3 - Study of or Packages

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Study of Operations Research Software Packages

1. ‘LINGO’

LINGO is a mathematical modelling language designed particularly for formulating and

solving a wide variety of optimization problems, including linear programming, integer

programming and nonlinear programming problems. LINGO's primary features include

Algebraic Modeling Language

LINGO supports a powerful, set-based modelling language that allows users to

express math programming models efficiently and compactly. Multiple models

may be solved iteratively using LINGO's internal scripting capabilities.

Convenient Data Options

LINGO takes the time and hassle out of managing your data. It allows you to

build models that pull information directly from databases and spreadsheets.

Similarly, LINGO can output solution information right into a database or

spreadsheet making it easier for you to generate reports in the application of your

choice. Complete separation of model and data enhance model maintenance and

scalability.

Model Interactively or Create Turnkey Applications

You can build and solve models within LINGO, or you can call LINGO directly

from an application you have written. For developing models interactively,

LINGO provides a complete modeling environment to build, solve, and analyze

your models. For building turn-key solutions, LINGO comes with callable DLL

and OLE interfaces that can be called from user written applications. LINGO can

also be called directly from an Excel macro or database application. LINGOcurrently includes programming examples for C/C++, FORTRAN, Java, C#.NET,

VB.NET, ASP.NET, Visual Basic, Delphi, and Excel.

Extensive Documentation and Help

LINGO provides all of the tools you will need to get up and running quickly. You

get the LINGO User Manual (in printed form and available via the online Help),

which fully describes the commands and features of the program. Also included

with Super versions and larger is a copy of Optimization Modeling with LINGO, a

comprehensive modeling text discussing all major classes of linear, integer and

nonlinear optimization problems. LINGO also comes with dozens of real-world

based examples for you to modify and expand. Powerful Solvers and Tools

LINGO is available with a comprehensive set of fast, built-in solvers for linear,

nonlinear (convex & nonconvex), quadratic, quadratically constrained, and

integer optimization. You never have to specify or load a separate solver, because

LINGO reads your formulation and automatically selects the appropriate one. A

general description of the solvers and tools available in LINGO follows:

General Nonlinear Solver

LINGO provides both general nonlinear and nonlinear/integer capabilities. The

nonlinear license option is required in order to use the nonlinear capabilities with

LINDO API.

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Global Solver

The global solver combines a series of range bounding (e.g., interval analysis and

convex analysis) and range reduction techniques (e.g., linear programming and

constraint propagation) within a branch-and-bound framework to find proven

global solutions to nonconvex nonlinear programs. Traditional nonlinear solvers

can get stuck at suboptimal, local solutions. This is no longer the case when usingthe global solver.

Multistart Solver

The multistart solver intelligently generates a sequence of candidate starting

points in the solution space of NLP and mixed integer NLPs. A traditional NLP

solver is called with each starting point to find a local optimum. For non-convex

NLP models, the quality of the best solution found by the multistart solver tends

to be superior to that of a single solution from a traditional nonlinear solver. A

user adjustable parameter controls the maximum number of multistarts to be

performed.

Barrier Solver The barrier solver is an alternative way for solving linear, quadratic and second-

order cone problems. LINGO's state-of-the-art implementation of the barrier

method offers great speed advantages for large-scale, sparse models.

Simplex Solvers

LINGO offers two advanced implementations of the primal and dual simplex

methods as the primary means for solving linear programming problems. Its

flexible design allows the users to fine tune each method by altering several of the

algorithmic parameters.

Mixed Integer Solver

The mixed integer solver’s capabilities of LINGO extend to linear, quadratic, andgeneral nonlinear integer models. It contains several advanced solution techniques

such as cut generation, tree reordering to reduce tree growth dynamically, and

advanced heuristic and presolve strategies.

Stochastic Solver

The stochastic programming solver provides the opportunity of decision making

under uncertainty through multistage stochastic models with recourse. The user

describes the uncertainty by identifying the distribution functions, either built-in

or user-defined, describing each random variable. The stochastic solver will

optimize the model to minimize the cost of the initial stage plus the expected cost

of future recourse actions over the planning horizon. Advanced sampling modes

are also available for approximating continuous distributions.

Model and Solution Analysis Tools

LINGO includes a comprehensive set of analysis tools for debugging infeasible linear,

integer and nonlinear programs, using advanced techniques to isolate the source of

infeasibilities to the smallest subset of the original constraints. It also has tools to

perform sensitivity analysis to determine the sensitivity of the optimal basis to changes

in certain data components (e.g. objective vector and right-hand-size values).

Quadratic Recognition Tools

The QP recognition tool is a useful algebraic pre-processor that automatically

determines if an arbitrary NLP is actually a convex, quadratic model. QP models

may then be passed to the faster quadratic solver, which is available as part of the barrier solver option. When the barrier solver option is combined with the global

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option, LINGO will automatically recognize second-order cone models, in

addition to convex quadratic models.

Linearization Tools

Linearization is a comprehensive reformulation tool that automatically converts

many non-smooth functions and operators (e.g., max and absolute value) to aseries of linear, mathematically equivalent expressions. Many non-smooth models

may be entirely linearized. This allows the linear solver to quickly find a global

solution to what would have otherwise been an intractable nonlinear problem.

Problems are entered into LINGO in a fairly natural fashion. To illustrate, consider the

following linear programming problem:

Maximize Z= 20x+ 31y,

subject to

2x+ 5y ≤164x– 3y= 6

x ≥0, y ≥0.

The screen shot in the top half of figure below shows how this problem would be formulated

with LINGO.

The first line of this formulation is just a comment describing the model. Note that the

comment is preceded by an exclamation point and ended by a semicolon. This is a

requirement for all comments in a LINGO formulation. The second line gives the objective

function (without bothering to include the Z variable) and indicates that it is to be maximized.

Note that each multiplication needs to be indicated by an asterisk. The objective function is

ended by a semicolon, as is each of the functional constraints on the next two lines. The

nonegativity constraints are not shown in this formulation because these constraints are

automatically assumed by LINGO (If some variable x did not have a nonnegative constraint,you would need to add @FREE(x); at the end of the formulation.).

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Variables can be shown as either lowercase or uppercase, because LINGO is case-insensitive.

For example, a variable x1 can be typed in as either x1 or X1. Similarly, words can be either

lowercase or uppercase (or a combination), for clarity, we will use uppercase for all reserved

words that have a predefined meaning in LINGO.

The ‘File’ and ‘Edit’ menu items (as shown in figure above) behave in a standard Windows

fashion. To solve a model once it has been entered, click on the red ‘bullseye’ icon. (If you

are using a platform other than a Windows-based PC, instead type the GO command at the

colon prompt and press the enter key.) Before attempting to solve the model, LINGO will

first check whether your model has any syntax errors and, if so, will indicate where they

occur. Assuming no such errors, a solver will begin solving the problem, during which time a

solver status window will appear on the screen. When the solver finishes, a Solution Report

will appear on the screen. Note, you can control whether the solution report appears

automatically or not by clicking on LINGO | Options | Interface | Output Level |

Terse/Verbose.

The bottom half of the above figure shows the solution report for our example. The Value

column gives the optimal values of the decision variables. The first entry in the Slack or

Surplus column shows the corresponding value of the objective function. The next two

entries indicate the difference between the two sides of the respective constraints. The

Reduced Cost and Dual Price columns provide some sensitivity analysis information for the

problem.

2. Microsoft Office Project

Project management is a broadly practiced art and science. At its heart, project managementis a toolbox of skills and tools that help you predict and control the outcomes of endeavours

your organization undertakes. Projects (such as a film project) are distinct from ongoing

operations (such as payroll services) in that projects are temporary endeavours undertaken to

create some sort of unique deliverable or end result.

Microsoft Office Project 2003 (Professional) is one of the most frequently used tools in

project management toolbox. It helps in building project plans complete with tasks and

resources, use the extensive formatting features, organize and format the project plan details,

track actual work against the plan, and take corrective action when things get off track.

Working with Project 2003 Pro:

1. On the Windows taskbar, click the Start button. The Start menu appears.

2. On the Start menu, point to All Programs, point to Microsoft Office, and then click

Microsoft Office Project 2003.

Project Professional window appears. Your screen should look similar to the following

illustration:

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The main menu bar enables you to give instructions to Project.

Toolbars provide quick access to the most common tasks; most toolbar buttons

correspond to a menu bar command. Like other Office applications, Project

customizes the menus and toolbars for you, based on how frequently you use specific

commands or toolbar buttons. The most frequently used commands and buttons will

remain visible on the menus and toolbars, whereas the commands and buttons you

don’t use will be temporarily hidden.

The project plan window contains a view of the active project plan. The name of the

active view appears on the left edge of the view—in this case, the Gantt chart view is

displayed.

The box labelled Type a question for help enables you to quickly search Project’s

Help for instructions on performing common activities in Project. Just type in a

question and press Enter.

The Getting Started task pane in Project is similar to the task panes you might see in

other Office applications. It is a convenient list of recently opened files as well as

another means of creating new files. In the Getting Started task pane, click Create a new project . The New Project task

pane replaces the Getting Started task pane. Click on Blank project. You should see

the following window (first).

Follow the steps in the Tasks pane and input the tasks, their durations, predecessors,

and start time for the specific tasks. The Gantt chart will be displayed in the right

window.

On the Gantt chart, right click and select Gantt Chart Wizard (Alternatively, you can

select this by clicking on Format menu.). Click on Next and select ‘Critical path’ . A

sample project with 9 activities is entered and the critical path is shown in the window

(second) below:

Other features such as Resources and cost can be used to understand ‘resourcesmoothing’ and total cost of the project.

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3. ARENA Simulation Software

Arena is an easy-to-use, powerful modelling and simulation software tool that allows the user

to construct a simulation model and run experiments on the model. The software generates

several reports as a result of a simulation run.

The Arena Window

To start ARENA, follow steps as Start menu > All programs > Rockwell software > Arena

(folder) > Arena. Arena window typically looks like the following:

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There are three main regions that can be identified in the main Arena window:

• The Project Bar , located on the left side of the Arena window and below the tool bars.

The project bar contains three panels: the Basic Process panel , the Report panel , and

the Navigate panel . Every panel contains several modules that are used in

constructing simulation models.

• The Model window flowchart view, located on the right side of the Arena window and

below the tool bars. This view is actually the workspace for the simulation model. It

will contain all the model graphics: the flowchart, animation, and other drawings of

the model.

• The Model window spreadsheet view, located on the right-hand side and below the

flowchart view. The spreadsheet view shows the model data.

Arena Modules

The construction of simulation models with Arena involves using modelling shapes, called

modules, from the Basic Process panel. These modules are used as the building blocks in

constructing a simulation model. There are two types of modules on a panel:

Flowchart modules. The user places flowchart modules in the model window and connects them to form a

flowchart, which describes the logic of model. The most common flowchart modules are:

Create, Process, Decide, Dispose, Batch, Separate, Assign, and Record.

Data modules.

The user can edit these modules in the spreadsheet interface. These modules are not placed in

the model window. The most common data modules are: Resource, Queue, Variable,

Schedule, and Set.

A model is constructed in the model window flowchart view, which is the workspace of the

model. From the Project bar, the user drags the flowchart mod-ules needed into the model

flowchart and connects the modules together. To edit a flowchart module, the user either double-clicks on the module shape and fills in the form, or edits its data in the spreadsheet.

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The definition of a data module is carried out by clicking on the shape of then module in the

Project bar to activate its spreadsheet. Then the user can edit the data of the module.

Flowchart modules exist both in the model workspace and as a row in the spread-sheet. Data

modules exist only in spreadsheet view. Data modules can be added or deleted via the

spreadsheet, while flowchart modules can only be added or deleted by placing the object or removing the object from the model workspace.

Using Arena

To build a simulation model and to carry out simulation runs with Arena, a user performs the

following steps:

1. Construction of a basic model: Arena provides the model window flowchart view,

which is a flowchart-style environment for building a model. The user selects and

drags the flowchart module shapes into the model window and connects them to

define process flow of the model.2. Adding data to the model parameters: The user adds actual data (e.g., processing

times, resource demands, others) to the model. This is done by double-clicking on

module icons and adding data.

3. Performing a simulation run of the model: The user runs the simulation and examines

the results.

4. Analysis of the simulation results provided by the automatic reports of Arena. The

user can expand the statistics.

5. Modifying and enhancing the model according to the user needs.

Arena provides a family of application solution templates (ASTs) built on the Arena

simulation system.

A Simple Model of the Carwash System

Vehicles arrive into a carwash shop to get a simple wash and clean up. The Carwash system

consists of a single wash machine, which provides the actual service to the vehicles. Arriving

vehicles join a line to wait for service. The vehicle at the head of the line is the one that is

next to be serviced by the carwash machine. After the vehicle wash is completed, the vehicle

leaves the system. The vehicles are considered the customers of the system, as they are the

entities requesting service by the server (the wash machine). Figure below shows a graphical

view of the conceptual model of the Carwash system.

The objects that flow through the system are the vehicles and in Arena, these objects are

known as entities.

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The first task in building the model is to define the flowchart of the model. To start the

construction of a new model in Arena, the user activates the File menu and selects New. A

new model is given the name Model-1 by default.

From the Project bar on the left-hand side of the Arena window, the user activates the Basic

Process panel and drags the Create module into the flowchart view of the model window.Then the user drops the module shape in a convenient place, on the upper left-hand side of

the flowchart view. Figure below shows the Create module in the flowchart view of the

model window. This is the first module in constructing the model for the Carwash system.

The figure shows only part of the Arena screen.

The Create module is the source of arriving vehicles into the system. To assign value to

attributes or properties of the module, the user double-clicks on the mod-ule shape and enters

the data requested in the small dialog window, as shown in Figure below.

The name assigned to the module is Arrival of vehicles. The entity type is Vehicles. The

arrival of vehicles occurs randomly and the time between arrivals (the inter-arrival intervals)

follow the behaviour represented by an exponential probability distribution with mean value

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of 7.5 in minutes. The data for the module could also be filled in the spreadsheet view, below

the model workspace.

The other modules needed to construct this simple simulation model are: a Process module

and a Dispose module. As mentioned previously, these modules must be connected in such a

manner as to represent the flow of entities through the system.

To place the two remaining modules in the model, the user selects the Create module, which

is on the model view. The user then drags the Process module in the Basic process panel on

the project bar to the flowchart model view and places it at any location to the right of the

Create module. The two modules will automatically be connected. Now the user selects the

Process module on the model view and drags the Dispose module in the Basic process panel

on the project bar to the flowchart model view and places it at any location to the right of the

Process module.

Figure below shows the complete flowchart of the Carwash model . The second module in the

model is a Process module with assigned name Wash station. The third module is a Disposemodule with assigned name Vehicles exit .

The properties of the Process module were assigned in a similar manner as for the Create

module. The user double-clicks on the Process module and opens the dialog window of the

module. The actual values to be used are then assigned to all the properties of the module, asshown in Figure below.

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The name assigned name to the Process module is Wash station. The Action selected for the

module is Seize, Delay, Release. This means that a vehicle that arrives will wait until the

resource becomes available, it will seize the resource, it will wait for the service interval, and

then it will release the resource. The Delay is actually the processing time or the service

interval.

To specify the resource that the vehicle needs for service, the user clicks the Add button onthe Resources area of the Process module. A small Resources dialog window appears. The

resource is specified and the name assigned to it is Wash machine. Figure below shows the

Resources dialog window.

To setup the simulation runs, the user selects the Run menu and selects Setup. The dialog

window that appears is shown in Figure below. This figure shows the project title in the

Project Parameters tab.

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The Replications Parameters tab of the Run Setup dialog window is shown in Figure below.

The main parameter set is the replication Length, which is the simulation period.

To run the simulation, the user selects Go from the Run menu, or presses F5. After the

simulation runs to completion, Arena will ask the user whether he/she needs to open thereports.

The various reports produced by Arena after a simulation run can be accessed and opened

from the Reports panel in the Project bar. Arena opens the Category Overview Report by

default. Figure below shows part of the Category by Replications report.

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From this report, the average wait time of a vehicle is 2.2082 minutes. The maximum wait

time is 4.4362 minutes. The average time that a vehicle spent in the car wash shop is 2.4005

minutes. The total number of vehicles that arrived is 106 and the total number of vehicles that

were serviced is 106, the rest remained in the system.

Figure below shows part of the Resources report produced after the simulation run. Theresource (wash machine) utilization was 100%. The total number of times that the resource

was seized was 73.

Figure below shows part of the Queues report. The average time that a vehicle spent on the

queue was 2.24 minutes. The average number of vehicles waiting in the queue was 16.85.

Changing the mean inter-arrival interval to 14.5 minutes, changes the output results as shown

in Figure 2.13. The total number of vehicles serviced is 49. The average waiting time is 1.969

minutes. The resource utilization is 0:6738 or 67.38%.

The basic animation possible with Arena consists of showing with a small visual object the

arrival of an entity and its accumulation in the queue. The default picture for an entity can be

changed by editing the Entity data module.

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The other animation consists of showing visually the states of the resource, Idle and Busy. To

place a picture to indicate each state, the user edits a picture in the Resource Picture

Placement dialog by clicking the Resource button in the Animate bar, which is the second

tool bar at the top of the Arena window.

Arena provides a facility to generate or draw dynamic plots of a simulation run. To define a plot, the user clicks on the Plot button on the Animate bar and enters the data on the Plot

dialog window that appears.

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