Essays and Surveys on Multiple Criteria Decision Making: Proceedings of the Fifth International Conference on Multiple Criteria Decision Making, Mons, Belgium, August 9–13, 1982

450 Pages·1983·9.718 MB·English

by  Samuel E. Bodily, Chelsea C. White (auth.), Prof. Dr. Pierre Hansen (eds.)

Lectu re Notes
in Economics and
Mathematical Systems
Managing Editors: M. Beckmann and W. Krelle
209
Essays and Surveys
on Multiple Criteria
Decision Making
Proceedings of the Fifth International Conference
on Multiple Criteria Decision Making
Mons, Belgium, August 9 -13,1982
Edited by Pierre Hansen
Spri nger-Verlag
Berlin Heidelberg New York 1983
Editorial Board
H. Albach A. V. Balakrishnan M. Beckmann (Managing Editor)
p. Ohrymes, J. Green W. Hildenbrand W. Krelle (Managing Editor)
H. P. KOnzi K. Ritter R. Sato U. Schittko P. SchOnfeld R. Selten
Managing Editors
Prof. Dr. M. Beckmann
Brown University
Providence, RI 02912, USA
Prof. Dr. W. Krelle
Institut fOr Gesellschafts-und Wirtschaftswissenschaften
der Universitat Bonn
Adenauerallee 24-42, 0-5300 Bonn, FRG
Editor
Prof. Dr. Pierre Hansen
Faculte Universitaire Catholique de Mons
Faculte de Sciences Economiques Appliquees
Chaussee de Binche, 151, B-7000 Mons, Belgium
and Institut d'Economie Scientifique et de Gestion, Lille, France
Sponsored by:
Faculte Universitaire Catholique de Mons
Fonds National de la Recherche Scientifique
Ministere de l'Education Nationale et de la Culture Franc;:aise
College Interuniversitaire d'Etudes Ooctorales en Management
European Institute for Advanced Studies in Management
European Research Office of the U.S. Army
Municipalite de Mons
ISBN-13: 978-3-540-11991-3 e-ISBN-13: 978-3-642-46473-7
001: 10.1007/978-3-642-46473-7
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© by Springer-Verlag Berlin Heidelberg 1983
Softcover reprint of the hardcover 1s t edition 1983
2142/3140-543210
PREFACE
The Fifth International Conference on Multiple Criteria
Decision Making, not suprisingly, had several objectives. First, it aimed at beinq
a forum for exchange and intensive discussion of recent ideas on theory and practice
of MCDM, following the now well-established tradition of the previous meetings in the
series, organized by H. Thiriez and S. Zionts in Jouy-en-Josas (1975), S. Zionts in
Buffalo (1977), G. Fandel and T. Gal in Hagen/Konigswinter (1979) and J. Morse in
Newark (1980). Second, closer contacts Nere desired between participants in these
meetings and other active groups in the field, prominent among which is the European
Working Group on Multiple Criteria Decision Aid. Third, participation of senior or
junior researchers who had recently developped important new methodolo0ies, such as
the Analytical Hierarchy Process, was actively sought for. Fourth, a synthesis of
the rapidly expanding field of MCDM was to be made through selective surveys by
leading researchers in the various areas it comprises. Fifth, cross-fertilization
and multidisciplinary research was to be encouraged through presentations on the
connections between MCDM and mathematics, economics, game theory, computer science
and other subjects. Sixth, much emphasis was to be given to real-world applications
of MCDM, particularly large scale ones and/or pioneering work in new fields.
The present volume reflects the general agreement observed among
participants that these goals were largely attained. Fifty papers were presented at
the meeting and many discussions were so animated that they continued during lunch
time and evenings. The pleasant and stimulating atmosphere was not even hindered by
the weather which chose to be bad during sessions and sunny during social events.
The conference could not have been organized without the substantial help
of our sponsors, to which warm thanks are due: the Faculte Universitaire Catholique
de Mo~s, host institution, for providing facilities and rooms, the Fonds National
BeIge de Ia Recherche Scientifique, the Ministere de l'Education Nationale et de La
Culture Fran~aise, the College Interuniversitaire d'Etudes Doctorales en Management,
the European Institute for Advanced Studies in Management, the European Research
Office of the u.S. ATIny for their financial support, and the ~~nicipality of Mons
for receiving the participants in the historic Town Hall.
The Vice-Dean A. Bultez welcomed the participants and took a constant in
terest in the meeting. The practical organization was done by the FUCAt1 staff; the
gracious help of A. Segond, D. Raulier and Y. 14illame, and the cheerful readiness of
P. Lietard allowed to manage smoothly all problems and are remembered gratefully.
Finally, the success of the meeting was due to the participants, who carefully nre
pared papers, presentations and discussions, chaired sessions, expressed their vieNS,
IV
criticism and responses and revised their papers for publication. They all deserve
warm thanks for their so active participation. The list of participants is given
on page 431, the program of the meeting on page 437. The table of contents is on
the next page, papers being ordered alphabetically by name of first author.
Pierre Hansen
1~ons, November 1982.
TABLE OF CONTENTS
BODILY. S.E. and C.C. WHITE:
"Optimal Consumption and Portfolio Strategies in a Continuous-Time Model
with Summary-Dependent Preferences" 1
BOGARDY. I. and A. BARDOSSY :
"Application of MCDM to Geological Exploration Planning" 8
COHON.J.L. and T. W. EAGLES:
"Analysis of Nuclear Reactor Siting Policy Using t·lultiobjecti \Ie 19
Programming"
CRAMA. Y. and P. HANSEN
"An Introduction to the ELECTRE Research Programme" 31
DUESING. E.C. :
"Mul tiobjecti ve Li near Programming and the Theory of the Fi rm
1. Substitution and Sensitivity Analysis" 43
GERSHON. M. and L. DUCKSTEIN :
"An Allgorithm for Choosing of a Multiobjective Technique" 53
FARQUHAR. P.H. :
"Research Directions in Multiattribute Utility Analysis" 63
FRIESZ. T.L. and P.T. HARKER:
"Multi-Objective Design of Transportation Networks: The Case of
Spatial Price Equilibrium" 86
GAL. T :
"nn Efficient Sets in Vector Maximum Problems - A Brief Survey" 94
GOLABI. K. :
"A Markov Decision Modelling Approach to a Multi-Objective
Maintenance Problem" 115
GRAUER. M. :
"Reference Point Optimization - The Nonlinear Case" 126
HABENICHT. H. :
"Quad Trees. A Datastructure for Discrete Vector Optimization Problems" 136
HINLOOPEN. E. • P. NIJKAMP and P. RIETVELD:
"The Regime Method : A New Multicriteria Technique" 146
HO. J.K. :
"Multiple Criteria Optimization Using Analytic Hierarchies and
Holistic Preferences 156
HOLIN.S. and M. PREVOT :
"An Application of the Multiobjective Programming to French Industry" 167
JAHN. J. :
"Mathematical Applications of MCDM : Vector Approximation and
Cooperative Differential Games" 177
KHAIRULLAH. Z. and D. KHAIRULLAH :
"Importance of Characteristics of Graduating Seniors with Respect
to Positions in Public Accounting" 187
VI
KORHONEN, P. and J. WALLENIUS :
"Principles of Solving Sequential Multiple Criteria Decision Problems" 195
KORNBLUTH, J.S.H. :
"Max-Min Programming with Linear Fractional Functions : Algorithms
and Examples" 204
KWON, Y.K. and P.L. YU :
"Confl ict Dissolution by Reframing Game Payoffs: Introduction" 214
LEHERT, P. and A. DE WASCH :
"Representation of Best Buys for a Heterogeneous population" 221
LAWRENCE, K.D., LAWRENCE, S.M. and R.A. MAROSE :
"A Multiple Goal Portfolio Analysis Model for the Selection of
MIS Projects" 229
LEE, S.M., SNYDER, C. and M. GEN :
"The Microcomputer: Experience and Implications for the Future
of Multiple Criteria Decision Making" 238
LOCKETT, A.G. and B. HETHERINGTON
"Subjective Data and MCDM" 247
MICHALOWSKI, W. and Z. ZOLKIEWSKI
"An Interactive Approach to the Solution of a Linear Production
Planning Problem with Multiple Objectives" 260
MORSE, J.N. :
"Banking in a Volatile World: Setting Country Lending Limits" 269
NAKAYAMA, H., TAKEGUCHI, T. and M. SANO :
"Interactive Graphics for Portfolio Selection" 280
NARULA, S.C. and A.D. NWOSU :
"Two-Level Hierarchical Programming Problem" 290
NYKOWSKI, I. and Z. ZOLKIEWSKI :
"On Some Connectioris between Bicriteria and Fractional Programming
Prob 1e ms" 300
REEVES, G.R. and L.S. FRANZ:
"A Simpl ified Approach to Interactive MOLP" 310
RIOS-GARCIA, S. and S. RIOS-INSUA :
"Portfol io Selection Problem with Multiattributes and Multiple
Criteria" 317
SAATY, T. L. :
"Priority Setting in Complex Problems" 326
SARIN, R.K. :
"Measurable Value Function Theory: Survey and Open Problems" 337
SERAFINI, P. :
"Convergence of Dual Variables in Interactive Vector Optimization" 347
VII
SPRONK, J. and F. VEENEKLAAS :
"Scenarios for Economic Development: A Feasibility Study by
Means of Interactive Multiple Goal Programming" 356
TELGEN, J. :
"An MCDM Problem in Banking" 372
WEBER M.O. :
"An Empirical Investigation on Multi-Attribute-Decision-Making" 379
WENDELL, R. E. :
"Efficiency and Solution Approaches to Bi-Objective Mathematical
Programs" l39
WHITE, C.C. and H.K. EL DEIB
"Multi-Stage Decisionmaking with Imprecise Utilities" 400
WHITE, D.J. :
"The Foundations of Multi-Objective Interacti ve Programming -
Some Questions" 406
ZIONTS, S. :
"A Report on a Project on Multiple Criteria Decision Making, 1982" 416
List of Participants 431
Conference program 437
OPTIMAL CONSUMPTION AND PORTFOLIO STRATEGIES IN A CONTINUOUS
TIME MODEL WITH SUMMARY-DEPENDENT PREFERENCES
Samuel E. Bodily
Darden Graduate School of Business Administration
and
Chelsea C. White
Department of Engineering Science and Systems
University of Virginia
ABSTRACT
A preference model wherein current wealth and a summary
description of past consumption condition preferences for future
consumption is used to develop relationships between optimal
consumption and portfolio strategies. Financial variables are
described by a continuous-time, continuous-state, stochastic process.
The results complement and extend results of previous models.
I. INTRODUCTION
Optimal consumption and portfolio mixture strategies are derived in this note
for a continuous-time, continuous-state preference model. In this model current
wealth and a summary descriptor of past consumption condition the investor's
preferences for future consumption. Our model generalizes the models in previous
work where the investor maximized the expectation of discounted utility of
consumption [3,7J, the expectation of a utility of consumption that depends on
time plus a bequest [2J, or the expectation of continuous-time analogs of an
additive or a multiplicative multiperiod utility of consumption [4J.
The investor's decisions are based on two separate considerations:
1. Investment dynamics - the investment opportunities and wealth to be
invested now and their evolution in the future.
2. Consumption preferences - the relative desirability of alternative
streams of consumption including the way in which they depend on the
wealth path.
This note begins by stating our models of these two aspects of the problem. Then
results are given relating optimal investment and consumption.
2
II. INVESTMENT DYNAMICS
At each time t in [O,t*] the investor selects a consumption rate c(t) and a
portfolio mixture x(t) indicating the fraction (O~x(t)~l) of available wealth
invested in a risky versus a risk-free investment. (The risk-free investment may
be, for example, a treasury bill and the risky investment an index fund for
Standard and Poors 500 stocks.)
Let w(t) and s(t) respectively represent the level of wealth and the level of
a summary descriptor of past consumption at time t. Assume these state variables
are generated by the stochastic differential equations
dw(t) = w(t) [x(t) (r-rf)+rf]dt-c(t)dt+w(t)x(t)de(t) (la)
ds(t) = g[s(t),c(t)]dt (lb)
where:
g[.,.] = a (sufficiently smooth) function relating the
effect of the present summary descriptor value
and presently selected consumption rate to the
rate of change of the summary descriptor value,
r = expected rate of return on the risky asset,
rf = rate of return on the sure asset,
e(t) = a Wiener process with de(t)-N(0,u2dt).
Definitions, references, and related discussions concerned with Ito and Weiner
processes ((la) generates an Ito process) can be found in [2]. Note that all of
the randomness in the wealth process is represented by the process [e(t), t~O].
An admissible strategy is a decision rule which selects the pair [c(t),x(t)]
on the basis of the triple [t,w(t),s(t)] for all t in the planning horizon [O,t*];
that is, it is assumed that throughout the planning horizon the investor/decision
maker selects the rate of consumption and fraction of risky investment at time t
knowing the current values of the level of wealth and summary descriptor.
The investment/consumption decisions would ideally be based on the future
needs and the likelihoods of future levels of wealth. The investor evaluates any
sequence of decisions, however, ultimately through enjoyment of the consumption
stream, as represented by his subjective utility of consumption.
III. SUMMARY-DEPENDENT PREFERENCES FOR CONSUMPTION
We assume that preferences are expressed by a von Neumann-Morgenstern utility
function u[t,t(t)] where t(t) = [c(e): e>t]. Hence, uncertain consumption
streams are ranked cardinally by their expected utility.
Previous continuous-time models have employed simplistic forms of u[t,~(t)]
such as the following:
t*
1. continuously discounted utility, J" t e-peu[c(e)]de, [3,7]
3
I t*
2. time-dependent utility, t u[e,c(e)]de [2]
3. continuous-time analogs of additive or multiplicative utility [4],
t*
a) It ae u[c(e)]de (additive)
b) -exp -8 {I!*u[c(e)]de} (multiplicative).
where the rate for discounting utility, at represents the weight on utility
p=
at time t and 8 is a parameter analagous to the interaction terms in a
multiplicative model (see [4] for an interpretation of these last two parameters).
Each of these utility forms ignores fundamental behavioral properties of most
individuals. They require, for example, that the investor has a steady enjoyment
of consumption which is unaffected by fortuitous surges in wealth or by the level
of past consumption. The model of preferences we adopt, however, allows the
investor's attitude about future consumption to depend on current wealth and past
consumption. The investor will generally not need to know the full detail of past
consumption in order to adjust his consumption to the "life-style to which he has
become accustomed"; the summary descriptor s(t) defined in the previous section
will suffice. The function g[s(t),c(t)] used to update this summary descriptor
will insure that if preferences regarding future consumption are equivalent for
two different histories of consumption prior to t, then the summary descriptor of
these two histories will be equal. (See [5] for models of summary-dependent
preferences where there is a summary descriptor of both the past and the future.)
We denote the instantaneous utility gain from consumption at time t by
a[c(t)lw(t),s(t)] which expresses the conditioning of consumption preferences on
the state of wealth and summary descriptor. A desirable property of the utility
function is that decisions made at t are consistent with decisions made at t+6t;
then u[t,t(t)] must be a positive linear transformation of U[t+6t,C(t+6t)], i.e.
u[t,t(t)] = a[c(t)lw(t),S(t)]6t + (1+b[c(t)lw(t),S(t)]6t)-lu[t+6t,~(t+6t)] (2)
where (1+b[c(t)lw(t),S(t)]6t}-1~O. Here b6t is the rate of discount which
relates utility for future consumption beginning at time t + 6t to utility for
future consumption beginning at t. Note that the consumption stream t(t) is
longer tnan th~2~onsumption stream t(t+6t); hence u[t,t(t)]>U[t+6t,t(t+6t)].
KeWrltlng \ } glVes -
U[t+6t,t(t+6t)] - u[t,c(t)] = u[t,t(t)]b[c(t)lw(t),S(t)]6t-a[c(t)lw(t),S(t)]6t
- a[c(t)lw(t),s(t)]b[c(t)lw(t),S(t)]6t2•
Dividing through by 6t and taking the limit as results in the following
6t~O
differential equation
Ii = bu - a. (3)