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AFIT/GOR/AA/81 0-1
MADAM:MULTIPLE-ATTRIBUTE DECISION ANALYSIS MODEL
VOLUME 11
T!IFSIS w T CAFIT/GOR/AA/81D-I Wayne A. Stimpson (J> CC' T
2Lt USAFR ~~FEB 1 9 1982
AFITj,0R/AA/81 D-1
Thes is
t", MADAM:
MULTIPLE-ATTRIBUTE DECISION ANALYSIS MODEL
Volume II
by
Wayne A.. Stimpson2Lt USAFR
Prepared in partialfulfillment of 1he
requirements fer aMasters Degr' e
December 1981
Accession ForNTIS Cr ' UDTt(, TkY
School of ErgineeringAir Force Institute of TechnologyWright-Patterson Air Force Base
Ohio
Volume II
Table of Contents
List of Figures and Tables....... .... . ..... .... i
Abstract .. .. ..... ..... ..... ...... ... v
1. Introduction. .. .. .... ...... ..... ....
11. Data Structures .. .. ..... ..... ....... 2
III. Sensitivity Analysis .. .. ... ..... ........ 7
IV, Hierarchy Manipulation. .. .. .... ...... ... 9Subroutines NODIN and FIND .. .. ... ........ 9Subroutines PRETOT, PRENEX, and NEXT. .. .. .... 11Subroutine SPAN .. .. ..... ..... ..... 13Subroutine CALC .. .. ..... ..... ..... 13
V. Variable List. .. ... ...... ..... ..... 15Variables Used. .. .. .... ...... ...... 1Pseudo-variables. .. .. ..... ..... ... 18Others .. .. ... ..... ..... ....... 18C,,cs Reference Map. .. ... ...... ..... 19
VI Program Structure .. .. ..... ..... ...... 20
Program Source Code .. .. ... ..... ..... ...... 23
List of Figures and Tables
Table 1 Pseudo-array Variables ..... ............ 3
Figure I Data Fields for Node Record........... 4
Table 2 Record Content ...... ................ 4
Figure 2 The Search Process (FIND) .............. 10
Figure 3 Logic Structure for NEXT ..... .......... 12
Figure 4 Logic Flow of CALC ..... .............. 14
I
~iii
AFIT/GOR/AA/81 D-1
Abstract
The compldx multifaceted decision situations present today sugqest
the need for a timely, automated too. A~decision-maker is fof ed into
comparing alternative actions or systems .over an entire set of different
measures of merit. This effort is an on-line, real-time, compiter-based
decision aid designed to assist the decision-maker in clarifyiog prefer-
ences in a complex decision environment. It is applicable to problems
which may be represented by a hierarchy of objectives to be satisfied.
The program is MADAM: Multiple-Attribute Decision Analysis Model, and it
is written in FORTRAN V and is implemented on the CYBER 175 system. MADAM
is designed to aid the decision-maker as he or she progresses through prob-
lem formulation, parameterization, sensitvity analyses, and a decision,
including storage of all data and rationales. Deterministic problems are
analyzed through Multi-Attribute Utility Theory concepts and an additive
value function is utilized for sensitivity analysis. Pairwise preferential
independence is tested bqtween attrithutes. The sensitivity analyses in-)
cludc a cumulaive weight analysis, a re.lative weight analysis, and an
attribute level analysis. The analyses may be conducted by fixing an ob-
jective to he considered and conducting the analysis across the alternative
4 systems or actions, or conversely by fixing the alternative to be consid-
ered nd conducting the analysis across a desired set of objectives.
t he werk is divided into two volumes. Volume I is a theoretical pre-
sentation and includes a user's manual. It requires no programming ex-ipertise and may be used independently of Volume II, Vulume I is a pro-
igraiikming manual including the source code. t may not be used independently
of Volume 1.
iv
I INTRODUCTION
This manual is designed to supplement the information contained in
Volume I of this thesis. The foundamental intention to this volume is to
provide decision analysts with an elucidation of the details of MADAM in
order to better understand the program and, hence, facilitate its imple-
mentation. Future analysts may also have the desire to modify or extend
the scope of problems suitable for analysis with MADAM, and the following
information will be very useful.
MADAM is written in FORTRAN V and implemented on the CYBER 175 system.
An effort was made to keep the code as machine independent as possible,
and for those situations where this was not possible, an explicit discus-
sion concerning Iodifications pre-requisite to transporting MADAM IS pro-
vided. All references to an example problem will refer to the 2xample
illustrated in Chapter V of Volume I.
*1 w • • • • •
II DATA STRUCTURES
MADAM utilizes a random access file for storing and manipulating data.
Throughout the program are pairs ofsubroutines and functi'ons which are re-
sponsible for setting and retrieving data, This is possible because FORTRAN
V will not recognize an array variable until it is determined that no func-
tion by that name exists. Thus, for example, MADAM uses the function ARAY
(I, J) to represent a pseudo-array variable. A complete l.ist of the sub-
routine function pairs which represent psuedo-array variables is given in
Table 1. Each record of the random access file is 100 words in length.
This 100 word record is divided up in to data fields as shown in Figure 1
for the first 500 records. The remaining records have data fields as shown
in Table 2.
r NOTE***The current ability to access both real and
integer (character) data from a record is dependent
on the fact that the CYBER 175 system uses one word
for both types of information. In order to imple-
ment MADAM on a system which uses two words for real
data and one word fur integer data, it would be nec-Iessary to modify the psuedo-array variables so thatthe desired words will be accessed. This will re-
quire manipulation of the record length and storage
: (retrieval) subscripts.
Each data file (tree) constructed will require about 300 PRU for per-
manent storage.
A§ illustrated in Figure 1, each node record contains information
about the position of the node in the objective hierarchy plus any node-
2
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Tablew 1 suoara aibe
ID3
i
Node Data Word(s) Variable~s)
Node Reference Number Digit 1 IRAY (I,')
First Descendant 2 IRAY (1,2)First Crosslink 3 RAY (1,3)
Backlink 4 RAY (1,4)
Relative Weight 5 ARAY (I)Cumulative Weight 6 ARAY (1,2)
Associated Attribute 7 LABEL (1)System Values 8 to (NSYS+7) VRAY (1,J)
Comments (Rationale) (NSYS+7) to 64 -none-
Objective 65 to 80 OBJCTV (1)
to OBjCTV (16
Figure 1 Data Fields for Node Record
Information Record No,
Node Record 1 to 500
Number of Nodes (NNODES) 501
Number of Attributes (NATT) 502
Number of Systems (NSYS) 503
Null Record 504
Regression Intercepts 505
Regression Slopes 506
Sum of Squared Errors 507
Regression Form Indicators 508
System Names 509
Attribute Names 510
Null Record 511
Worst Attribute Levels 512
Best Attribute Levels 513Table 2 Record Content
44
i i
specific data. rhe positional information is provided by tile first four
words in the record. These words contain the node reference number digit,
the first descendant, the first crosslink, and tile backlink respectively.
The tode reference number digit indicates where this node is on its span.
For instance, in the sample problem, the node reference number digit of
the node with the objective: to maximize aircraft survivability, is two.
The first descendant pointer contains a number of the first child of the
given node (if any). Absence of a first child (IRAY (1,2) <.0) implies
that the given node is a data node. The first crosslink pointer contains
a number of the immediate siblings of the given node (if any). The back-
link pointer contains the number of the node which has this given node as
a first descendant or a first crosslink.
The remaining words in a node record provide the data for identifying
the node and incorporating it into the decision analysis. The fifth word
of the record (ARRAY (1,1)) contains the weight of the given node relative
to its siblings. These relative weights are normalized to a unity sum
across the span. The sixth word of a node record (ARRAY (1,2)) contains
I the cumulative weight of a given node. It is automatically calculated by
MADAM during the "folding-back" of the objective hierarchy (see subroutine
4 CALC), and it is a function of the node's relative weight and the cumulative
weight of its parent. The seventh word in a node record (LABEL (I)) con-
tains the attribute label to be associated with that node, it is relevant
only for data nodes, and is left a null field for all noJes interior to the
tree.
INOTE*I*All character data is designed around theCYBER's 10 letters/word fcrinat. In order to
implement MADAM on a system with a differert
5
1storage format, it will be necessary to scale
all input data or data structures to incorporate
a different number of characters per word.
The next set of words in a node record (VRAY (1,J)) hold the values
of the alternative systems relative to a given node. These values are
either calculated by MADAM (for an interior node) or indirectly input by
the user (for a data node). Only as many words as needed are used for
this information baseo on the number of systems. Those words between
the system vaiues and the 64th word are used to hold comments or ration-
ale concerning either the relative weighting of the children of a given
node or the input attribute levels of the alternative systems. Thus, the
amount of space for these comments is inversely proportional to the number
of alternative systems. Also, because of this structure, the number of
alternative systems is limited to 57. Finally, the objective associated
with the given node is contained in the 64th to the 80th words.
51
fi
6
III SENSITIVITY ANALYSIS
The sensitivity analyses are controlled by the routines in the pri-
mary overlay (4,0). The types of analysis handled by the program are:
relative weight analysis (RSA), cumulative weight analysis (CSA), attri-
bute level analysis (LSA), and a system analysis (SSA) based on one of
the first three types. The first three types of analysis involve deter-
mining a fixed node and conducting the appropriate analysis for all sys-
tems at that node. The last type of analysis (actually three subtypes
SSA/RSA, SSA/CSA, SSA/LSA) involves fixing the alternative system and then
conducting the appropriate analysis over a set of nodes,
The entry point of the overlay, routine SENSTV is used to determine
the main type of analysis (CSA, RSA, LSA, or SSA). For any of the first
three types or sensitivity analysis, control is shifted to routine DETNOD
which is used to fix the analysis to the desired node. Routine DETNOD also
establishes the range over which the factor (cumulative weight, relative
weight, or attribute level) is to be considered. For the last type of
analysis (SSA), control shifts to routine SYSSEN which in turn calls upon
the routines, SENVAL, SENTYP, and NODSET to establish the fixed system,
the factor to be considered, and the set of nodes over which the analysis
is to be conducted.
Regardless of the type of analysis to be performed, once the initial-
ization process (as described in the preceding paragraph), has been com-
pleted, control shifts to the routine COMPUT. This routine utilizes the
equations presented in Chapter IV (of Volume I) to generate a matrix of
overall values. Each row of this matrix corresponds to a different level
of the factor under consideration. For the CSA, RSA, and LSA, each column
7
corresponds to a different system. For the SSA, each column represents a
diffe-ent node.
IAfter the overall values have been calculated, the routines GRAPH
and TABDIS are used to display the information in a graphial or tabular
manner respectively (see Figures 4.1 through 4.4 in Volume I). At the
conclusions of the desired type of sensitivity analysis, control is turned
over to the main option selection.
iSi
I
4."
-i8
IV HIERARCHY MANIPULATION
Subroutines NODIN and FIND
These subroutines are used to allow the user to enter the tree struc-
ture at a desired node. If the desired node is not an element of the tree,
FIND will identify that node which is closest to the input node. All nodes
are referenced by their node reference number (NRN). Except for option
***MOD)***, the input of a non-validated NRN will be interpreted as an in-
dication that the user desires to exit from the option. Program control
will be return to the calling portion of MADAM. For option ***MOD*** an
invalide NRN is interpreted as a desire to introduce a new node having
the input NRN, so the appropriate branches (and dummy connecting nodes)
are constructed so as to create a vaiid environment for the input node.
Subroutine NODII. This routine allows the user to input a desired
NRN. If anything but a null string (space followed by <CR>) is entered,
this routine will call on FIND to establish the existence of a node cor-
responding to the input NRN.
Subroutine RIND. This routine implements a modified breadth-first
search of the tree to search for a node corresponding to the input NRN.
With each digit of the NRN representing a level, FIND starts with the
first digit and attempts to locate a node with the desired NRN digit by
crossing the span at that level. This process is repeated for all re-
ipaining levels (digits) of the input NRN. If a match cannot be estab-
lished at a given level, this indicates that the desired node would be
4 an added crosslink at that level. If a match is established, the next
digit iF brought up For c,'nsideration. if no more downlink path is
available (a dat node has been reached) the routine is terminated.
9)
* F 4
Figure 2 1lustrates an example of this search process.
Input NRN: 1.3.2
Iteration Result Rehadks
1 Fi'rst digit is satisfted
2 1 No Match
3 1 No Match
t 4 Second digit is satisfied
I I 13
No Match
I6 All digits satisfied soexit
Figure 2 The Search Process (FIND)
10
Subroutines PRENEX, PRETOT, and NEXT
These routines drive a depth-first search of the tree structure. SUbp
routines PRENEX and PRETOT are used to initialize the search process at a'
desired node ort at the root node respectively. Once all variables have
been initialized, subroutine NEXT performs a depth-first traversal, advant-
ing one node each time it is called.
Subroutine PRENEX. This routine elicits a NRN from the user by in-
voking NODIN. If a valid NRN is entered, the traversal will begin at the
node corresponding to the input NRN. All descendants of this input node
will be encountered in the resulting transversal.
Subroutine PRETOT. This routine initialized the variables required
by NEXT so as to run a transversal of the entire tree structure, It is
usually invoked just prior to a potential application of PRENEX, thus al-
lowing the, user to gracefully opt a tour of the entire hierarchical struc-
ture.
Subroutine NEXT. This routine tours the hierarchical structure begin-
ning at the node specified by either PRETOT or PRENEX. Since a check is
made as to the validity of the input node before any processing is done,
it 'is pcssible to exit the current option by entering a null string during
option '?RENEX. The logic implemented in NEXT 'is illustrated in Figure 3i
i I
START)
Do ne
KICONT=O)
'A ~~one ~ TR~
I a Downik i n DoTNeRTR
I-Is
ISet DownlinkTravelled GetFlag and Add Crossi ink
new Downl ink
-T{ ~Qonti nue(ICONT=l )
RETURN
Figure 3 Logic Flow for N'EXT
1?
~Subroutine SPAN
This routine allows for the input of the objective hierarchy stru;-
ture by sequentially providing nodes in a depth-first fashion. The user
inputs immediatedescendants of the current node. Subroutine CHECK is
used to establish a satisfactory set of children for the current node.
Once a satisfactory set is established the first descendant of the
current node becomes the new parent node. When a data node is reached
(no descendants are input)i the, crosslink to the current node becomes
the new parent node. If no more siblings exist, the routine will back
up one level and establish the first crosslink as the new ,parent node
(see Figure in the main thesis text).
Subroutine CALC
This routine calculates intermediate values (collapses the tree)
by implementing a modified depth-first search. The tree is examined by'
p, each path from the root node to a data rode, and the cumulative weightsare calculated. System values based on the attributes are then computed
for each node. The logic flow of CALC is provided in Figure 4. The
cumulative weight of each node is given by:
CUMWT (NODE) = CUMWT(PARENT)* RELWT(NODE)
The system value at a particular node are the products of the systemIt value at a data node and the cumulative weight of the upper nodes for
each system.
11
I
Vi+
€+ 13
Calculate CUMWT ofnode
his a NoClear Obt& 1nData Node System -0'next
Values node
~yes
For each level abovethe current node foreach alternative system,
add the product of theCUMWT at this node and-the value at this node
tthe value at theuprlevels.]
Figure 4 Logic Flow of CALC
14
V. VariablesLi st
Variables Used
The following i's a list of variables used in the program. This list
includes only important variables and does not include scratch variables,
do-loop indices, and dummy arguments. Psuedo-array variables are in the
next section.
AIN - vector of relative weights
ARRAY - used to read and write to the data file. It holds onerecord worth of information
ATTAX -maximum level oT attribute
ATTMIN - minimum level of attribute
ATTNAM name of attribute being perturbed during sensitjyityanalysis
ATTRI - name of first attribute
ATTR2 - name of second attribute
BO - intercept of linear regression (linear form)
I BOEXP - intercept of linear regression (exponential form)
BOLN - intercept of linear regression (logarithmic form)
I BOROOT intercept of linear regression (square-root form)
BOSQR - intercept of linear regression (squared form)
Bi - slope coefficient of linear regression (linear form)
81ExP - slope coefficient of linear regression (exponential form)
BILN - >lope coefficient of linear regression (logarithmic form)
BIROOT slope coefficient of linear regression (square-root form)
BISQR - slope coefficient of linear regression (squared form)
-' BAND - boundaries of indifference curve window
CMD - main option selection
'15
DELl - change in first attribute,
DEL2 - change in second attribute
ERRFLG - counts the number of consecutive errors in user entryduring main option selection
FACLVL - level of attribute
FINDST - set of IFIND for SSA
ICHECK - flag if using between-node check0 - not using checkI - using check
ICONT - flags whether or not to continue processing0 - stop1 - continue
IDATA -flags whether or not node is data node0 - interior node
1 - ddta node
FADD -flags relationship of current node to input node.~Determines how to add th input branch to the existing
f 'I branch." . ) . 2 - IFIND is parent to input node
3 - IFIND is sibling to input node
IFIND - points to toe last node of the branch contained in INNRN
INDERR - flag for PPI0- PPI holdI - PPI fails
INDX - NRN digit for IFIND
I INDXST - set of INDX for SSA
t IQUIT - flag to continue processingI1 0 - continue
1 - stop
IRRAY used to read and write to the data file. It holds onej record worth of information.
ISAVD flags whether current information is saved on data filein case of abort0 -not savedI saved
- - ISIN - record number of record currently in memory (in ARRAY orIRRAY)
16
7£" i ISYS - number of systems being considered during sensiti.vityanalysis.
ITOL, - tolerance during PPI testing
ITOTL - flags typeof tree traversal,0 - not a total tree traversal1 - traverse ,all °descendants
KIDSET - set of NCHILD -for nodes during SSA
LEVEL - vector containing branch to node, IFIND(*,1) - location of record containing node *
(*,2) - flags whether or not visited by PRETOT-PRENEX-NEXT(*,3) - used in copying
LINE - one line of data for plot
LVL - length of LEVEL vector
MATRIX - pairwise.-comparison matrix
MAXI - maximum level of first attribute
MAX2 - maximum level of second attribute
MINI - minimum level of first attribute
MIN2 - minimum level of second attribute
MTYPE - type of SSA to be done
NATT - nuiroer of attributes
NCHILD - number of children for a node
NCROSS - number of siblings on a span
NDEEP - deoth of tree (maximum number of levels)
NDIFF - number of digits in INNRN not matched by routine,,:IND
NLOUD - number of allowed nodes plus four
NLVLS - length of INNRN
NNODES - number in tree plus one (master)
NSYS - number of alternative systems
NTAPE - defines which data files is in use
tNTREE - maximum number of simultaneous data files
17
(9OBiCT-V.- objective assdc'i'ated ,with- 'pdrt-iAcular node
SENS - type of sensitivity, analysis;
SSE - sumrof squared error (linear form)
SSEEXP - sum of squared error ('exponential-fo )' .
SSELN - sum :of squared error (logarithmic form)
SSERT - sum of-squared~error (square-root form)
SSESQR - sum of squared error (squared form)
TOLER - tolerance for PPI testing
TOP - objective of parent node during between-node check
USER - user identifier
VAL - attribute levels which define data points for theindividual value function
!I WHOLD - matrix of overall value of systems during sensitivityanalysis
WMAX - maximum level of factor during sensitivity analysis
WMIN - minimum level of factor during sensitivity analysis
Psuedo-arry Variables
The following are functions which are treated as if they were array
variables (se.e Table 1).
ARAY(I,J) relative and cumulative weight of node
ATT(I,J) best/worst levels of attributes
ATTI(I) attribute names
CRAY(I) comments or rationale (subroutine)
I LRAY(I,J) node position information
) oLABEL(I) name of attribute associated with node I
' ° OBJECT(I,OBJCTV) objective at node I
PARAM(I,J) regression parameters
r n • •18
(j. SYSLBL(I) alternative system names
VRAY(I,J) system values at node I
Cross Reference Map
The listing contains a partial load map, and combined with the com-
ments within each program unit, a corss reference map of where each varY-'
able is used or modified may be generated.
1
if
t2
y
Ir19
, , VI. Proqrani Structure
MADAM is divided up into five overlays (one main, four primary)
which reduce the required field length for loading to about 60K. These
overlays are machine dependent, but they may be removed by deleting the
overlay statements, changing the program statement following each over-
lay statement to a subroutine statement (except for PROGRAM MADAM), and
changing all overlay calls to subroutine calls to the subroutine making
entry into the described overlay. Each primary overlay is designed to
operate independently of the other primary overlays. Only the main over-
lay and one primary overlay are in the user's field length at one time,
thus considerably reducing the required core memory allocation. The
following is a list of routines in MADAM in the order in which they ap-
pear in the source code.
OVERLAY (XFILE,O,O) - main overlayPROGRA14 MADAM
FUNCTION ARAY(I,J)SUBROUTINE ASET(I,J,V)FUNCTION ATT(I,,3)FUNCTION ATTI(1)SUBROUTINE ATTLBL(I,ATTRIB)SUBROUTINE ATTSET(I,ATTRIB)SUBROUTINE ATTVAL(I,J,V)SUBROUTINE COPYRSUBROUTINE CRAY()SUBROUTINE CSET(1)SUBROUTINE FINDSUBROUTINE HELPSUBROUTINE INTROFUNCTION IRAY(I,J)SUBROUTINE ISET(I ,S,M)
FUNCTION LABEL(I)i' , iSUBROUTINE LSET(I,LABELT)
V SUBROUTIC: NEXTSUBROUTINE NODINSUBROUTINE OBJECT(I,OBJCTV)
4 -SUBROUTINE OSET(IOBJCTV)FUNCTION DPRAM(IJ)
20
K. SUBROUTINE PRENEX
SUBROUTINE PRETOTSUBROUTINE PSET(I ,J,V)FUNCTION SYSLBL(I)SUBROUTINE SYSSET(I,SYSLBL)SUBROU-INE TLOADSUBROUTINE TSAVEFUNCTION VALU(X,LABEL)FUNCTION VRAY(I,J)SUBROUTINE VSET(I,K',V)FUNCTION XLEVEL(X,LABEL)
OVERLAY (XFILE,l,O) - primary overlay
PROGRAM DUMMYSUBROUTINE ADOSYSSUBROUTINE ASK(I, X1,X2,XMID)SUBROUTINE CHECKSUBROUTINE DELSYSSUBROUTINE GRAFIXSUBROUTINE INITTSUBROUTINE M4ASTERSUBROUTINE MODIFY
SUBROUTINE NEWSUBROUTINE PICTUR(INDEX)SUBROUTINE PHISUBROUTINE PRUNESUBROUTINE RDATTSUBROUTINE RDSYSLSUBROUTINE RDTTLSUBROUTINE REGRS(INDEX)SUBROUTINE SPANSUBROU2TINE STATSUBROUTINE TAPERSUBROUTIN't VALUE
OVERLAY (XFIL1,2,0) - primary overlay
PROfGRtAM WV LOADSU6ROUrINE CALLSIJIROUT INF DVIDE(NAJ))
11,1101TINE GMVEC (NCROSS , I FI ND , AI1N)SUL"ROUT INF RrivS1HBROIJT It'll RDWTFUNCTION SUM(N,A)SUBRCIITINE NVLODI(OPT)
OVERLAY (Xf-ILV,3,O) - primary overlay
PROGRAM NUMSUBROUTINE DISPLASUBROUTINE DSPLOfSUBROUTINE NEVIPGSUBROUTTIE jNUMREV
21
OVERLAY (XFILE,4,O) - primary overlay
PROGRAM SENSTV- SUBROUTINE COMPUT
SUBROUTINE DETNOD3: SUBROUTINE HEADER(I ,OBJCTV,ANSWER)jSUBROUTINE SENVALSUBROUTINE TABDIS
22
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UNCLASSIFIEDSECURITY CIASSIFICATION OF THIS PAGE (When Data Entered),
REPORT DOCUMENTATION PAGE READ INSTRUCTIONSN PBEFORE COMPLETING FORM* REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER
AFIT/GOR/AA/81D-1I OF
4. TITLE (end eubtte) TYPE OF REPORT A PERIOD COVERED
MADAM: MULTIPLE-ATTRIBUTE DECISION ANALYSIS MS ThesisMODEL
6 PERFORMING OIG. REPORT NUMBER~VOLUME 1 1"
7. AUTHOR(s) I. CONTRACT OR GRANT NUMBER(e)
Wayne A. Stimpson, 2Lt, USAF
9. PERFORMING ORGANIZATION NAME AND ADDRESS IC. PROGRAM ELEMENT, PROJECT, TASKAREA & WORK UNIT NUMEERS
Air Force Institute of Technology (AFIT/EN)Wright-Patterson AFB, OH10 45433
II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
December 198113. NUMBER OF PAGES
16414. MONITORING AGENCY NAME A ADORESS(II diffirent from Controlling Ofice) IS. SCURITY CLASS. (of thie report)
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ISe. OECLASSIFICATION/ dWN RADINGSCHEDULE
iS. DISTRIBUTION STATEMENT (of thia Report)
Approved for public release; distribution unlimited
I?. DISTRIBUTION STATEMENT (of the abstract eitered Ein Block 20, if differe t her Rept)
28 JAN 198.1S. SUPPLEMENTAnY NOTES ~(
t'1VED FOR PULI- RELEASE' AFR 190.17.FMRIC C. LYNC1 ,Major USAFDirector of Publc ALI;?.
19. KEY WORDS (Continue on reveree aid* If neceeary md Identtf) 6y bfack numbr)
Multi ple-Attri bute 7r r/ce h stiuo of Thhnd?~, (ATO}Decision Analysis " 'a- ...... ,, i, O 5i " "Computer AidPreferenceValue20. ABSTRACT (Continue on reveree side it neceeeary and Identify by Wlock numbet)
The complex multifaceted decision situations present today suggest the needfor a timely, automated tool. A decision-maker is forced into comparing alterna-tive actions or systems over an entire set of different measures of merit, Thiseffort is an on-line, real-time, computer-based decision aid designed to assistthe decision-maker in clarifying preferences in a cooplex decision environment.It is applicable to problems which may be represented by a hierarchy of objec-tives to be satisfied. The program is MADAM: Multiple-Attribute Decision Anal-ysls Model, and it is written in FORTRAN V and is implemented on the CYBER 175
FORM
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system. MADAM is designed to aid the decision-maker as he or she progressesthrough problem formulation, parameterization, sensitivity analyses, and adecision, including storage of all data and rationales. Deterministic problemsare analyzed through Multi-Attribute Utility Theory concepts and an dditivevalue function is utilized for sensitivity analysis. Pairwise prefe'Aenti'alindependence is tested between attributes. The sensitivity analysers include acumulative weight analysis, a relative weight analysis, and an attribute levelanalysis. The analyses may be conducted by fixing an objective to be consideredand conducting the analysis across the alternative systems or actions, or con-versely by fixing the alternative to be considered and conducting the analysisacross a desired set of objectives.
The work is divided into two volumes. Volume I is a theoretical presenta-tion and includes a user's manual. It requires no programming expertise andmay be used independently of Volume II. Volume II is a programming manual in-cluding the source code. It may not be used indepeadently of Volume I.
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