

.

*t.3.4 Required Freight Rate

The Required Freight Rate (See Figure 7 for Definition)

is that cost that must be charged to break even with the

costs of operation, including depreciation or some return

on the original investment. This calculation does not re-

quire knowledge about revenues and is insensitive to change

in tax rates.

k6

CRF = I.- (2. + 3. +5.)

6.

RFR (*/T0N ) = 2. + 3. + 4.

7.

Where

:

I. - Annual gross revenue

<- - Annual operating cost

O. - Annual loan payments

4. - Annual depreciation allowance

O. - Annual tax payment

6. - Gut of pocket investment

1. - Fayload weight in tons

^igure 7

*7

CHAPTER V.

ALTERNATIVES

5. 1 Decision Variables

The decision variables were selected to simplify the

determination of the objective surface used by the optimi-

zation technique. The model must incorporate variables that

would first identify the physical form of the ship; second,

identify the loaded condition, and finally identify the oper-

ational capabilities. By using the linear dimensions and

the coefficients of form, the geometry was determined. The

specification of the draft and the displacement determined -

full load condition. The only ship performance investigated

was the speed of a transit. Thus the ship's speed was used.

The following is a list of the decision variables.

X. ....... . Displacement (A )

X2

Length (L)

X3

Beam (B)

X^ Draft (T)

X5

Depth (D)

X/;. ...... .Prismatic° Coefficient (CP)

X?

Speed (V)

Table 2

Note that the midship coefficient is a dependent varia-

ble. CM = CB/ CP.

^8

5. 2 Design Alternatives

The various alternatives that will be investigated can

be identified as a set of the design variables. For each

alternative, other parameters are held constant except when

sensitivity to changes of these parameters were tested.

This method of alternative identification was selected to

maintain simplicity in the design model and to facilitate

its understanding. Also areas of scarce information played

a role in the final set of variables.

The ship capabilities which have a major effect on the

ship owner are the load capacity, speed, and endurance of

the vessel. Prior to evaluating any design these must be

known. Each contains a continuous range of possible values.

For this problem, the endurance will be treated as a fixed

quantity. The speed and load capacity of a given size and

shape ship are now related. After the propulsion plant con-

figuration is determined, it is possible to evaluate the

available space and weight for cargo. The size of the pro-

pulsion plant is a strong function of speed for any given

ship geometry. It should be obvious that the alternatives

can be identified by the decision variables listed earlier.

In the search for the better alternative designs, the

feasible space must be identified. The following areas are

discussed to identify the limitations of possible alternatives

studied by the design model.

2*9

[,, ^*—^ arrangements of„ the

The various basxc space

englne reom a. or amidships <~£ZZL*~ - -

engine space vary are ^^ ls not

«—"" reaS°n. n

"p .—* ^ capability. »unique.for any given P «

dlfferenoes in the lccat.cn—*

payioad

;rr,ncU» »—

—

the

of engine spaces are^ ^^ ^ ^^ the

preliminary deslgn. Unle _the proble» of trim in

wi*m "hv introducing xne pi

scope of the problem by » ^ ^Uicaticns.

the benefits of a -ore ^^^ rf optimiza-

prcve useful. It ^ iooawon Qf the engine

tlon which would identifyof this

• .„ alternative design. The c

separate procedure may «This

. norease

tude as the cost of the rest of the P ^ ^^ta costs was treated as unreasone«.. ^^„ is not the intent to «*-"^

deslgn altematives

be built, but rather to^Alternatives are restricted

in a preliminary pnase. Thu

s„a <voace located aft.

by having their -*-J^^ location. the propul-

In Edition to

" on the number of

aion Plant configuration

50

propellers and shafts in the design. In the model either

a single or doable screw arrangement may be selected. These

restrictions are imposed by the program user. The model

only adjusts the number of engines and the associated opera-

ting levels and does not handle the actual engine arrange-

ment. The differences in the weights of units other than

the engines are not considered significant for the differ-

ent configurations. There is, however, an adjustment made

for the differences in appendage drag.

5.2.2. Ballast

As used in this paper, ballast is not considered part

of the payload. An upper limit on payload for each alter-

native would occur when no ballast is being transported by

a proposed design. There may be a configuration where bal-

last is transported. Of course, this is not an intuitively

appealing situation, but there may be a configuration where

ballast may be advantageous. This may occur if the ship is

stability limited. If by carrying extra ballast an addi-

tional container is transported, the benefits could out-

weigh the costs. Even though ballast may be 'off limits"

to most designers and operators, the only direct cost asso-

ciated with the ballast in a design with a fixed displace-

ment is in the initial installation. The inclusion of bal-

last impacts on the payload carried at the specified speed

and endurance. For the purpose of this study, the cost of

installed ballast will be taken as $1,000 per ton. This51

is higher than the real costs experienced, thus should help

to minimize ballast wherever possible.

5.2.3 Full load Condition

It is realized that designing to the fuel load condi-

tion does not reflect all of the possible operating condi-

tions which exist. The program does not address directly

the backhaul or other ballasted conditions. Through inter-

action with the program, however, it may be possible to

develop a design model that could incorporate such a ballast

transit. This would require that the designer interact with

the program and the results be carefully interpreted. The

design model could in this way serve as a small part of an

overall system design optimization.

5.2A Volume

Using a similar argument as that for disregarding en-

gine space location, the volume constraints of the problem

were ignored. Except for the obvious case of determining

the container configuration, the volumes were not tested.

A final hand calculation of volumes was accomplished for

the final results. From these hands calculations, it was

found that the designer may wish to be more careful in the

handling of the volume constraints. First, it was thought

the ship may be only weight limited for all but the container

configuration. That would mean that the space not used by

52

the container configuration would be ample for the volume

of any other weight group such as fuel.

5.2.5. Containers

The variation in container sizes has been standardized

since 196l. The American Standards Association standard

container dimensions are given in Table 2 . In this study,

only the 20• X 8' X 8 r non-refrigerator containers were

used. It was assumed that they would possess the strength

necessary to stack the containers six high. This standard

of the ASA is not accepted internationally, the International

Organization for Standards (I.S.O.) calls for the stacking

9of only four high,

5.2.6, Terminal - Interaction

The various interactions with the terminal were

treated as parameters in the design. It was assumed that

the ship relied on pierside handling and the average port

delay time was not sensitive in the range of the loading

capacity of the ship. This could have been modeled but

again this level of detail was beyond the scope of the

problem. There was one factor of the interaction that was

incorporated. The model is constrained to a maximum number

of containers per trip. This relates to the capacity of

the terminal facilities.

53

000) I—

1

rH

m o

to (0 (0 CO CO

i s c c c Go o o O ou -p -p P -pO -P.c; • W) hO WJ hO

3 -rH

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5*

5.2.7. Propeller Alternatives

It was decided to handle single or double shafts se-

parately. However, the effects on the overall propulsive

efficiency due to different propeller designs were ignored.

The problems associated with the propeller design could have

been incorporated at the expense of simplicity. Instead, it

was decided to test the sensitivity of the overall results

to changes in an arbitrary propulsive coefficient. This

would then indicate if more detail would be necessary.

55

CHAPTER VI.

DECISION MODEL

The objective of the optimization model will he to

maximize the net present value of cash flows to the ship

owners due to the initial cost and annual cash flows.

Each alternative generated will be subject to restric-

tions from rules imposed by the regulatory agencies, the

restrictions due to navigational considerations, and restric-

tions due to either data limitations or owners requirements.

The following is a simplified mathematical model of the

problem. The expressions are given in a simplified form.

The decision variables were covered in Chapter V.

6.1 Objective "Function

As determined earlier, the net present value measure

for the capital decision problem could be one of the cri-

teria used in making choices among alternative designs. Our

decision model determined the net present value of the cash

flows to the owner by calculating the initial building and

subsequent annual costs. The objective of the program will

be to maximize the net present value of the design. The

objective function is not expressed solely as closed form

equations, because some of the data is extracted from known

56

tables.

6. 2 Constraints

During the design process, there are several con-

straints that must be observed. These can be defined as

either soft or hard constraints of the problem. They help

determine the feasible set of design alternatives. The

hard constraints refer to the constraints imposed by tech-

nology and the laws of nature. These would include the maxi-

mum draft limitation due to the channel depth and the limi-

tations on geometry of the ship due to strength limitations.

The exact value of the hard constraints are sometimes diffi-

cult to determine. For example, the limit of strength is

not well defined. In these cases, rules of thumb have been

developed. These are the result of attempts by the regula-

tory agencies to quantify the factors involved.

The soft constraints, on the other hand, have no phy-

sical significance. They result, not from ship design

alternative, but from requirements of the owner or designer.

These could be imposed in order to insure compatibility with

other elements in the total design of the ocean transporta-

tion system. The maximum constraint on containers permitted

per trip is an example of such a soft constraint. It could

also be a limit indicating the range of data or experience.

The limit is obvious in the powering calculation. The soft

constraints thus limits the set of feasible design

57

alternatives. Even though there may be good alternatives

outside the experience of a designer he may not have con-

fidence in its potential. For this problem, we have im-

posed soft constraints due to the availability of data.

If these become tight constraints during the final itera-

tions of the design then a direction will at least be iden-

tified for further investigations.

For this problem, we have segregated the constraints

into four areas t Those due to the requirements of regula-

tory bodies, navigational restrictions, interaction restric-

tions, and data restrictions. (See Figure 8)

58

MATHEMATICAL STATEMENT OF THECONTAINERSHIP DESIGN PROBLEM

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59

CHAPTER VII.

OPTIMIZATION TECHNIQUES

The optimization problem as stated in the last chapter

is a mixed integer, non-linear, mathematical problem with

some expressions not given in closed form. The relation-

ships used to determine the powering requirements of the

ship are a combination of working graphs and tables. The

relationships between several decision variables are in-

volved and any simplifying assumption necessary to obtain

a closed form expression would introduce unacceptable errors.

Without such a closed form solution, analytical solution

techniques cannot be incorporated. For a survey of the

approaches applied to this problem, see Appendix to

Reference 51.

One method of determining the powering requirements for

design alternatives has been tabulated in working graphs.

The Taylor Standard Series of model tests is an example which

presents the powering requirement as a function of five varia-

bles. (Displacement, beam to draft ratio, volumetric co-

efficient, and speed to the square root of length ratio).

There have been attempts at determining the analytic form

of the relationship, hov/ever, one or more of the independent

variables are usually set equal to constant values. These

60

variables selected are indicative of a special type ship. Be-

cause the relationships are not available for containerships

in general, these analytic forms were viewed as being too

restrictive. The solution methodology used must be compati-

ble with the data in its available format of graphs and ta-

bles. The identification of an objective surface is possible

using the available information. Also the constraints can

be readily evaluated. This situation suggests that some form

of search routine will be able to locate the location of the

optimal objective value which meets the constraints.

7.1 BASIC SEARCH ROUTINES

7.1.1 Random Search

The Random Seach Technique applied to the ship design

process is covered by Kandel and Leopold. The method in-

volves searching each variable sequentially, each time sam-

pling at random from the acceptable range of the variable.

As the procedure progresses, the search is concentrated

around the more attractive solutions. This results in the

determination of a solution for the first stage. The pro-

cess is iterative, it is started over many times, with the

best solution of previous iterations being retained. How-

ever, there are drawbacks to its use. First, there is

the large amount of computational effort required. Secondly,

there is difficulty in identifying the feasible range for

61

each of the variables searched. It maps out the surface dur-

ing the process which provides additional information to the

designer. Unfortunately, its randomness makes it difficult

for the designer to interact with the program. The random

nature does, however, help to insure adequate coverage given

enough iterations.

7.1.2 Climbing; Techniques

The Hill Climbing Techniques employ the information

gained from the gradient of the surface to determine the di-

rection for the next move. This technique is often used in

conjunction with other techniques which determine the dis-

tance to jump. The methods require an initial point and the

derivatives at that point, The process is usually slow to

converge due to possibility of rapid oscillation in the move-

ment vector as the solution is approached. Problems due to

special surface forms have been handled by variations of the

technique. Many of these include systematic rotation of the

coordinate axis.-^ The major difficulty with this technique

for our application is the problem of keeping the search

within the feasible region.

One method of insuring that the search remains in the

feasible region is to impose severe penalties for violating

the constraints. The Sequential Unconstrained method uses

this barrier technique successfully as discussed in the next

section.

62

7.2 SEQUENTIAL UNCONSTRAINED MINIMIZATION TECHNIQUE (SUMT)

Ref [15]

7.2.1. General

The name of this technique is very descriptive. It is a

process which transforms the constrained problem into a se-

quence of more easily managed problems without constraints.

The set of solutions to these problems possibly converge to

the solution of the original, constrained problem. There is

no single method of determining the sub-problems nor the

associated solution method. Presented here is one method

that has proven useful.

The SUMT is designed to solve the optimization problemi

Minimize +(x)

SuBxec-r to: *£(5c) > o L*l,2-,3, ,

•*»

Whcrc X - (x, ,Xi ,X3 ..., XK )

Tis e\ r\-T>\rlz«j h ,o*J column vfctok.

The technique applies a minimization method to a modified

objective function P(x,r), where r is a given parameter.

P(x r) = fOt) - rt^fP) + Z LW*tf/r

From the function F(x,r) one can associate the additional

terms to a penalty. Depending on the value of "r", the pen-

alty takes different forms as illustrated in Figure 8 .

In the limit as "r" approaches zero, both penalty terms

63

NPV (* 10 *)

2LU

>-

b<LUa.

oUJZD_J

LE NGT H

•

-I. -*

INEQUALITY CONSTRAINT

2ccLU

>

<z.LUQ.

LU

_J<>

NPV O'o')

Y«-|: (CB-^5-C,)ASSUME Cf=.6

SSS"

EQUALITY CONSTRAINTFigure 9

64

represent barriers. The systematic reduction of the value

of the parameter "r" and the solution of the associated

modified objective functions, under suitable conditions,

will result in a sequence of minimums approaching the

solution of the original problem.

mm. P(x.r) = X'(r)

UM. X'(r) -- X"*

LlM. f LX'C03 = flt'l - Vy- -* o

VvH^RF >^' IS TmF «-PTia-\4C SCLUTto/V TO T^F ^oBi-EM.

12The suitable conditions are as follows:

(1) The feasible region is non-empty.

(2) fo^ a™ $fc) , J- >,*, ••. »i are convex and

continuous and ^jC*"), j - m-n

, m-vz., m+r

are linear function.

(3) "or some constant K , "the set £x| f<J) - K;

is bounded. (This prevents a "minimum

at infinity")

(4) P($T,r) is strictly convex for all r> ° *

65

The objective surface of interest is not necessarily

convex. This means that the results of the technique may

be local optimums as opposed to a global solution. It must

be emphasized that there is no guarantee of finding the

problem solution in a single iteration. Additional runs

with various starting positions would be necessary so that

the characteristics of the surface could be fully explored.

Only then would confidence in a single solution be justified.

In this thesis, the application of the technique to a non-

convex surface will be successfully demonstrated.

There are a variety of ways to implement the SUMT

method. The one utilized here can be described as follows.

Given a starting point, the method determines if the point

is feasible. If not, the technique is applied to find such

a point by using an objective function in the first phase

which measures the degree of non-feasibility. After a

feasible point is found, the value of the modified objec-

tive function P(x,r) the first, and the second derivatives

with respect to the decision variables are determined at

that point. The direction for the next move is calculated

using the Newton-Raphson Method. If it is not possible to

determine the inverse of the Hessian Matrix (See I age 69),

the matrix of second partials is perturbed and a move is

determined when the matrix inverse is able to be calculated.

This results in an "Crthoginal Move" as identified in the

66

program. Once given the direction of the move, the Golden

Section Search is employed to find an improved point in the

move direction. This process is continued until the mini-

mum of the program is found. This completes the first sub-

program. Next the value of "r" is reduced and the process

is repeated. This continues until the sequence of solutions

converges. The result is the solution of the original prob-

lem with constraints.

In the next sections, the Newton-Raphson Method and

Golden Section Search is discussed in more detail.

7.2.2 Newton Raohson Method Ref [52]

This method is used to identify the move vector. It is

an indirect method for solving simultaneous non-linear equa-

tions. It utilizes the necessary conditbn for a point x

to minimize a function Y(x). All the partial derivatives

must disappear at that point.

yj(*Vo }= '.*. --.*

The Newton-Raphson Method then solves the system of

equations by using the derivative to estimate the functional

value in the neighborhood of a point. This is done by per-

forming for each equation a Taylor Series expansion of

\\i) about i . If the higher order terms are ignored,

the following equations are obtained.

67

The determination of x= K+I requires the solution of

these simultaneous equations. If we define the Hessian Ma-

trix of second partial derivatives}

H(xR) 5 HK ^

Y* Y",11

HiY,

Y'

v' V" "- v"'hi '*« Inn

WHERE

THEN;

XK~ = X

k

-H;''(vY^))T

WHfRt H K H k- 1 , THF /-C^MTiTV MATRIX

68

For the determination of the move vector, we are inter-

ested in the direction along which to search for a better

solution. The direction vector is defined by -j-j. (vYCT 1

^)

for each step. The next step involves calculating the dis-

tance to move. The procedure is then repeated until the

functional values of ^(x 1"') become small. This process may

not converge to a unique solution as seen by the graphic

example given by Wilde and Beightler 1 3 in Figure 10. Assu-

ming the system of equations has only one member, then this

curve could represent the functional value of an equation.

The roots or values of the independent variable X for which

the function goes to zero is represented by the intersection

of the curve and the X axis. In this case, there would be

two possible solutions at points a & c. Depending on the

starting position for the Newton-Raphson Method, the con-

vergence to a root (solution) takes on different character-

istics. The zones of definite, possible, or non-convergence

are identified. The program using this technique identi-

fies the non-convergence condition when it occurs.

7.2.3 Golden Section Search Ref [52]

The Golden Section Search is a method for determining

the optimum of an objective function by successfully elimi-

nating regions for investigation. This method is used to

search along the direction determined by the Newton-Raphson

Method to find the best solution. This new solution

69

QWooKOh

o

I

oCM

0)

0)

PS

•HCl

70

point is then used as the starting point for the next itera-

tion in the minimization of the objective. This method was

originally designed to search a set interval. The SUMT pro-

gram determines this interval in each case by searching

along the vector until a functional value larger than the

initial one is found. This defines the search interval.

The upper bound f^ is determined by looking at successive

points until a larger value than the initial one is found.

The distance between successive points is taken as Ou. .

e; t ^ biS)L

L^O

then

h • f (*° + e« s ) - fo)

where 0^ is defined with the smallest non-

negative integer which satisfies the above

equation and S is the unit vector in the

move direction.

SEARCH INTERVAL

Pi

e*tt

1 1

<.

X D "\

Iaj rriAup£>l«T uppee

Bou/o*

"Figure 11

71

After the interval is defined, the search proceeds to

determine the optimum value. This is accomplished by divi-

ding the intervals into two parts and looking at the deri-

vative at the intermediate position. This would indicate

in which section the optimum v/ould most likely occur. The

process v/ould continue until the optimum is found. The

method which minimizes the number of iterations without

additional information can be shown to be a method of

partition which divides the remaining interval into sections

of the ratio t (1 .618033989) . This technique converges to

a unique solution provided the objective function is strictly14

unimodal as defined by Wilde and Beightler.

IF *, < X^ < *

THENy. < Yt < y*

AS, IP X* < X, <Xe

TH-FM y* > y, >y*

y

(comowe

)

(CO-UTIMUOUS} (ATOiTftMX)

'igure 12 UNHIODAL FUNCTIONS

72

7.3 SUNT COMPUTER PROGRAM

The optimization technique previously described has

been programmed by the Research Analysis Corporation as out-

lined in Reference 16 . This program requires that the user

provide four subroutines. These include first a subroutine

that reads in values as needed by the user in the other

supplied subroutines; secondly, a subroutine which defines

the value of the objective function and constraint func-

tions; thirdly, a subroutine which determines the partial

derivatives, and finally a subroutine which provides the

second partial derivatives of the objective and constant

functions.

The program was written with the capability of linear

interpolating for the required first and second derivatives.

This required that the objective function be developed from

the design model. Such a routine would provide the required

objective value for any value of the input variables. This

routine thus describes the objective surface upon which the

optimization technique v/ould search and is used in the in-

terpolation of derivatives.

The development of any objective routine must insure

that for each combination of the input variables, there is

defined only a single objective value. The program used

defines several surfaces, one for each set of input para-

meters. The tabular .inputs for powering calculations were

73

easily handled in this method. Simplified expressions for

these would lead to the use of closed form expressions which

could then be handled in other optimization techniques, one

of which would be geometric programming as used in Refer-

ence 10. The model developed in the next chapter attempts

to incorporate sufficient detail during a preliminary de-

sign stage so that the full capability of the STMT optimiza-

tion technique can be explored.

The program requires the selection of an initial

starting point and various control parameters. The author's

experience with these and other features are covered in the

concluding chapter. The reader is directed to the user's

manual, Reference 4-3. A complete explanation of this appli-

cation of SUI.iT with input, set-up, and a sample run is

covered in the Appendix.

7^

CHAPTER VIII.

DEFINITION OF THE OBJECTIVE SURFACE

8. 1 General

The strength of the search technique depends upon the

explicit nature of the objective surface. The selection of

the decision variables and design relationships has focused

on the need to determine an explicit, single valued objec-

tive as a function of the decision variables. The general

application of an optimization technique as described ear-

lier in this paper requires the determination of such a sur-

face. The actual surface defined is intended to be repre-

sentative of an actual decision, however, the main interest

here is in obtaining a model with which to test the optimi-

zation technique.

In this chapter, the containership design model which

is used to determine the objective surface will be described.

The actual relationships and other data used has been com-

piled in the Appendix. The methodology used to construct

this model may assist in the understanding of its final form.

The first step involved defining a tentative set of

variables. The decision variables introduced in Chapter V

represent the primary, independent variables chosen. It

would be possible to define the surface in terms of only

these variables, but the comnlexity of the expressions would'

75

lend the model awkward. Instead of following the usual pro-

cedure of Introducing these new variables which are depen-

dent upon the primary variables and then structuring the

objective function in terms of these secondary variables, a

more convenient method was used. This also helped to mini-

mize the number of secondary variables defined. The trans-

formation defining secondary variables were viewed as "black

boxes" or subproblems. Often explicit relationships between

the output and inputs were available. At other times, the

relationships were given in terms of tables or graphs.

The construction of the model started at the end where

the output objective was desired. Using the subproblem

technique, the model was built up from the objective end.

This systems approach facilitated the model construction.

As subproblems were defined, their inputs became outputs of

the next generation of subproblems. The goal in defining

the subprograms was to determine the inputs necessary and

the relationships required to obtain a simple and single

valued relationship with the required output. It was found

efficient to make extra subproblems whenever the relation-

ships between the variables could not be expressed in a

simple, single, closed form algebraic expression. This

would provide the definition of new variables. Another ad-

vantage of proceeding in this manner would be the capability

of having several groups working simultaneously on the

76

model after the first few steps. The assignment of subprob-

lerns should prove to be manageable in a real design effort.

The following black box exemplifies the subproblem tech-

nique.

NPUTSMODEL

t

APW=A-Zwi

i=l

w,

W? .APW

. >•

Wt ,

OUTPUTS

The process culminates when inputs to all the subroutines

are either the primary decision variables or outputs from

other subroutine. Only as the process is near completion can

the final set of decision variables be identified.

The following block diagram depicts a single design iter-

ation. The diagram represents only a small part of the total

computerized program. It shows the development of the ob-

jective surface in terms of the design variables. The output

of the program is then used in conjunction with the SUKT to

obtain new solution points as shown diagramaticly by the feed-

back loop. Evei though the Net Present Value objective was

selected, it would be a simple matter to change to some other

objective for the problem. See Appendix A for definitions.

The relationships that are used in the black boxes can be

found in Appendix E by their assigned number. The program was

designed so that the user could substitute other relationships.

77

o-\

u

I 1 1 l J oj i

•

!

I_J CD h- Q O >

78

®o

o —

•

<u.tr3 H(f> cr

<TUJ O>V-oUJ—>COO

3u.

P.

vn

a>

u3W>•Hfx,

o o 80

I

cc > u_L_ CL crCC 2 o

-?-

X>' occCLno <

Q.

i

H-UJ

C9 Z) OCO ^

2<

\- cr^> CD

Z) oCO

q_

i

O Ld

O COO CL

_cx»

oouj

LJ UJ

Li_ -^

u

H

<

81

There are three blocks in the flow graph that require exten-

sive calculations and additional explanation. These are the

blocks which determine the required propulsive power, the

power plant selection, and the container configuration.

8. 2 Required Propulsive Power

Given a specific ship's form, methods have been devel-

oped to predict the required propulsive power to drive the

vessel at different speeds. The process involves the use of

model tests and correlations involving past design experience,

The best approximation requires that a separate model be

tested for each design alternative investigated. This is too

expensive a procedure to follow when there are several differ-

ent alternative geometries. Over the years, systematic stu-

dies of the resistance properties of ships have been conduc-

ted. These have resulted in several hull forms being tested

and the results compiled in working graphs. Each of these

series of tests typically limited the number of independent

variables by fixing the value of one or more shape coeffi-

cients. It should be obvious that the use of any one series

to determine the power requirement for an alternative would

be only an approximation if the geometry of the design does

not match that of the model series.

In the program developed, the Taylor Standard Series

was used. In this series, the relationship between two of

82

the decision variables is fixed. For the Taylor Standard

Series, the block coefficient is related to the prismatic

coefficient as follows:

It was found necessary to impose this as a restriction in

the mathematical model because of the strong relationship

between the block form and the revenues generated by the

design. When this constraint was not imposed, the program

would select a box shaped midship section to house the con-

tainers. The resulting changes in powering requirements

could not be calculated using the series data. Even if ano-

ther series were used instead of the Taylor Standard Series,

the program would experience similar difficulties with other

pairs of decision variables. This constraint reduced the

number of decision variables by one.

8. 3 Discrete Fower Plant Selection

This model assumes that given a required SHP, a pre-

ferred engine configuration can be identified. The problem

of discrete power plants experienced with gas turbines has

been incorporated into the program. Because the speed and

distance values remain constant for the selection, the gas

turbine engine alternatives are ordered according to their

initial cost and specific fuel consumption. An engine con-

figuration is identified by the number of gas turbines in-

stalled. In this problem the GE built L.M. 2500 is used.

As the SHP increases, there may be discontinuities83

in costs. Because the gas turbine is available only in dis-

crete sizes, there exists many situations in which the in-

stalled turbines may not be operating at maximum rated power.

The following decision rule is proposed for the selection of

the number of gas turbines for installation.

It is assumed that the initial cost of the power plant

monotonically increases with the SHP required (See Figure 21 ),

The variables cost for fuel varies proportionally to SFC for

a fixed required SHP (See Figure 22). Because of the nature

of gas turbines, their SFC decreases monotonically as the

power output is increased. It is, therefore, desirable to

install turbines that operate near full power. It is assumed

for this model that the best engine configuration is the one

that is just able to meet the SHP requirement. Any combina-

tion calling for fewer engines cannot provide the power re-

quired and is thus non-feasible. A combination that operates

extra engines will run at lighter loads and thus at a higher

SFC. The desire of minimizing initial fuel costs associated

with the power plant selection is consistant with this deci-

sion rule. This ignores the change in maintenance costs with

the variation in engine loading.

Past history has demonstrated the reliability of gas

turbines and it compares with other types of propulsion units.

Typically more units have been designed into the plant as

reserve power sources. This increases the reliability of the

84

total system at an increase in cost. This model permits the

designer to require additional standby units as desired.

8.^ Payload Configuration

There are two steps in determining the configuration of

the containers carried on board a ship, The first determines

the available space and weight available for the payload. The

second determines the loading so as to meet the weight and

stability requirements. This reduced the number of constraint

programs.

The space is determined by obtaining the maximum dimen-

sions of the available space for the containers, then divi-

ding the ships into decks. The weight available for the pay-

load is determined by incorporating Archimedes Principle. The

payload and ballast weights must equal the difference between

the displacement weight and the sum of the other weights pre-

viously determined. The program then loads each deck sequen-

tially until one of the constraints is met. The number of

containers per deck is calculated as follows. The containers

carried on decks below the waterline were treated together and

assumed to have a shape factor relating directly to the ship

block coefficient. For those containers carried above the

waterline and above the main deck, each level was considered

to have a shape factor equal to the coefficient of the water

plane area. The program assumes that the coefficient of the

85

water plane area can be expressed as a function of the pris-

matic coefficient, The shape factor is used to determine

space for containers on each level by multiplying the shape

factor by the dimensions of the cargo space.

The model test for the stability constraint uses a cal-

culation of the available weighted moment at the designed

displacement. The program starts by placing all of the

available weight as ballast in the double bottom of the ship

without regard to space limitations. This automatically in-

sures that the weight requirement is met. If this results

in a feasible solution, that is, if the non-linear stability

constraint is not violated, then small increments of weight

are removed from the ballast location and placed in the form

of containers in the cargo hold. The only change in the

weighted moment would then be due to the movement of the

weight in the form of ballast in the double bottom to a

position at some higher position that would correspond to

the position of a container. This process is continued se-

quentially until the actual full load GK is reduced to 5 per

cent of the beam or one of the restrictions is encountered

resulting from stacking the containers, "or ease of calcu-

lation, the model groups the containers. Each deck is filled

one tenth at a time. The program starts with the lowerst

possible level and fills each deck sequentially. The model

v/ill stack containers external to the main deck. The

86

designer can limit the number of levels in this configura-

tion. The sample problem assumes that the maximum number of

containers that can be stacked is six. This is consistant

with the ASA requirements for this size container. Also,

the number of levels above the main deck was limited to two.

8.5 Input Parameters

Associated with many of the subproblems shown in the

flow chart are parameters that must be provided to complete

the calculations. These constants may be supplied by the

program user. The input parameters are listed in Table k.

The adjustment of these parameters permit the designer to

approach the real design problem and to introduce the

effects of other criteria expressed by the ship owner.

The ship availability refers to the per cent of time

that the ship will be operational. The design and cost

weighting factors are provided to permit the user to modify

the equations used in the computer program.

87

PROGRAM

Table b

INPUT PARAMETERS

PARAMETER SYMBOL.....

VALUE

DESl&M PaiWMGTERS

PAOPU LS IfC COEFFlClGAJT PCEHDUHAKtCt £

Dist/Wc<? QETidGrv Ports DBPsntT> awl/iBk-itv AVAlLwaMbt^ op shahs MSMAFT

"MlN. No. of Eu(riAjeb* NsveuW(9. OF VPARF EWG-l^fS A/GXTR*

HA-/-. pAVcOAb va^~. WWHlw. PaYloAD WT. WPMIAJMAX. COa/TAIaAFW SlACKlMfr KIX)

f^TA-x. stackia/6- ABdx/F X>k. IHT)•

AVSZAGF dO/JiftwZH *JT. wcBfFecnu& COajT. LFA;&T71 ELENtrT

ewcmi/e coajt. wi-d-th £WI"DTH

SrFECPue <?<WT. "DfTTtf Et>EPTW

DouBlf Bottom H£t6Hr "OouPjUG

B/ULAbT V/eifrf+T K6-. K^rB

MAX. 5»fP Fo* Sw6<.e 6«& S|4PM

S6/q 5PtfT) F/»CT o a? Ber4 1

5PC FACTO* BeT/t£

H(SC. \A/ei(rH7 wxxMISC.. U^FlG-HT KG-. X.K6-X

E>F5I<9/«J W/t(&-<4TW6- FACTOKS

Factor fo« OwTPrr u/r. y/Wo

FACTOR FOR STFFC \ajt. wwsFACTOR FOfi. \AAc\MAJeRi Wl V/WM

* fje^A-ri^t- vacw<? fA»t>ic4T65

88?>/«0PUt-Si©/O

PROGRAM

Table 5

INPUT PARAMETERS

PARAMETER

.

SYMBOL VALUE

NAVIGATION CoUttRAiVTS

MAX. LEM6TH LE^&TM

MAX. BEAM BEAMMMAX. D«AFT BRflFTM

ECONOMY WMMETfcRS

FRPIG-HT RAT£ FRPO^T QALL F££ PcfPA-iLY "f>oAT F££ D?FprtlCt or Fufl PR|C<^

AWVUAl k>Sc<R/WC€ RATE AIRASSET Uf£ NNSALVAGh S/ALUG SV

DISCOUNT FACTOR DP' SubsW Kat& SUSIDR

p&AGJE'JT FlHANC&b PFIMTFRE5T RATt RAreCortT. Tax R^t? CTR

INV£3TMEA/T T4X CtftTMT A^TC.

COST Wer(0rHT/A'G- FACTORS

F/KTO/e Fofi OJTFil COST CCo

F7K.TOA- fox 5TteC CjO^T CCSFactor Fo/2. MAc^we*** c, £C.M

PR06KAM PARAMETERSOBj^CTlt/c 5fC£<-T(OA/ Itffo?

COMSrAAjAJT 5£ajS (Til/ ITY DFLtAC^

89

CHAPTER IX

ANALYSIS

Responding to the needs of the owner as outlined earlier,

the optimization techniques are applied to the ship design

model. The results of the investigation are presented to de-

monstrate the capabilities of the computer programs. Prior

to discussing the actual problem solution, an attempt was

made to validate the design program by comparing the program

results with three containership designs.

9. 1 Program Validation

The design program was used to develop details of three

separate preliminary containership designs. The first design

was developed by George G. Sharp, Company, during the evalua-

tion of gas turbine "-power plants. The remaining two designs

are products of the Maritime Administration CMX Project. The

designs were developed separately by Bath Iron Works and the

Newport News Shipbuilding and Dry Dock Company. The follow-

ing tables indicate the similarity in results. In each case

the design program was given the principle dimensions of the

ship. The input parameters used in each of the designs corres-

ponded to the values obtained from the respective preliminary

designs.

90

MODELTable 6

VALIDATION

VARIABLESG.G Sharp MODEL

bisPL/ictMewr JOfe^ ZoGS-'r

Length 75-3. isr*

REAM 93 <?3

DR4FT ^1.3 =0.3

DfPFH 5-S".o rs".

PtfiSMAT/c doer. .4,i_

.65"

©Lock Coff. ,5T>t ,60

VOLUMt CotP, .OO^S" OO^f

Vt^oCITY /tS". 8 2S\1

Fuel wt. Iflo jc?3r

MA-ch. wT. II 23> /I Zf

OC/TFfT WT. 1 fe.r'f /5TfeO

ST&EL WT. 9o30 d*i/i>

M.lS<L~ WT At? 3oo

Ballast wt. O /38fc

T^YLoATi WT, 15" 3 «? f '^637

fi-M |.">3 e. 1

Mo. Q-owrAi^t^S 75"' ll^\

Top? ffc>s M 3

IStLow "fee* N/\ 6

No . Sh-zift^ X 3

TPY K)A nsShF Rfq 5SS"oo b"5~6tO

CdstI 25 .5-8 ^O.tJ

Aod- 2.S"* '.'.If *

RFR NA \o.S~

CJRF MA .To

FR W A S~0.

NPy AJ/5 n.rs

1 1

1-1 Fun e*jTE>ic\ i-j erneo*

91

MODELTable 6

VALIDATION

VARIABLES

NFWPoy?i

News hottc

B^TH1 So//

no'ia

DiSPUceMw 3A2oo 3^Joo 3ll7o 311T0

Len&tH 696 6«?t 64<T &4<r

Beam I 03 /03 86 84

DRAFT a<?.J XHS 3f.S 31. J

DE"PTH 6o Go STA.8 54.7

PRISMATIC t. S4 8 5*8 .63? •439

bLoCk COEF. .S32 •S"32 .£2t .($24

VOLUM. CoSF. .0033 .0033 .DOH .OC=f-

Velocity ^3.3 A3.

3

3.0.H 2c4

Fuel wr. 33oo. 34*5" 3S~io 31i?

MACH- V/T. (((2. !2?2 MA 10732

Out Frr WT. /gS-3. /6 3o MA 3oo2

STFtL WT- ^US, 8 s? 4T MA (>& 59

HiSC. WT. *A3. 3oo HA 3oo

i5/}LL/4srwr. 367. l5rg>o ^3(,oo ° 5"°°o

PAY^o/T^ \vt. /6 0^0 I5"03g NA lo(,lo

&M -2.<f 6.^i~ MA 4.37

f\/o. CoAJT^ive/Ci i3S~o '268 <?22 ^33

TO?>S(T>f -x 3 2 3

bcccw "Deoc 7 ^ 6 6

Mo. 5rtAFTS [ 1 1 /

TPY ^4 /r-8f MA n.3«

S rt-P Rts

.

3 5~oo a 35"fo JMooo Z<t Voo

CCSTI W4 I8.1 AM 22.*

/foe M 4.1 wA ASRPR AM V.H AOA 37.93

CRF A//f.5"! WA ,14

F« AM SO WA 5"0.

MPv AM /7.t NA 4.9

2 t * 3 3

* LI«icTc*)

(J) -^,/HJ-A^T u enciw-r fox; sno/er<.-< ue7Kio-i

92

9.

2

Program Inputs

The application of the decision model to the scenario

requires several input parameters. Unless otherwise stated,

these parameters were used for each of the designs analized.

The parameters are categorized as either design, economic

or financial. The design parameters include the assumptions

necessary to determine the ship design as well as several of

the constraint values. The economic parameters cover the

various costs and revenues generated by the design. The fi-

nancial parameters relate to other economic aspects that in-

directly relate to cost by indicating the owner's preferences.

Table 18 gives the values of the coefficients used in the sam-

ple problem.

9.

3

Procedure

The application of the minimization technique requires

the identification of a starting position from which to

search the objective surface. The primary concern is to start

each search with a feasible solution to the problem. From

this point, the STMT Frogram will take over the procedure and

then locate a local optimum. Because the objective surface

is not always convex over the feasible domain, other starting

points or solutions may result in the search culminating at

different local optimums. The concern is then to start the

93

program a sufficient number of times, at different locations

so that the surface characteristics can be deduced and the

best local optimum can be taken as a solution to the prob-

lem at hand.

The procedure was to select four starting solutions,

each different, so that the total search would encompass

most of the feasible surface. The first starting point,

which is labeled Alternative 2 on the next page, represents

a modification of a design used by George G. Sharp Company.

This alternative has similar characteristics of the actual

design which is • shown as Alternative 1. The major differ-

ence is in the number of shafts in the design.

The second starting solution was chosen with a higher

displacement. Alternative 3 was used for a starting point

even though it had been an output of a previous optimization.

The third and fourth starting points, double and single

shaft arrangement for a smaller ship. They are shown as

Alternatives 5 and 7,

The remaining alternatives show the results obtained.

Not shown are two attempts to start the program at non-

feasible initial positions on the surface. This resulted

in an unsuccessful attempt by the program to find a feasi-

ble starting point. "or the nonfeasible alternatives, the

measure of effectiveness was most easily minimized by re-

ducing the size o^ the design. No revenues were generated to

94

IDENTIFICATION OF ALTERNATIVES

^ALTERNATIVE\\N

V/HRlABlFSX ©. © © ©DISPLACEMENT 30>5<i. 30,fe£9. 31,tsf. HS^lo.

Length iro. 1iO. 133,. 7fcl.

BEAM <?3. S3. <IH.I ^8.S

DRAFT 5*7.3 J1.3 J*.2 3-i.f

DEPTH 5t>. »5. 5"8. 7 yt.t

PflisM/vne Co. .61" -4«T .(,<? .ts

BLock CoeF. .5k ,st .43 • t3

Yolum. CoeF. .002.6" .002.S • oo3fe .0034

VELOCITY ^r.T as".*? ax. 8 a.3.^7

Fuet wt 4U<;.3 "7I"W.< S^bO.7. 7 dlj.l

MAC-tf. wt. lo7o.3 1 1 HI,

3

^fe^.T 1 ia?. T)

OUTFIT WT. S-330.2 5^33o.7 ^1 2.1 ."? S-^Tf./

STEEL WT. $ 7 is -7 SliS-.*! gUC 3 ?r?v

H'SC WT 'boo. 3oo. JOo. 3oo

QALLA5T WT. 23.6 IHJ-.V a.fcs'.i 3.0^M,9

?A\LOfKt> wt fS-5-J.fe 7,? <tu *» J 8(

S"«,1 v**-

&M IT.S lt,.l 4.8t 8,o<f

Ko. Cewr.4i.ve*s 5"<8 47 s ( I25-

1 (7o

ToPST>t O Z 2

BeLOuj ]>£<:* s <f 6 fe

Wo. -5H4FTS 1 a 2 Z.

Mo. Faj&iw?5 3 4- 2. +

Shp rfq. 57,231. 6r, 63m. h-jT.377. rt,j"o

CO JT 1 31.2b 31..U, M.38 '

3t.fefe

/}©G (o.fV iz..2a 9.18 IZ.il

KFR 82. ST /oo-fes" i.8.33 Y3.70

Cf^F .13 ©+.7*1 .57

FR /oo. 100. lOO, /oo.

MPY lO.H? 0" 78. OS S"Oo

Pko&rak NA. IWPuT ouTTvr/,»«,"T OmtPWT

4 (_1 imncATes NAC.rn/f value

Table 7

95

IDENTIFICATION OF ALTERNATIVES

X ALTERNATIVE

s.

VARIABLE^ ©. © © ©Displacement /5",ooo. 11,111. If.ooo, £8,38*.

LENGTH too. 4*?f. feOO. 67o.

BEAM to. 7 8.2 50. 7?.Z

DRAFT Z5.0 28.t 25\o 32.4

DEPTH HS. 45". **s. *?.«

PRISMATIC to. .bo .40 .40 .62

Block coef. .t* •53 .1-4- .57

\jOLUn. COEF. .002.4- .002fc .002.4 .0033

VELOCITY 2.0. o 20.0 2o.o 20.5"

FU?L WT. l,?5"8.-7 2,375.8 2.,?0O.f-

MACd. WT. 843. t ssr.j ?To.8

OUTFIT WT, 2.,13H.3 3, fos. i 3.<iHt,.S

STEEL Wr 5>M>.*t i.cni.t 6,H"2S".o

Mist. WT 3oo. 3oo. 30O.D

b/ALLAsr wr. 28/7 1.4 2, Uv.^

P/VfLo/TD WT 3,tl>8.3 ?, 65-?.f> /Z, Zi^.U

• GrM IHS 5". 4 ff.f 6

K|0. CONT/(W#S 2.IO 5gr 74 C?

LEV/. ToPSi"De 1 2

Lev. Bev*^ £>fck 3 5" rMo. SMAFT3 2 £ 1 i

Mo. FajG-I^es L 2. Z* 2*

Sh? «cq. '3. W). '4,?/7 2/jOoo.

COST 4. lo.o x2 2.oZ 2H.yi

AOt S.Z 5". Co 4.5-r

RFRCRFFR too. loo loo. loo.

WPV <E> //.'Ti- © 21. 9

PRofcM^ \uVuT ourPjr lAJ-puT G urfpuT

* USEP> Fo«cet> £xtRa FAjbiA/e For Reci/qsiciTY.

Table 7 (cont.

)

96

counteract this tendency. Suggestions for future modifica-

tions are covered in the concluding chapter.

9.4 SUKT Trajectories

The following tables show the trajectories followed

during the search by the SUKT program. The starting point

and program optimum alternatives are given in terms of the

decision variables. The intermediate solutions are shown by

the incremental differences resulting in the changes between

successive steps. The tables also indicate which constraints

are constraining the solutions. These intermediate solutions

represent the solution for each of the subproblems associated

with the successively decreasing value of the program para-

meter 'r'

.

Most of the improvements in the objective seem to occur

in the first few iterations. This indicates that the process

could be streamlined by imposing looser convergence criteria.

This would permit the program to terminate its search earlier.

It would not be necessary for the penalty terms introduced

in the modified problem to be diminished by an even further

reduction in the parameter *r*. The execution times for the

optimization procedure are given for each of the problems.

The comparison between results is not possible here. The

differences in the objective function result from various

freight rates used. The final table of comparisons account

97

SOLUTION TRAJECTORY /LTERNATIVE^^^

DESIGN

VARIABLESSTARTINGPOINT

CHANGSUB

1

1 IN

PROBLE2*

MLUEM NO.

3

IN

4

FINALPOSITION

Displacement 50^57, f e.iio. -s. 39,«H|

LENGTH ISO. -if. -8. ^ZJ.

BEAM 93. +i. fr.l 9^.i

DRAFT 2-7.3 +*. + .9 32}

DEPTH ss\ +3. -f .1 5-8.1

PRISM. CoFF. • fcS" •+.0T — .492

VELOCITY 2?.n -2.* -.1 22.

g

CONSTRAINTVALUES

TlMe

I.OIO 12.390 If.CJ'o If.oS

FREET504RD UnKjl

STAEN&TH (L/d-^)

Max. LEng-th(9oo)

Max. Beam (ho.)

Max. draft (37)

Max. V/c (1.2)

MW. V/VT (•?)

M4k. £P (.70) Tlfa+CT TltrHT T 16-HT

MM- CP (48)

MAX.B/r (3V5-)

M/a/. Vr (2-W)

MAX. CV (.oefe)

M|A|. Cv (.ooi)

CB - .^25 CP TltrHT T|(r«T TlirHT

OBT£CT(VS 4

( KJPV Xio'V35-. 8 8 + 890 t ST. 129.88

*. SouxmoN c*«ve*freb at -rv,e sa>%

OP 5>/f»P«ogLf/rt 2..

(.—

)

IU^lt*T«T M% CM<l(,f

Table 8

98

SOLUTION TRAJECTORY ALTERNATIVE^-*^

DESIGN

VARIABLESSTARTINGPOINT

CHANGSUB

1

I IN

PROBLE2

y/ALUE

U NO.

3

IN

4

FINALPOSITION

Displacement 3*? 6H0. + 5 tfcO—

•» 10. *+5",3io

LENGTH "»23,o + 38.- 1u,

BEAM 9*f.| +«tt M ns

DRAFT 32.2 + i.ac— - —

33.H

DEPTH 5-«.7 + .J?4— — — sys

PRISM. CoEF. .492— — — —

,(,?2

VELOCITY 22.8 + .«?— — — 27.1

CONSTRAINTVALUES

TlMt.960 +.460 5^0 6.4^0 e.zio 8.2.7o

FREEBOARD (iFfcJ

STRENGTH ( %-^M4X. Leng-th(9oo)

Max. Beam (no.)

MAK DRAFT (37j

Max. Vsc (1.2)

MW. V/vTT (•*)

M**. CP (.70) TlOrWT TltM-T TlfrK-T TI&kT TltHT TIC7-H.-T

MW- CP (48)

M/tt.B/r (375)

M/M. B/r (*W)

MAX. cv (.oofe)

M|A/. Cv (.001)

CB - .925 CP T16-HT TlfrH-T TiOt+T TlfrWT t'Ch-t Tifrttl

OBTECTiVS *

(wpv Xio'cJ

/I2t.2 + 11. H + 0. + 0. -» 0. 131.4,

Table 9

99

SOLUTION TRAJECTORYALTERNATIVE(5>(6)

DESIGN

VARIABLESSTARTINGPOINT

CHANGSUB

1

E IN

PROBLE.

2

VALUEM NO

3

IN

4

FINALPOSITION

Displacement i5;ooo. +•7,14,0, -18fcO. + 2,t8o. -4. IZ, ***)(.

LENGTH bOO. 0. + 1, + 7°. —fc****.

BEAM fro, 4- O -1.9 + .t—

78.2

DRAFT £5. -*s\z -1.8 O —28.<<

DEPTH 1£ + + * O — H5

PRISM. CoEF, -to _ - - —.to

VELOCITY 2o.o — — - —-2o.o

CONSTRAINTVALUES

T/MC

,?fio 7.620 10. UO IZSoo /3.37o 13-770

FREEBOARD UfO Ti&mT "rifru 1

STREN&TH (L/D -^) TI&MT TlCrHT

Max. lemg-th(9oo)

Max. Beam (ho.)

Max. draft (37J

Max.v4c (\,z)

MlM. %T (-5)

MA*. CP (.70)

MlM- CP (40)

MAX.B/r (3-75-)

M/a/. Vr (2.W)

MAX- ^v (.oofe)

MlM. Cv f.001)

CB - ,9£5CP

ObTECT(V£ *

( KJPV X IO"CJ

3.5T4 +2*7.1 4 l.t + 5-.Z 4 0. "J1.H

* FR^ZOO./ton

Table 10100

SOLUTION TRAJECTORY ALTERNATIVE©"*®

DESIGN

VARIABLESSTARTINGPOINT

CHANGSUB

1

E IN

PROBLE2 *

VALUEM NO

3

IN

4

FINALPOSITION

Displacement 15, 000. + 13.38*.— 20,384-,

LENGTH bOO. +7o,—

670.

BEAM So. -i.—

79.

DRAFT IS 47,fe— 32.6

DEPTH ts 44.7—

^9.7

PRISM. CoFF. .4 -f 08*-

.68

VELOCITY 20.0 + ,5— 20.4'

CONSTRAINTVALUES

FREETi04RD (£FB»d

STPvEN&TH (L/D^l?)

MAX. LEN G-TH (9oo)

Max. Beam (no.)

Max. draft (3vJ

Max.v4t (1.2)

Ml* V/SC W

Max. CP (.70)

MlM- CP (48)

MAX. ^f ^•75')

M/a/. B/r (2A5)

MAX. CV (.oofe)

MIA/. CV (.001)

CB - ,925 CP Tlfc-*T •TIG- (41

OBTECTIV6 t

( K/PV X io"t

>)L.bS + r7.<>t + .0 5«.32

F* •*«• /ro*

iwe?«o-Bi-rM ** Table 11

(,— ) iXfciCA.'cS VO <M*V6-r

101

for these differences and presents the results based on a

freight rate of $100/ton.

9.5 Ranking the Alternatives

After conducting the individual optimization problems

with the various starting points, a comparison of results was

desired so that the best design could be identified. The

various alternatives were compared using three measures of the

economic worth of the designs. The following table gives the

Net Present Value of the design based upon $100/ton received

in revenues. Also the Capital Recovery Factor based upon

the total investment and the Required Freight Rate are listed.

The RFR depicts the rate that must be charged by the opera-

tion of the ship so that the revenues would just cover his

costs which include depreciation charges.

The matrix shows that no single ship is preferred using

all these criteria. It also shows the improvement obtained

in the measure of effectiveness using the SUMT Program. Al-

ternatives 3 and k switch position in relative ranking as the

objective is switched from NFV to CRF or RFR. The solution

to the scenario with the given assumptions would be Alterna-

tive h. Other scenarios may result in one of the other de-

signs being a solution. Each of the designs carry a different

payload. The differences in worth per ton transported is not

.so great which indicates that two smaller ships may be

102

RANKING OF ALTERNATIVES

BY VARIOUS CRITERIA

f_) |/OblcATSS fJSGAllije VALUE

Table 12

ALTERNATIVE NPV (^ o\f B KFR */T\ A- 30fo59.

\J_y L Shaft10.^8 b .13 B 82-37 5

>s3/ 2. SHAFTS (-) a (-) I0D.&5" S/Z\ A= 3964-1.& z shafts < 48.08 S ,7f 35.35 m(a) A -4-5-3/0.W 2. SHAFTS P-i'^ m .57 B 43.70 s^3J 2 5wm K-) a (-) a 1Z3.4? 7

/£\ A ^ 22i

77 '- b -37 H 47?£ Bfj\ A = \5,ooo.

Viy J_ Shaft (-) a (-) a — D(q\ A -28,38*.^—/ 1 Shaft

27.10 b .^8 E 4-2.80 1]

103

preferred over one larger ship. The increased flexibility-

available to the owner may make a number of small ships an

attractive proposition.

9.6 Discontinuities

During the design of the various alternatives, discon-

tinuities were observed in the objective surface. These were

the direct result of the discrete characteristics of the en-

gine and installed cargo. The following graphs show the

effects of the discrete factors in the design and additionally

show the performance of the search routine in the neighborhood

of the discontinuity. In order to demonstrate these factors,

the ship hull design associated with design Alternative k

was held constant as the design speed was varied from nine-

teen to twenty-seven knots. This provided a profile of the

objective surface along a single dimension. A similar graph

is also developed for Alternative Number 3.

The effects of the discrete power plants are evident as

the speed is increased. The graphs note the speeds at which

additional engines are required. The cost function reflects

the additional costs involved in the transition. In the graph

for Alternative b, the quantum drop in the objective function

just before twenty-four knots is due to the cargo capacity

lost when the engine box was enlarged. The same integer num-

ber of containers could no longer fit in the length available

104

OBJECTIVE SURFACE PROFILE

FOR DESIGN ALTERNATIVE FOUR

SHIPGEOMETRY

A 4-5,3/0. to«5

L 761.'

B 98.4'

T 33.4-'

D 59-1='

CP • 6?

2 SHAFTSFR^200./ T0Ay

w38-

37-

"b 36-

2S 35-

8 »H<

31-

30

6?

21 .o

(2) e^&i/ves

Q"

NPV

C0ST1o —

- H .

C 3

.£>

20 21 2e

.72 X .80

2AO—I

3f.l

(4) EN6-INE5

3-DQ- P

•6!.©-©-

23 2« 25"

.63 .87 .11

«H.S V.4 ^n

"(6)*

-130

-120,

lt-0

UO

-100

90

O

X

>

7 VBUOC (KT5)

% x its *v SHP (% t03

J

5TACKI»J<f--»f«— WEI6HT-

* cost of ballatt wt. KEMoweV

Figure 17105

OBJECTIVE SURFACE PROFILE

FOR DESIGN ALTERNATIVE THREE

SHIPGEOMETRY

A 39,64-/. tovs

L 723.'

B 94.1'

T 3Z.Z'

D 58.7'

CP .6?

2 SHAFTS

FR = Szoo./TOtJ

NPVIT Q"

oX

Hc/)

oo

fe) £WC.IME5

C0ST1-to G>-

2° 2l

.7^ •78

2i.f

a-

D-

22—

r

23

.82 86

-(4) EN&INE5

— ©'

-1

—

24- Z5

.M .13

to

-.©-

24

.*?7

2C.4- J2.3

STABILITYLmnrt

STABILITY

VTAC.Kl'Jt-

STABILITY

STACK !»*

'"WFldHf*

rai vta lOl.o

i.lMtT7T>

t cost of ballast wt, senovet>.

Figure 18

106

cp

£7

W

oX

>CL

Veloc (KTS)

illA

L

6HP (x lo3 )

and this resulted in a loss of about fifty containers. As

stated earlier, the length of the engine box was modeled

solely as a function of the required shaft horsepower. If

the engine box were modeled more accurately, the loss of cargo

may have occured at the same time that additional engines

were added. The graph of Alternative Number 3 shows a simi-

lar drop in the value of the objective function. This is

again associated with the engine box size. At the bottom of

each graph, the tight constraints are listed for the various

design speeds.

9.7 Sensitivity

The final segment of the analysis is concerned with

determining the sensitivity of the design solutions and the

associated objective values. Only a limited effort was pos-

sible in this area, but this section should help to re-enforce

confidence in the results of the previous sections. The re-

sults of this step will point out the critical assumptions

made in the design model and where additional effort may

prove rewarding.

In order to obtain a sensitivity analysis in a general

search routine, it is required that perturbations be made in

the values of the decision variables and the input parameters.

Here we will study the sensitivity of the design Alternative

/*• due to variations in discount factor, propulsion coefficient,

10?

midships coefficient, endurance, freight rate and the number

of extra engines that may be required for increased relia-

bility.

The procedure was to start with the best alternative

available, and determine the affect of changing one factor

at a time. The changes on the worth of Alternative k are

noted for each perturbation. In Column B of the table, the

NFV objective resulting from the change is recorded. This

design was used as a starting point for the SUKT Program.

Column C indicates the worth of the design resulting from

the optimization, A qualitative indication of the overall

changes are also given.

The most critical factor in the design was the assumed

value of the discount factor. A variation in this input

parameter caused the greatest change in the design. There

are several other elements that deserve explanation.

The sensitivity of the design to the assumption of P.C. may

be more important than indicated by a quick look at the fig-

ures. The reduction in the F.C. resulted in a design with a

higher block coefficient. This would cause an even further

decrease in the F.C. for the design. The other interesting

effects are noted on the table. The design incorporates

a severe cost on the design for ballast. When the ballast

is replaced by fuel, there is a sufficient increase in the

NFV of the design. This appears twice in the analysis.

108

Table 13

SENSITIVITY ANALYSIS

P

VALUFDF

p=p,

YflLUt-

or

P-P,AP

OBJECTIVE VALUE

B-CB-C

EFFECT ONDESI6-N

ReF£»>t»JCE"t> FWH

ASOLUTION

V P,

BSolution

Vw/ JJ,

c

«// P*

DF .20 .15 -.05 47.2 62.4 67.3 -^ ft. SHi?

DF J5T .10 -.05" 67.

3

87.1 78.3 -7.1 184.Scowe f<

SH-ip

PC ,fc5" .625 -025" 47.2 43-1 43, fc- ,5" 10.

SultrHTLYi+ife-H-cve

Block coep

Ol*'

.725" .950 t025~ 47.2 47 2 4fi" -Z..o -80.

SLLtrHTLY

SH-F?

wo.

2 4" *2 472 46.-53 44.37 -.04 -.OZ.

SLIGHTLYUO aJ fe c- ^

Ski?

£MT5l/7^t*Xr IZ.,SoO lb, 000 +2.500 47, a f5~,0 WS* -4.5- —

FR WO. ?o. -10 47 2. 38.9 59.0 -.1 .01

SU6-WTLV

1

.

Change which could cause a further decrease in FC2. Effect on powering not assessed3. Ballast replaced by fuelh

.

Two engines as on line spares5. Ballast replaced by fuel

109

CHAFTER X

CONCLUSIONS AND RECOMMENDATIONS

10.1 General

As the first iteration of the design procedure is cul-

minated for the sample problem, it is important to put the

discussion in context with the overall design philosophy.

The preliminary design was pursued in this problem with a

broader interpretation of the owner's requirements as was

made possible by the quantification of the owner's prefer-

ences. It was found that this approach resulted in a

streamlining of the design step which permitted a larger

range of alternatives to be evaluated. The results from the

sample problem would be presented. In the proposed design

process in Figure U-, the next step would involve an evalua-

tion of results of each system design by the owner. This

would be followed by a possible decision to iterate in the

design of the ship with modified criteria.

The ourput of the design step should provide useful in-

formation of the owner so that future iterations will con-

verge faster to the design selected. There will be many

occasions where the owner will want to have results of a

design based on the traditional requirements of speed and

payload capacity. This approach used should prove adapt-

able. The information on sensitivity would be obtained.

110

10.2 Optimization in the Design Process

We have seen that the computational efficiency of the

computer has permitted extensive parametric study of the ship

design. The interaction between the problem formulation and

the solution technique has been demonstrated. The application

of the Sequential Unconstrained Minimization Technique re-

sulted in a straightforward design sequence that could be

used to evaluate many design alternatives. The ship design

model was developed to provide the information necessary

to identify the objective surface for an optimization proce-

dure. In the sample problem, the surface was generated using

the net present value for measuring the cash flows expected

over the ship's lifetime.

The thesis has shown that partial optimization of a

ship design is possible if the problem can be structured. It

was also observed that interaction of the designer with the

program is needed to achieve the maximum benefit from the

programs.

10.3 Experience with SUTT

The experience with the SUMT program generated several

observations releveant to the design process. The first is

that a programmed search which requires derivatives of the

surface, could be employed using linear interpolation of the

111

derivatives and remain relatively efficient. The SUKT Pro-

gram used such a linear interpolation scheme to determine

the partial derivatives of the objective surface. This

efficiency was improved by deriving the design constraints

so that interpolation of their derivatives would not be

necessary. For those constraints which were not expressed

in closed form, they were handled internal to the design

model by insuring that the ship designs would satisfy these

constraints. The non-linear stability constraint was handled

this way because the change in stability could not be deter-

mined from the decision variables along, but must include

the effect of the container loading. The design model was

constructed to insure that all alternatives would meet the

stability constraint by controling the loading of containers.

A second observation dealing with data restrictions

should be imposed external to the design model. When they

were introduced internally, it was difficult to assign

appropriate penalties within the design model to keep the

design feasible. No matter what reasonable level of pen-

alty was assigned, the program would find alternatives that

did not satisfy these constraints.

The imposition of the equality constraints was not

found to be practical in this design application because

none of the intermediate designs were feasible. It was only

after the parameter "r" was sufficiently small that the

112

equality constraints imposed sufficient penalty to the modi-

fied objective function. It was preferred that the equality

be replaced by only a single one way constraint. If two

inequalities were imposed, the associated penalty in the ob-

jective function would be of infinite value and as such would

obscure the real driving factors in the problem. This

approach was used for the equality constraint of the block

coefficient in the sample problem. The nature of the prob-

lem caused the program to design ship alternatives with as

large a block coefficient as possible. The equality was

replaced by an upper bound.

There are two other observations on the application of

the program which should benefit future users. The first

deals with starting points for the program and the second

with the selection of the value of the parameter "r". With

the regard to the first, in the present form of the SUI-T

Program, it is recommended to start the search with a

feasible design. The program is capable of finding its own

feasible starting solution, however, the barrier penalty

technique used in the optimization program requires a sepa-

rate method for finding a feasible starting solution and

attempts to employ its use has resulted in unreasonable

alternatives. A feasible starting solution would prevent

the excessive costs experienced when this feature was tried.

Finally, it is recommended that the selected value for

"r" and for the associated reduction ratio which determines

113

the successive values of "r" be determined as follows. Look-

ing first at the modified objective function, it is impor-

tant to have the values of the constraint and objective

functions of the same magnitude during the first iteration.

This will insure that the program encounters both the affects

of the objective surface and the constraint penalties in the

initial phases of its search. If the value of the constraint

were larger than that of the objective function, the first

several iterations would produce solutions that did not ob-

serve the contour of the objective surface. If on the other

hand, the objective value were larger, the program may sat-

isfy the given convergence criteria prior to reaching a

local optimum on the surface.

In the sample problem this sizing was accomplished in

two ways. First, the objective value was expressed in

millions of dollars. This resulted in the objective value

being of the same order of magnitude as most of the penalty

values that were possible from the constraints. For this

reason, the value of "r" was set equal to one. Other com-

binations have worked as well. The selected value of the

reduction ratio depends on the convergence of the sequence

of subprogram solutions. Most of the improvements in the

sample problem optimizations were made in the first few

iterations. The remaining iterations were to decrease the

11^

penalty values so that the convergence criteria would be

satisfied. I would recommend using a higher ratio than

twenty which was used in the sample problem.

10. ^J- Areas for Additional Study

future applications of the design program could pro-

vide even more realistic results if the following improve-

ments were incorporated. They were not included in this

program due to the limited resources available. The follow-

ing comments cover most of the areas that could use addi-

tional effort.

Propulsive Coefficient

The sensitivity analysis showed that the solution is

sensitive to variations in the propulsive coefficient. As

the design alternatives develop blunt sterns, the efficiency

of the propulsor will decrease. The ship propeller inter-

action should be included. The determination of the actual

propeller would also prove helpful. One approach to deter-

mining propeller fit is covered in Reference ^5 .

Other Constraints

Additional constraints commonly handled, such as the

requirements on the period of roll should be included. This

would require only a slight change in the program. Also

the volume requirements were used only to determine feasible

container configurations. The addition to the model of

115

restrictions due to fuel and ballast volumes should be de-

veloped internal to the model. The volume requirements of

the engineering space should be more carefully defined, es-

pecially since the length of this compartment is used to cal-

culate the length available for containers.

Velocity in a Seaway

The additional resistance experienced in the seaway

causes a loss of speed. The program uses a simplified model

to predict this loss. A subprogram would prove useful in

determining the value more accurately.

Interaction with Terminal

The program presently uses a very simplified inter-

action measure. The model could be expanded for a specific

situation to determine the actual turnaround times and

charges. This would require information on the container

handling capabilities, both in terms of speed of operation

but also the inventory capacity.

Backhaul

Any actual study should investigate backhaul opportu-

nities and incorporate their effects.

Maintenance

Maintenance was assumed to impose an annual dollar

cost. If an overhaul policy is known, the cash flows should

be adjusted. The Net Present Value objective function is

the only measure which could handle the non-uniform cash flow.

116

Seakeeping

An effort should be made to determine the seakeeping

qualities of the design. At the least, limits of perform-

ance could be included in the constraints. One such limit

would be the deck wetness criteria of Reference 39.

Powering Prediction

This program used the Taylor Standard Series to predict

ship resistance. Other predictors such as the Series 60

could be easily employed. Of primary concern is the power-

ing predictions for designs with large block coefficients.

Another alteration would provide calculation of resistance

for the different ballast conditions.

10.5 Applications

The design model was developed for the preliminary de-

sign of a containership. There are other ship types which

could be studies with the existing program. For example, a

LASH or Barge Ship could be considered, also bulk carriers or

oil carriers could be designed. This would require an ad-

justment in the input parameters describing the size and

weights of the containers. The barge is a large container

and the analogy is obvious. The bulk carrier on the other

hand is loaded in a continuous way. By loading small

blocks of oil, the program could approximate the cargo

117

carried.

Another application of the program would call for its

use to test the effects of governmental policies on the

nation's merchant fleet composition. The effect of subsi-

dies has the effect of changing the economic preferences

of ship owner's for different ships. The model could show

the trends in the fleet population that were due to these

policies and regulations. Of more immediate concern is the

effect of oil prices on the design.

The last suggested application involves using the

programs as a teaching aid in a graduate course in ship

design. The following characteristics make this applica-

tion attractive. First, the student is required to provide

a feasible starting point for the design. This could be the

result of a hand calculation and as such provides an oppor-

tunity to understand the design methods. Secondly, the

design program could then be used to generate the data to

check the student's design accuracy for his selection of deci-

sion variables. Finally, the optimization program would pro-

vide other design alternatives so that the student could be

exposed to a higher level in the design process. As such,

this would provide an interactive tool to permit a more

complete design effort in the more advanced design courses.

118

1. Ref

.

16

2. Ref

.

11

3. Ref. 20

4. Ref. 38

5. Ref. 22

6. Ref. 29

7. Ref. 35

8. Ref. 5

9. Ref. 8

10. Ref. 3?

n. Ref. 42

12. Ref. 42

13. Ref. 52

14. Ref. 52

FOOTNOTES

P. 1-5

P. 34

P. 17

p. 46-50

P. 7

P. 3

P. 55

P. 219

119

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3. , "Measures of Merit for Ship Design," MarineTechnology, October, 1970. pp. 465-4-76.

4. . "Engineering Economy in Tanker Design,

"

S.N.A.M.E. Transactions, Vol. 65, 1957, pp. 775-838.

5. H. Bierman, Jr. and S. Smidt, The Capital Budgeting;Decision , The MacMillan Company, 3rd. ed. , New York,N. Y., 1971.

6. T. D. Boumis, "Computer Definitions of Ship Charac-teristics," Marine Technology, July, 1968.

7. Capt. C. Bryant, USN (ret.), "Ship Systems PerformanceSpecifications, Preparation and Use," Paper presentedat the Symposium of the Technology of Ship SystemsDesign, Naval Ship Engineering Center, Hyattsville,Maryland, February, 1972.

8. A. D. Carmichael and R. C. Percival, "Design Optimi-zation of Waterjet Propulsion Systems for Hydro-foils," M.I.T. Report No. 72-15, Department ofOcean Engineering, 1972.

9. C. Chrys.sostomidis, "Optimization Techniques Appliedto Containership Design, "M.I.T. Thesis, January,1968.

10. J. P. Comstock, Principles of Naval Architecture,S.N.A.M.E., New York, N. Y., 196?.

11. R. J. Duff in and E. I. Peterson and C. Zener,Geometric Programming -

-

Theory and Application ,

John Wiley and Sons, Inc., New York, New York, 1967

12. S. Erichsen, "Optimum Capacity of Ships and PortTerminals, "University of Michigan, Department ofNava3 Architecture and Marine Engineering, Ann Arbor,Michigan, Report No. 123, April, 1971.

120

13. "Evaluation of Steam and Gas Turbine Fower Plants inContainership Ships, " George G. Sharp Company,New York, N. Y. , September, 1969.

Ik. J. H. Evans and Dan Khoushy, "Optimized Design ofMidship Section Structure,: S.N.A.M.E. Trans-actions, Vol. 71, 1963, pp. 144,

15. J. L. Everett, A. C. Hax, V. A. Lewinson, "Optimi-zation of a "fleet of large Tankers and 3ulkers:A linear Programming Approach, "Marine Technology,October, 1972.

16. A. V. ^iacco and G. P. Mac Cormic, Nonlinear Program-mine; Unconstrained Minimization Techniques, JohnWiley and Sons, Inc., New York, N.Y., 1970.

17. wranz A. F. ^risch, "Notes on Freight Analvsis",April, 1968.

18. J. S, Folkers, "Preliminary Fleet Design by Geo-metric Programming, 'International ShipbuildingProgress, October, 1969, PP« 308-326.

19. Gas Turbine Propulsion Machinery , Frait and WhitenyAircraft, June, 19-9.

20. Morton Gertler, "A Preanalysis of the Original Te stData for the Taylor Standard Series," DT.-"3

Report , No. 806, March 1954-.

21. Jan R. Getz, S. Erichsen, E. Heirung, "Design ofa Cargo liner in Light of the Development of aGeneral Cargo Transportation," Paper No. 6,Presented to the S.N.A.M.E. Annual Meeting,1968.

22. J. R. Hancock, "An Economic Planning Model of anIntegrated Ship, Terminal and Container System",M.I.T. Thesis, June, 1972.

23. Handbook of labor Statistics , U. S. Department ofLabor, 3ureau of labor statistics , U. S. Govern-ment Printing Office, i960 and 1969.

24-. R. I. Harrington, "Economic Considerations in Ship-board Design Tradeoff Studies: Marine Tech-nology, April, 1969.

121

25. J. J. Henry, "Containerships", S.N.A.M.E. Transactions,Vol. ?4, 1966, pp. 305-320.

26. W. C. Hewitt, "Ship Power Plant Selection, M.I.T.Thesis, June, 1972.

9 7. E. L. Holmboe, J. M, Sheehan, A. D. Evans, "A Guideto Assess the Operational Implications of NewShip Design Concepts", Operations Research TechnicalReport No. 667, Silver Sorings, Maryland, June 11,1971.

28. E. C. House, B. J. Wooden, "Numberical Methods and theOptimization Problems in Engineering Systems",S.N.A.M.E. New England Section Paper, 1959.

29. R. P. Johnson and H, F. Rumble, "Weight, Cost and DesignCharacteristics of Tankers and Dry Cargo Ships",Marine Technology, April 1965, pp. 148-173.

30. D. Kavlie, J, Kowalik, S, Lund, and J. Moe, "DesignOptimization Using a General Nonlinear ProgrammingMethod". European Shipbuilding, Vol 15, 19&5.

31. R. L, Keeney, "Multidimensional Utility Functions:Theory, Assessment, and Application", TechnicalReport No. ^3, M.I.T. O.R. Center, October, 1969.

32. LM-2500 Marine Gas Tubrine Installation Design Hand-book, General Electirc, Marine Industrial Department,Cincinnati, Ohio, MID-IDM-2500-2, April, 1970.

33. T. Lamb, "A Ship Design Procedure", Marine Technology,October, 1969.

3^. T. A. Louakis, "Computer Aided Prediction of SeakeepingPerformance in Ship Design", M.I.T. Report No. 70-3,Department of Naval Architecture and Marine Engineer-ing, August 1970.

35. P. Mandel, C, Chryssostiomidis, "A Design Methodologyfor Ship and Other Complex Systems", Royal Societyof London, Transactions, A. 273, 1972, pp. 85-98.

36. P. Mandel, "An Evaluation of General Cargo Ship Weightand Cost Data for Use in Ship System Studies",Cambridge, Mass. , June, 1967

.

37. . M.I.T. Subject 13. ;+1 Lecture Notes, 1973.

122

38. P- Mandel, "Some Hydrodynamic Aspects of AppendateDesign", S.N.A.M.E. Transactions, Vol. 61, 1953,pp. 464-515.

39. P. Mandel, R. Leopold, "Optimization Methods Appliedto Ship Design", S.N.A.M.E. Transactions, Vol. 74,1966.

40. M. D. Mesarovic, D. Macko, Y. Takah^.ra, Theory ofHierarchial , Multilevel Systems , Academic Press,New York, N. Y. , 1970.

41. R. D. Murphy, D. J. Sabat and R. J. Taylor, "leastCost Ship Characteristics by Computer Techniques",Marine Technology, April, 19-5, pp. 174-202.

42. D. S. Miller, "The Economics of the ContainershipSubsystem", University of Michigan Faper No. 033,October, 1968.

43. W. C. Mylander, R. I. Holmes, G. F. McCormick,"A Guide to SUMT-Version 4: The computer ProgramImplementing the Sequential Unconstrained Minimi-zation Technique for Nonlinear Programming", ResearchAnalysis Corporation, RAC-P-63, McLean, Va. , October,1972.

44. H. Nowacki, F. Brusis, F. M. Swift, "Tanker Prelimi-nary Design — An Optimization Problem with Con-straints", S.N.A.M.E. Annual Meeting Faper No. 9,November, 1970.

45. R. I. Newton, "Comouter Aided Marine Power PlantSelection", M.I.T. Thesis, Kay, 1973.

46. E. G. Pollack, E. G. Frankel, "Aspects of Ship Opera-tion Effectiveness", International ShipbuildingProgress, May, 19^7.

47. E. G. Pollack, G. N. Novaes, E. G. Prankel, "On theOptimization and Integration of Shipping Ventures",International Shipbuilding Progress, July, 1965.

48. W. R. Porter, Subject 13.43 Lecture Notes, 1972.

49. J. W. Schmidt, "Preliminary Ship Design with the Aidof a Comouter", S.N.A.M.E. New England SectionPaper, May, 1964.

123

50. R. J. Scott, "Containership Design", S.N.A.M.E., GreatLakes Section Paper, 1962.

51. G. R. Snaith, M, N, Farker, "Ship Design with ComputerAids", Transactions of the North East Coast Insti-tution of Engineers and Shipbuilders, Vol. 88,1972, pp. 151-172.

52. G. E. Wanddahl, "The External Penalty Function Optimi-zation Technique and its Application to Ship Design",University of Michigan Dept. of NA and ME. RenortNo. 129, June, 1972.

53. J. v. Weston and E. F, Brigham, Managerial Finance .

Holt, Rinehart, and Winstor, 3rd ed., New York, N. Y.1969.

5^-. D. J. Wilde and Charles S. Beightler, Foundations ofOptimization , Prentice-Hall, Inc., 1967.

12^

XIII. APPENDICES

125

Appendix A

VARIABLE DEFINITIONS

126

Table Ik

DEFINITION OP TERMSftD^Tv - AMNHAL A WIN Ami) 41 SC' W ~RAT I M!V Z OTS\i :. - \ \ i.uw i nt.Jkanj.. l ;o..i

AT 5 - <* J \MIA! l MSIJP lyM"? -Mil*ai. 3ha r w r

*_-"*'

^

l a JF. ini-'-ita c)-"

-iic T F\ir

AN'NJ ' - MvNH r R O r fiW'llN-'i l\JfS1'A|_ED I \) TH-_ SHI 3

AN'J V - M-1 PRESENT VA_J =

ao: = ammual o j£watimij :osrsAPT = AM JIJAL POHT CO iT

APV = AVAILABLE PAVI. )A0 WEI3HTAVAI.i - SHIP AVAILA'UI. 1 T f

ftV'M = AVAILABLE WEIGHTED M)M-:NT FOT ^A y_ JAO ANJ ^Ai'^ST3.D3 = ^EAM-DPA'T RATIO=*F = rrr ECTIvE HFAM 0" TH r

i S°ACE ON THE SHIP ~3* r')NTAlN-RS3FA^ = SHIP REAM3FA^ = "UXIM.UM BEAM3M = ^TACFNWIC HF1CHT AlOv/E THP CENTER OF R-JOYAsiCYCASH] r TvjiriAL COST T) 0rfNlE3"

CR = SHIP RL'KK COF r ICIE^rCC = ASJNlUAL. C^EW COSTSCM r SHIP MIDSHIP S-.CTI3M COE r ICIENTCOSri : IVJITTAL HUlLOlM'i :OST 3r THF SHU 3

rnsn = :o^>r or halastCOST 1 = ~OST 0^ MACHINERYrn = :o->r or outfitCP = SHIP PRISMATIC COMMENTCRCWlO) = ? r :>lD'.lAL RESISTANCE :OEF. FOP TSS DOWFSIM3 CaLCWL^TTONCS = COST or STEELCT? = CORPORATE TAX }AT r

i

CV = SHIP VOLUMETRIC COE r ICIEvjTCW 3 = SHIP WATEHPLANt C")E~ICI~MTOR 3 = II STANCE P-ETWF- M ^0-?TS0C r - STANDARD CORRECTION -"ttCTOR ^O 3 3 E->ISTANCE CorrlcIiNJTIF = -:

r:rECTW: DEPTH Tr> S^lACE OM THEl S-tl 3 FOR C-»NT AlNE -<S

0F 3 TH = SHIP DEPTHOF = OTSCOUNT FACTOR r OP A^ 3 V C AL C J.IA T I ONOIS°.l = SHIP DISPLACFM-NTOOJR.F = HEIGHT 0^ DOUBLE BOTTOM0P~ = OAILY PORT FFFSORA r T = SHIP D9A r T

OR&-TM = MAXIMUM OPAFT• - EN")URA\)CE ^ I ST ?v JC E 1

EDE P TH = --'F.rTW; OFPT-t 0-~iA COMTAlM'RELEN3T = ELECTIVE LENGTH OF X COMT A I \)E ?'

fWlOTH r ELECTIVE VIOTh 0-"i A CONTAINERFC = rUEL CONSUMPTI JNri^AM' = "T^ANCEOr R = r REI3HT RATE C^P~,E3 " }R TRAvJS^ORT 0OLLAR~> oER T JmPA4MA = SPECIFIC GPAVlfY ")F SEA WATE 3 '

mV :- &NMISMFVieffl&* ,n*n 127

GN J

<H

<m<g=,

<gx

LFLFNGTLF W T -1

L^LP

SfPC

NIP vMOMO r

MFMGml-:

NN=>C

3f r

3F

3RICE

5AT"OM*1AK

SFZ

RU^Si J

SI 3S<svTOtpvve_o:vflo:evf_o:sVL3VOL 1

WR

wcWFWl^JGTWM

CONVERSION FACIO} ^-OMCFMT'R : ' HUOYANCY

GRAVITY 0"

graviiy )r

SPAVHY :)"

grav I I v .)-"

grav I I v ):

<TS TD r P ;

C E N T - R

cent* <

- - Ni 1 ~R

O c 3MAST V~ISHFMACHINE ?Y rf* I .?Hf

^ J T ~T T rfEI^HI

;t-*:l whisht*ISC WFT3-W

c NGTH-REAM i? A I 1 >

_t" \JG1 H-D" PTH RAT 1 I~ rrF.CTIVE LENGTH }F

^HIP l.PMfiTH

<4AX.lM.lH LKNGTH_c"NGTH F SHIP_r\JGTH O r SHIPMAXIMUM MiJf-l'-iFP

M ri S°AC r

' DN i +1 1 SHI OP COMlATNFRS

SPACiimac -m ME *«Y

P->A<l T'^KS0-"C<S )

ri CONTAI -Jrpt>

DR rONTAl^r^S

S-tTP

OF SHIP

T A < P \J J >l RYT A<FM J D AY

AMMIJAL MAINT AO PE D M *' TOST S

MlJM*fER n r COMT'kl NJf^tJ ACRDSSMAXIMUM MJMHFR 0" INTEIIOR ::C<S "

MjM^Fp ,-) c CONTAINERS Vm 3

NJ'.HH r P OF TUPRTM'S' iMSfALFO I M j-\-

M.H^P 0" CONTAINERS L0M3ITUTI NiAJ-Y3--JI00 0- INTEREST "DP LOAM AM 11 _H r E^PJ^JLSIVL COF r ICTEMT3"WT PALL FFFS p ~ 1 ^DUNO TRI*^^-(CFMT 'iNANCiO^IC r O^" FUEL IN

ANNUAL REVENUESintepesi raif )M

*4AXlMiJM -MGHTl JG

5 3£CTFIC FUEL CONSUMPTIONSHAFT HORSE P0-JE3MAXImom CONTINJ'JJS S-)P OC A S I ^r; _r 3AS TJR-iI\|E

MAXIMUM SHP AVAl_A-<L-:i r PDM ^ PO^i I „lS I ON PL A\J I

^EJJI^EO Shp 11 ->3lV-:i SHIP AT *- J>MTY ViLJCANNUAL SUPPLY AN") STDCX COSTSVJ3S1TY

DO_.IA}S °FR T")M

_0A^'vlOMINT AVAI.lA^Li r0^ PAYL'JAO AND 3ALAST

TIMi IN 0AY5

= VJHM.7V i-.TE

- 'ALVi^E i/ALUF= AVERASE IMPORT OEiLftY

= -n.JNI T^IPS PF. v VIA*- SHI^ VELOCITY= -:\J)UPA\JCE VFLOClTir: ^HIP S°EEO MAO-: 3303= v/^LOCI ty-sojar:; •? do t

r ship oisplacFd vd.uh-:i

=3AL*ST VEIoHT= AVERAGE WEIGHT 0" A ZO^iTAlN"?' IM= r 'j:L WEIGHT= WIMG TAN< Sl/F (IMClJO'S ROTH T A >J

= V'I3HT DF MACHI 4l?Y 12Q

l\(i SEAWAY")-"' LFNGTH 3*ri>

I DNS

' s>

WO = V r I'HT O r OUTFIT*/P = MfLOA") WE I3HTWP<^ = 3T5HTlM(i WMF NT 1"l -MY.OAO^P^ak. : ^.vHum rft"I'»HT *WA 1 -<H .E F03 3 *YJ><0US = a'-:1>-ht 0" STFF_ww = -iA < I mi im ^FiciHT o- ^r'jAi pnMurOiWX : mSC ^IGHTyf: = ashuai. fjl'l ro->T

AND Rv L (\ST

129

Appendix B

EQUATION DEFINITION

Contents

Equation definition for design model.

Graph of speed reduction factor for speed madegood during transit.

Curve of machinery weight as a function of shafthorsepower.

Curve showing model for determining SPC for gasturbine power plant as a function of shaft horse-power.

S?C nlot for various gas turbines.

130

Empirical unci Other Equation* Utcd lor CargoShip Model

Tin- equation-, presented in this ap|te:idix tin;

taken from rvfen nee 1 1Iand form tin basis fur the

computations that are carried out in stvp '.'* of

each sampling ryrlc. These equations crnilil

undoubtedly l>i' presented in different fonii with

imprt>vv<l accuracy. The equations arc listed in

seven major groups: (I) Weights. II'. (2) Volumes,

V, (3) Freeboard. /•'.( I) Stability, A'. (.">> Cost. f.

(0) Power. /'. inn! (7) Miscellaneous. U.

I Weights (nil weights arc given in long toils),

'••-»'4 <"r,

r

w

(a) Approximation to oiiilit weight

X b) K,

UNI

A', m 0.080

Approxinmtion to steel (Wight

(c) . Approximation to wet machinery weight

W. - 7.18 SUP"" (311')

(rf) Weight o f iucI oil required to sail tnc

specified distance. £ plus ID percent allowance, at

a given speed, (!').

(Ill)

W,m (I.lllE) XSHPX Fit

22-10 X V11.491 X III-

"IE X SUP X FRS] (III')

am

(0110F, 2 4.21 + 3.50 -j^ +

(«) Approximate fuel rate

FR - 0.5SHP/(SIIP - *.->;>)

(/) Miscellaneous deadweight

W, - 300

(|) Actual payload weight

W, - A - II'. - It'. - H'„ - W, - W. (7110

where A « (sec Table 1).

2 Volumes (all volumes given in cubic feet),

(a) Approximate gross bale cubic of the ship.

This value applies to all dry-cargo ships except

where excessive sheer is used. This expression

includes machinery space volume and excludes

the double-bottom, settler, and peak tanks

CHC - ().873|Z, X U X D X C„\K, (1 n

RtF [39J Optimization Methods Applied to Ship D»ugn

<li) Approximate fuel oil eapaeilv ill the double

bottom. This equation i-. used ill coiljlllU'liou

withe<|U.ilioii (.". I'l todeleriiiine whether adequate

Volume exists to aeeoiiiinodate the fuel oil com-

puted by equation i III)

(Vol),. - [(A'» X /.) X H X (A', X D)

X (O.G'J C„) !

- 0.7N.SA', XGHC (21')

where

A', <= o.ll

t"» block coefficient al LVVL; factor till |kt-

ccnt is u correction for («) structure in

inner boi loin, and (//) correction to obtain

C» at the \VL height equal to tank top

height. Fuel-oil stowage factor is ;17.2

cu ft/ton

(c) Approximate fuel-oil settler-tank capacity

(Vol)A - 5000 cu ft (150 tons) (:M')

(rf) Approximate machinery space volume

(Vol). - 47,032 + 7.112 (SUP) (41')

(c) The actual payload volume is

Vol, - GBC - VoU»,„„ - [37.2 If,

-(Vol„-f-Vol /,)j (.jl')

(J) The towage factor is

sf - voi,/ir, (or)

3 Freeboard (all freeboard dimensions are in

inches).

(a) Available freeboard. Equation assumes

3-in. margin line and that the uppermost con-

tinuous deck is the freeboard deck. Equation will

differ for a shelter-deck ship

F. - 12 [D - (0.25 + T)] (If)

(b) Minimum permissible freeboard from

USCG Load Line Regulations.

For:i S 400ft:

71 (]¥»)' (2/-)

For: 400 ft S L S 7 50 ft

•, i - 77.07 + 42.5SL

100" ogo (4)'

fa* Li "wo-ft

oos (4)'

Fr fc .232* »l-

(.(/•)

131

4 Stiilitlily (mints which are Mated In cli>1lnrs liy a factor n(

(>/) A|ipin\iltialiiill In (III' transverse inertia between I and .M "

cnvllicieill <il llu ilvMxll Innl water plaiu'. n « l>i| • limit costs

trans. watcrpl.ine inertia//./)'

u - H.ltWlC, - IIJHJ:' (1.9)

(/') A|i|>rn\iiiialiiiii In (lie KG i if stni

ac. - a-

, DA, - 0.01 (25)

(c) Approximation In the AC of outfit

kg. - a, nA. « 1.011 (.15)

(rf) Approximation to tlic KG of payload

AC, - A-

, DA, « 0.03 (45)

For.O £ II'. S IIiki tons

C. - {1 1 (Ml - iiiii.'I II'. .f. (11.112 x I0-")IIV

- (11.1:12:1 x n> «)ii'. ,|ii'. (in

For: MINI < II'. < 2000 tiHIs

C. - 124.10 - I 02S II*, + ("722 X 10") II'.»

- (11.1191 X 10 •) ll'.'l H'. (20

For: II'. fc 2(1110 tons

C, - HIM II'. (3C)

(4) Approximation to steel cost

(e) Approximation to the KG of miscellaneous ft ~I21S.4 — 2l.-1.sl --- ^ 1

deadweight

" MB(iono)

,

-W ,*(Ss),

],r

'(4C)AG, - A", D

A. - 1.00 (35)

(/) Approximation to AC of fuel oil in settler

tanks

AC„ - AV> + 4.S0

A. - 0.11

(c) Approximation to machinery cost. (SHPis normal shaft horsepower.)

For: SHP £ 13,000

(65) C.-

(g) Approximation to KG of fuel oil in double

bottom Frr :•-:•"-' '*,:p- ,r"» •« •.!.-»,. •»« («!/.")

(tank top height)

AC* - 0.07 K,l) (75)

(A) Approximation to machinery AC, with

boilers full niul fur conventional arrangement for

steam-turbine plant

137.7 - zzSHP

75.32 + (SHP)

"iSF (3-K>.

SHP

For: SHP g; 13,000

C - SHP3.249 (SHP) - 173.05

ioo"

AC. - 55 D (S5)

(0 The available CM in the full-load condi-

tion uncorrected for free surface is approximatedby

(rf) Annual fuel cost

CM. - A,r +LB'

C, - KwRiWtV/EAw > 5205 for this study

A, - 3.09 cost pts/ton

SHP (00

(70

35 X A

-Kir. ac. + ii'.ac. + irjcc.

+ ("'/ - VV»)AG„ (95)

+ \V„ KG„ + II'. AC, + IP, KG, |/A

A, - 0.54

(7) The required CM is

GM, i 0.03 H

An explanation of A'K is given in section 8 of this

Appendix.

(e) Total annual cost. Cost

The yearly fuel cost {equation (7C) ] is included in

this cost which is computed as follows:

Cost - 0.0050 X (C. + C, + C) 4- C, (SO

where the fraction I KioO reduces the total initial

(105) building cost to a yearly cost usin^' the assump-

tions :

(This required (",M is also for th. /full-load condi-

tion, uncorrected for free surface. I »Th, term ens, p„i„„ i, used in HI to avoid dire*,o Costs (all costs are given ,,, terms of cost a>«nci;t<ion with dollars

Optimization Method. Applied to Ship Des/gn

132

.9

ooo .8oUJQ 7< • i

2

Q p;UJ ,pLlJ

Ol.

COh-

.5(T C/)

O 2U- <

ce

ccK-

.4oH- oo Z<u_ 5

3 .3

2 Qo~

.2oDQ1 i 1UJor: .1

VELOCSVELOC 2. - EXP (.0075X VELOC

)

10 20 30

CALM W^TER DESIGN SPEED (KTS.)

—

r

40

Figure 19

133

I

z.LUz<c

oCD

OrO

CLX oo

XIT)

CXI

rO

il

CD IT) sj" rO r\J O CD

'00SN01)

to

in

O

OrO

O

OoOO

OOX

o CCcr> LU

Oo n.00 Id

COnroX

o(O \-

U-<

n xur> to

otf-

orO

O00

1H9I3M AH3NIH3VW

Figure 20

134

I

oUJ

<c

X

XOJ

X

4-

o_XCO

X<sCD

O

rO C\h O CT> 00 CD

( 01 X$) AH3NIH0VW JO 1S009"

^igure 21

135

IT)

M

u.

o

o

oI- rO

O

O

OO

oCO

o

oCD

OID

o

orO

Oc\J

- O

OOo

X

crUJ

OClLjJ

COcro

u_<CO

EXPLANATION CF S^C I.:CD3I

The graph in Figure 22 shows the minimum

S?C as engines are added to the power plant to

achieve a given installed shaft horsepower.

The initial segment shows the S~C curve for a

single engine. "For the multiple engine install-

ations, the same minimum SFC is achieved at in-

stalled shaft horsepowers of multiples of 18,700

SKF. For the intermediate powers, all engines

are assumed to operate at equal levels.

136

om

s

orO

O(M

O O- oo

8 x

IT)

CDrO

aLdorCLXCO

X<

en i)

01UJ

co Q_UJCO

o cr^ o

X

CM

oLi-

CO

oCD

Oin

o

<m00

*1

orO

O

z

O 2

- o

en oo n- CD m rO C\J

OJS 'igure 22137

170

I to'

ISo

O

FT -<t^

esvr F^et. TwFcefi^vcf ["32.3

Ln- Z.5T30 /I

Wo -

l3o -

\to

l\o

FV .its-

\

\C-V5„A

CD \ \

\ \Q

V\^

lOO

'SHp't

—I

—

+0

—1

—

4o

-1

—

803o 50 70

°/o SHP

S?C CURVES FOR MARINE GAS TURBINES

Figure 23

138

<?o loo

Appendix C

INPUT FARAKETERS

139

N.N.S. DESIGN

PROGRAM INPUT PARAMETERS

PARAMETER SYMBOL VALUE

DPSi&M P/wwurrtRS

PftOPULSlWG COfFFlC/GAJT PC .*?£" (/WPUM6-6 '-03^

EHVUHAhlCt £ I^Soo

Dis-|/)aJc6 BrrueEA/ PoRrs DBP 5"ooo

StffP /h/4'L/lBl UTY AVA 1 L •98

wuMbt* op stt/vrr'b NSH^fT 1

MlK. NO. OF £-AjG-(/U<rS* N£AJGU (-3

|UO. OF SP/^RC EWW^^S /vexTR^ OMAX. pAV(.0/4b WT- ww -?0,000

Ml/v. ~?AYloAX> WT. wpmia; Omax. coa/t/)ia/(?^ st/kki^g- MD V

MA*. stacking- /4Bo^ X»k. MU ^

AV£ZACyF £OaJ7%iajE*1. *JT

.

WC H.8G

BfFBCTIOt COaJT. LFA/(^T7f ELENOtT 23-o

BliC-C-TlVG COWT. vvi"CTH E W lt>T H 8.75-

EFF&aiue QoArr> t>£PTtf EhZ-PTH 8.02

DouBlf Borrow TwickAteis t>oui$u£ a.r

B/ULAbr wei&^r k&-. K£rB 2.0

M/\x. 5hp fo* si*j6<.£ e>o& S|4?M N.A.

Sg* SPcfeU F/}ct o a? Bft/9 I .co^r

5fc factor BeTA2- •3tr

Misc. weKri-iT wxx o

MISC.. uyerfCrHT KG-. XK6-X

Df5K»aJ U/t((^4T7V6- F4CT<3«5-

F^CTo^ Fc5* OwTF(-r i~T- V/Wo i

R4CTOR Fop, stffc wr. WWS j

,

F^CTo/? Ffl/2 MAcHWe/^w VWM i

,

Table 15 1*4-0

N , N.S. («>»t)

PROGRAM INPUT PARAMETERS

PARAMETER. SYMBOL VALUE

NAV16ATIOM CoW5TRAi*JT5

MAX. LEKIGTH LE/v/tTM 9oo

M4X- SEAM T3EAMM Ho

MAX- DtfAFT DRflFTM 3^

ECONOMIC PA"AAMFT£K5

FRFlCrl-fT RAT£ FR So.

PO/^T GALL FEE PCF (OOO.

PA-iLY TtoftT F££ T>P F looo.

PftlCt OF' FUEL PR I c ET ife.S

AwWU/Il IvSUR/WC£ RAlt AIR .1

Asset UFt NM AS"\

SAiAMGk value SV cDiscount factor DF ,2o

'Submw Kate SUSI"DR .5S

pE/<2C£/<->JT FNA/VC^~b PF lb

interest rate RATE AO

Co<7>. Tax H/\tg CTR .ne

INVE3TMEA/T TA^ CtfttMT A/TC ,o7

Cost weight/ a; 6- factors

Factor Fo/<? outfit Cost CCo 1.

Fflrt-TOA FO* ste-fc Cost CCS 1.

Factor FO/e. ma^ia^/cy c, C-CM 1

PRoGR/lM PARAMETERSCBjFcn^c StcECT'OAy ItfftJ 1 (/J>u\

DtLTACil Ate C°

)

Table 15 (cont. )

141

B.I.W. DESIGN

PROGRAM NPUT PARAMETERS

PARAMETER SYMBOL VALUE

DESIGN P/w?AM<=TER5

FRCPU LSifCT COeFFlC|£A/r PC .70 (Af^FATMGe i.05)

EKiDUHAKftt £ 12,5-00.

Disr/Wce BETiJeFA^ PoRT*> DBP S^ooo

Si4i7> AVAtL/HSlurV AVAIL .9&

WUMBF* OF SHAFTS nsuaft 1

' tMti. NO. OF £AJ6-(Aje-S* NeAJfetJ c- >

HO- OF "STPARG ENb-WCS a/gxtr/i

HA/-. pAV<-0/4b ^T- WW io,ooo

Mia/. "P^VLo/qb WT. WPMIa^MAX. COa/7/1W<Ev\! S7/KK(^&- AJD 3

MAX. stacking- ABoi/f "Dk. M*) 6

AVCZAGF COAJiqi<uF>{ vJT. we 11.5"

BHC-CTlUt CoaJT. LFAJ&T71 ELENGT 33.0

£7FF<lTii/(F Co/uT. WyfDTH EWFDTH 8/JS-

ErFtCTWf QOaJT- "beVTif EbfPTU e.oz

DouBlf Bottom thick/u^s "D^aT^uf 4.5"

B/ULAbT V</fi6rMT kfr. K<^B A,r

MAX. 5f+P Foa? scufrce &u& S|4PM /sf.A .

Sea 5P<ffT) factoa> BET/? i .OOTS"

5 F C FA^TO/"? BftAE. ^feS"

M<sc w<fi6tW7 W)<X O

M(SC u;f<&-ht KG-. XK6-X

E>F5i<s*J u/t((344T?v6- FAcrartS

Factor fo# Out^ct <*n. \</Wo f.

FACTOR FoR STFFC wr. wws 1.

fa.cior Fofi. ^AMt4iAj£/a vn vwm 1.

1 2|>2Table 16

P>/« O PU«- Si OAJ.

B.I. W. (<o*n\

PROGRAM INPUT PARAMETERS

PARAMETER. SYMBOL VALUE

NAVIGATION Cow 57 RA ia/TS

MAX. LEM6TH LEA/&TM ?0O . FT.

M4X. BEAM T3EAMM 11© . FT.

MAX- CXAFT DRflFTM 3*7. FT.

ECOMOMlC P/OV\MET£R5

FRFlfrWT RAT£ FR 5*>.

PO^T CALL F££ PCF (6>CO.

PA-iLY "PoAT F££ "DP F lOO<?.

PKlCE OF FUEL PRICE Ife.5"

AHVUAl \\)SURA*JC£ RATE AIR .1

Asset lifS NH *S" '.

SALVAGE VALUE SV O

Discount FACTOR DF .Zo

"SuBSW tfATf SuSlftR .5"5"

pe>«(Le*/T Fltf/4/VC*T> PF .75"

IWTFREST RAT? RATE ./o

Coiflf?. Tax RATE CTR .**8

INV&3TM6/JT TA> C*tT>IT AlTC,

..on

COST WC'EHTl^G- F^CTO^S

FACTO* Pofi OUTFil COST CCo i.

Facto a. fo* Srcec Cd^t CCS I.

Fa<ctoi4. Fo/e. MAmi/je/ci t. C-C-M i.

PRobRAH PARAMETERS0"Bjfctwc Stctcrrfo-N/ IC>^>^ 1 (jJP\j)

D#-T*(tf -4U C<?^

Table 16 (cont.

)

1^3

GEORGE G. SHARP

PROGRAM INPUT

DESIGN

PARAMETERS

PARAMETER. .SYMBOL VALUE

NAVIGATION C.0W5TR/WWT3

MAX. LEM&TH L£a/&TM fs-o

M4X. BEAM T3HAMM X oo

MAX- DM FT DRfl FTT/M tfe

ECONOMIC PfyTKAtAkTERS

FRFIC-HT RATE FR So.

Po£T call fee ?CF ( OOo.

V>M Ly 7>oflT Ft E "DP F (OOO,

PRICE OF FUEL. PR ICE- 1/ *16.5

AMKIUAl. \\)SUR/\ajC£ RA-T& AX R .1

Assey Lif£ HH XS

SALVAGh VALUE SV o

Discou^ factor DP • 2o

SU'SSW ftATB SUSI"DR <SS

PF^CjFaJT finance PF •7r

INTEREST RATE RATE ie>

Co<P. Tax RATE CTR ,fS

INVFSTMPA/T T4* CtfeTMT AfT^ .o*7

Co ST W<?'G-HT/a;G- FACTORS

Factoa? Pofi. OUTFCT Cost ceo /

F/KSTOA PCA ST&fC Cd%t CCS 1

FA-CTOA FCA- MAQ+l-VP/tT' C. C-cM I

PROGRAM PARAMETERSOBj^CTXc/c SecEcnTOA/ lc?R>? 1 (wpu)

DELtA-C^ Ate Co)

fTMTCTKr^ '^ cUKOK

Table 17144

G. 6. S. (cowt )

PROGRAM NPUT PARAMETERS

PARAMETER SYMBOL VALUE

DFSl&W P/^AM<=T£R5

VkOVU LSlUiE CO£FFKM£AJT PC .7o (^^Pe^Tj/ice l.o?)

EAJDUHAMdt £ 5^ooo.

DiStAaJCS BeTuJeE^ Ports DBP- tv 8oo.

Si4fP AvWL4B(UTV AVAIL .98

WUMBe/4. OF SHAFTS MSH/\F7" 2

'

tf Itf . A/o. °F e'AjG-t-u^s* N£AJ&U 2

W(3. Or SP/ARt EUG-[AJGS AyexTR/i

HA/-. 'pA^LOAh wyr. ww ^OOOO.

Ml/J. PaVloAD WT. wphia;MAX. COa/TAia/<F^ STACK(^6- KiV 6

MA-x. ST/Kki/W- /4Bo^ "DK. MD 5

Ave^AC^F Coat^/a/cX vjt. wc ^0,5"

&W-ECTIU& COaJT. LtAlb-Tli ELEN&T 3§.o

EFItFdTiWF COWT. WfDTtt EWlt>TH e.ti

EFFECT! OF Q.OAJT. DtTTtf Eb&PTH 8.02

DouBLt Bottom th feloness "Dcja'BL-^ 3.r

B/lLLA^r W/f|fri4T KG-. K^B 2..0

MA/- 5H-P Foa? swg-cf e/uG S|4PM 1 S,*)^

Se^ 5P<FF?) F/Jctoa7 Bfta i .oo"?S"

5FC F4CTO* BetAE, •T^r

Misc. w<f»^wt WKXMisc. w/enG-HT- kg-. XKG-X

Dfsi&aJ \A/fe((^i4T?Ay6- factors

FACTOR Fc?*? OuTFcr i~t. VWo 1

Factor for stfec wr. wws i.

factor for MAcHwe/e^w wv/m 1.

* MPOATIiJt- V4LMI- |A)t)it^TB Stf^l T"U-<Ol^fc- ^^PUt-SiO/O,

Table 1? (cont. ) 145

SAMPLE PROBLEM

PROGRAM NPUT PARAMETERS

PARAMETER SYMBOL VALUE

DLrS(GM P/\rtAM<=TER5

PAOPULSlUE' C.OC-FFlClGA/T PC .65

EKJVURAMlb £ 12,500 WmT

DiSrAfJce i$eT<JoF*J Ports DBP 4,600 MM?

Sl+fi9 AVAlLABlUTY AVAIL .98

WUMB^* OP SHAFTS AJSH/\fT 2

ttltf. NO. OF EUCxikJC** NeAJ6f 2

W0. OF S"PAR(F e^W^G'S VEXTRA o

HA*. pAVcO*b WT> WW.

"^oxooo toa)5

HlA). PaVlo^D WT. wpmia;MAX. tO/s/TAi/v&t S1ACK[*J<t ^D <o

MAX. stacki/V6- ABo^ "DK. NV"b X

AvetfAGF CcW74ja/£X v*JT. wc I fc.5 TOa^s

BHFCTIU& COajT. L£"A/Gr7H ELENGrT 2-3. FT,

eWF«TH/e COAJT. WiVTH £W l"DT H 8 ,VS F7

EFFECTi oE <?<WT. DeTTM1 ET>EPTH 9,oZ FT

"DouB'-F Borrow TWick/oess ^DOUPoLf <t.S FT

B/ULAb~ VC£fi6-i4T kfr. K4-B *.:T FT

MAX- 5H-P Fo* s/<vG<* aix» S|4P^ ^7oo 5HP

S^a SPfFt) FActo a7 BFT4 i • 007F

5fc factor Beta 2,3fcy

M(SC WCT6-H7 wxx 0.

Mi St. wf<&-HT KG-. XK6rX 0.

E>F5<6aJ U/e(k(-fTW6- FA^TtftfS-

F/tcro^. fov 0"TPtr u/r. . y/Wo 1.

Factor for stffc wr. wws L

factor fa* Nvke+wtv^w VWh I .

Table lg6

^OPULSiO-M.

SAMPLE On)

PROGRAM INPUT PARAMETERS

PARAMETER. SYMBOL VALUE

NAVIGATION CowS'l RAtVl^

MAX. LEM6TM LEA/&TM 800, FT

_M4X. BEAM BEAMM IIO. FT

MAX- OtA FT BRflFTM 3*7. FT.

ECONOMIC P/mAMETtRS

FRFlEHT RAT£ FRPO#T QALL FEE PCF lOOO. / (Ml*.

PA-iLy >oAT F£E "DP F ^looq/tMy

PRlCt OF FUFL PRICE- •* 63-V/niAw^uAc |ajskR/wc£ RA-nt AIR .©I

AsseT ^-(Ft NM 25-. YeMS

S/lLV/IGt VALUE sv

discount factor DF .^0

SuBM~£>Y K/rre SuSiDR .ST5-

Pl-ACJEaJT F"|NA/Vd^"b PF 7S"

INTEREST RATE RATE .10

CoR*P. Tax rate CTR .H8

lNVF3TMfA/T tax c/eet>iT Aire,

.07

Cost w<F'feHT/^6- factors

Factor Fc?/« cutfct cost CCO /,

Fa<ltoA fo* 57CR. Cost CCS 1.

FA<CTOA FOA. MA*U-flA/e/C"f C-, C-C-M 1.

•

PROGRAM PARAMETERSOBOCCTt^c Sc <-Hc_t(Oa/ iota 3 1 (/J-pv )

DCt-TACt'j /ILL (O)

ftfFCfCTs ho<( Cu<«c^T T«eA^S ft FuFe "&*«* CTWfO? i<«,<i (.PuR.)

Table 18 (cont. ) 1/|?

Appendix D

USE OF SUMT FROG RAT'S

^

1^8

USE OF THE SUMT PROGRAMS

Two programs were developed to obtain the output used

during the analysis stage. The first utilizes the SUMT rou-

tine to develop attractive alternatives. These alternatives

are identified by the values of the decision variables and

the objective function. In addition, a second program is

available which gives a detailed breakdown of a single de-

sign alternative. This second program does not employ any

optimization technique. It merely identifies a design in

terms of its weights and costs. The inputs for each of

these programs are outlined in the next section.

Input ^ormat

The input deck for the SUMT program contains two

major elements. The first lists the parameters used by the

optimization technique and the second contains the data used

by the design model in defining the objective surface. The

cards are listed in the order of appearance for the input

deck of the SUMT program. (See Figure 25 ) The second pro-

gram uses only the design data as its input. See Figure 26.

CARD 1: Problem #1 Parameter Card (See Guide to SUMT)

1^9

CARD 2: Initial X Vector of Decision VariablesFormat (6E12.6)

Displacement j length? Beam; Draft j DepthPrismatic Coefficient.

CARD 3: Initial X Vector (Continued)format (6E12.6)

Velocity.

CARD 4 « First Design CardFormat (5F10.2,5X,I2)

Propulsive Coefficient j Endurance; DistanceBetween Ports; Maximum Shaft Horsepower of aSingle Engine; Average Fort Delay Time; Maxi-mum Stacking of Containers.

CARD 5: Second Design Data Cardformat (5F10.2.5X, 12)

Maximum Payload Weight; Average Weight of aContainer; Effective Container Length; Effec-tive Container Width; Effective ContainerDepth; Maximum Containers Stacked Above Deck.

CARD 6: Third Design Data CardFormat (5F10.2,5X f 12)

Port Call v ee; Daily Fort Fee; Freight Rate;Price of Fuel; Annual Insurance Rate; Indi-cator of Objective.

CARD 7: Fourth Design Data CardFormat (5F10. 2,5X,I2)

Percent Financed; Subsidy Rate; Interest Rateon Loan; Salvage Value of Ship; Discount Fac-tor; Asset Life.

CARD 8 j Fifth Design Data CardFormat (5F10.2, 5X f 12)

Investment Tax Credit.

CARD 9: Sixth Design Data CardFormat (5F10.2,5X,I2)

Maximum Ship Length; Maximum Ship Beam; Maxi-mum Ship Draft.

150

CARD 10:

CARD 11:

CARD 12:

CARD 13:

CARD m-t

CARD 15:

CARD 16:

CARD 17:

CARD 18:

Seventh Design Data CardFormat (5710. 2,5X, 12)

Double Bottom Thickness; Center of Gravityof Ballast Weight Above Keel; Ship Avail-ability; Annual Corporate Tax Rate.

Eighth Design Data Card, Sensitivity DataFormat (8? 8. 2)

Betal; Beta2; WWOf WWSi WWMi CCOj CCS; COM.

Ninth Design Data CardFormat (878.2) .

WXXj XKGX; WPMIN.

Tenth Design Data CardFormat (313)

NSHA7T; NENGU; NEXTRA.

Eleventh Design Data Card, Sensitivity DataFormat (14-F5.2)

(DELTA(I),I= 1,14)

First Option Card (See Guide to SUMT)

Tolerance Card (See Guide to SUMT)

Second Option Card (See Guide to SUMT)

Problem #2 Parameter Card for Next Program,Repeat Other Cards As Necessary.

151

/ //

'_ / /

S^OO^A} OPTION CA~i*X> \ /

TfLtA?,4XJCc CAhTD

OPTio/O CMt)

^es/fe^ >>AT-4 C4«i>S

Initial Xe v/tCTo< ca^>t

P*06u?/--i #£. PARMierez c^<d

StCO/0"b OPTlO/yJ C/Kb

Tote*Auct tyWt>

OPTIOaJ tA<b

De5i6Aj t>ATA C4rtt>S

IWrriAL Xo VeCrOrf CAiVb$

PROBLEM #1 PARAMETER CARb

1/

t-A^'D 1*1

CA<£T> tfc

CAftT> ,?

1/ CA<OJ 3- IH

CAftt^i.*- 2-

CAM) L

PRO&RAM PATA DECK .5TRUCTUR,fc

Figure 2k

152

SAKPI.E DATA CARDS ?0R SUIuT FRCGRAWc

c

c

IT < (\ — U— (V

c a Ifif C"

—

—

i

c • • • •

u (V a•

ccv

<) IT In cr cr

• r- r- cr <Jr • • « •

r c a Nl

i

c J>

u vt• r\

c .—

c a• • 1

—

a cr. cr

J c • c 1 • * • A »—• c m c r^ .—

1

Ca a rv *-. r~

c <j

cr

I

cr•

u cr• c —

*"~

. L1/

Lf LP

•

cr CO • 1 • • t • 1

•S *In c

c c c c1—

i

«J cr .- if\T •— vT c —r^ r •

L • c

L U u r-

• vT [»• c 1/ c c.

• 1

—

c c c s* r- cr c c« c c c c f\ c

c c c o c c«

—

t- c — • c •

r • rv c fv •

u r c c-3 r c

p igure 25

153

SAMPLE DATA CARDS TOR DESIGN MODEL

r• r-r •

a irrv

a<r if

ccv c <r

rv • • •

cr cr cr•

• a •— cr rv c• i_r • • c • c (V. • <rC LT i ^-t • ^ • #—< • *—i •v£ <J cr a » c

cr

c cr c.• • •

IT U" P c c cr criT «N . « .• c •

O • cr • -*> ^ cu"iS # <X —a s c cr

~ a cr ir r- - cr -j- cr(\ r- <t • n- • -o • •

o # c- a a "" c

• i~- #— c r- •-» cr

r*" • • f • oc c c • c • ••f—«cf\cr a c cr • c cr vf crecu- c • cr a Lr r- <j •

OLT • cr <t c- • crf r~

\s • c • cu • c • <r

• • c • c •

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Figure 26

154

Sample Output

Figure 2? shows the output to the program giving the

detailed design.

1. Values of the decision variables.

2. Weight break down of the design.

3. Container configuration.

k- , Cash flow statement.

5. Value of objective functions.

Figure 28 shows the output to the SUMT Frogram. The

following annotations apply:

1. The values of the SUMT parameters used for this prob-

problem.

2. The initial X vector of decision variables with the

associated objective value (F), Also an internal clock

is referenced. (Use of design alternative h)

3. The starting feasible point (same as #2 in this problem)

k. Recording of orthogonal moves made by the routine.

5. The solution to the first subproblem after 10 moves

r = 1.0.

6. The solution to the second subproblem after 12 moves

r = 1./20

7. Final solution of the first problem.

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160

Appendix E

SOURCE LISTING 0? CClvIFUTER PROGRAMS

161

FROGRAM MAIN

Routine that calls design model and

outputs a detailed ship design.

Calls subroutines?

RSADIN

RESTNT

162

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16^

SUBROUTINES USED IN SULIT FROGRAM

includes routines

READIN

RESTNT

GRAD1

MATRIX

Notes

Subroutine RESTNT Calls

Subroutine Object

165

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includes subroutines

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SHPREQ

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Subroutine object callssubroutine SHFRQ

Subroutine SHPRQ callssubroutine RESIS

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T»T^SEP74 DISPLAY

S 1 5 1 9

Thesis 153603F623 Fortson

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Application of the sequential unconstrai

3 2768 001 95933 1

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