Multi-Objective Programming and Goal Programming: Theories and Applications

364 Pages·1996·17.124 MB·English

by  Mehrdad Tamiz (auth.), Dr. Mehrdad Tamiz (eds.)

Lecture Notes in Economics
and Mathematical Systems 432
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Mehrdad Tamiz (Ed.)
Multi-Objective
Programming
and Goal Programming
Theories and Applications
Springer
Editor
Dr. Mehrdad Tamiz
University of Portsmouth
School of Mathematic Studies
Mercantile House
Hampshire Terrace
Portsmouth POI 2EG, UK
LIbrary of Congress CatalogIng-In-PublIcatIon Data
Multi-objective programming and goal programming: theories and
applications I Mehrdad Tamiz (ed.)
p. cm. -- (Lecture notes in economics and mathematical
systems ; 432)
"Papers ... presented at the first international conference in
Multi-objective programming and Goal programming theories and
applications (MOPGP94) ... held at the University of Portsmouth,
United Kingdom, from 1 to 3 June 1994"--Pref.
Includes bibliographical references.
ISBN 978-3-540-60662-8 ISBN 978-3-642-87561-8 (eBook)
DOr 10.1007/978-3-642-87561-8
1. Multiple criteria decision making--Congresses. 2. Programming
(MathematiCS)--Congresses. I. Tamiz, Mehrdad, 1958-
II. Series.
T57.95.M82 1998
519.7--dc20 95-28207
CIP
ISBN 978-3-540-60662-8
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© Springer-Verlag Berlin Heidelberg 1996
Typesetting: Camera ready by author
SPIN: 10516176 42/3142-543210 -Printed on acid-free paper
Contents
1. Introduction ......................................................... 1
M ehrdad Tamiz
Part 1: Multi-Objective Programming and
Multi-Criteria Decision Making
2. Dynamic Choices in Economics: A Compromise Approach .......... 11
Enrzque Ballestero, Carlos Romero
3. Application of Multicriteria Analysis to Ranking and Evaluation
of Water Development Projects (The Case of Jordan) ............... 25
B. AI-Kloub, T. T. Al-Shemmeri, A. D. Pearman, J. P. Brans,
B. M areschal
4. Multi-Criteria Efficiency Profiling ................................... 41
Chrzstopher Tofallis
5. Nimbus - Interactive Method for Nondifferentiable Multiobjective
Optimization Problems ............................................. 50
K aisa Mietiinen, Marko M. Makela
6. A Graphic Search Based on Active Sets for Nonlinear Convex
Multiple Objective Programming with Linear Constraints ........... 58
Rafael Caballero Fernandez, Lourdes Rey Borrego,
Franczsco Ruzz de /a Rua
7. A Sequential Network-Based Approach for the Multiobjective
Network Flow Problem with Preemptive Priorities ...... '" ......... 74
Hermznza I. Calvete, Pedro M. Mateo
8. MOLP Formulation Assistance Using LP Infeasibility Analysis ...... 87
John W. Chinneck, Wojtek Michalowski
9. Optimizing the Yield of an Extrusion Process in the Aluminum
Industry .......................................................... 107
K Masrz, A. Warburton
10. Projective and Symbolic Degeneracy-Reducing Techniques for
Multiple Objective Linear Programming ........................... 116
Jean-Michel Thizy
11. Interactive Multiple Criteria Optimization for Capital Budgeting
in a Canadian Telecommunications Company ...................... 128
Jean-Mzchel Thizy, Savvas Pzssarzdes, Surendra Rawat,
Danzel E. Lane
VI
12. The Ekeland's Principle and the Pareto f-efficiency ................ 148
G. [sac
13. Generation of Pareto Solutions By Entropy-Based Methods ........ 164
A. M. Sultan, A. B. Templeman
Part 2: Goal Programming
14. An Overview of Current Solution Methods and Modelling
Practices in Goal Programming .................................... 198
M. Tamiz, D. F. Jones
15. Goal Programming in Networks ................................... 212
Saul!. Gass
16. Solution of Nonlinear Field Problems by Goal Programming ....... 235
Kevin Y. K. Ng
17. Incorporating the Decision-Maker's Preferences in the Goal
Programming Model with Fuzzy Goal Values: A new Formulation .. 257
Jean-Marc Martel, Belaid Aouni
18. A Formulation of a Fuzzy Linear Goal Programming Problem
with Fuzzy Constraints and Fuzzy Target Values ................... 270
Arenas Parra M. Mar, Rodriguez Una M. Victorza
19. A Two Staged Goal Programming Model for Portfolio Selection .... 286
M. Tamiz, R. Hasham, D. F. Jones, B. Hesnz, E. K. Fargher
20. Application of MOP and GP to Wildlife Management (Deer).
A Case in the Mediterranean Ecosystem ........................... 300
Julio Berbel, Ricardo Zamora
21. Flight Trajectory Optimization by Goal Programming with Fuzzy
Objectives ........................................................ 309
Shinji Suzuki
22. An Application of Goal Geometric Programming to Equipment
Replacement Under Fuzziness ..................................... 331
Valentin Vitanov, Nikolai Mincoff, Tanya Vladzmirova
23. An Exploration of Linear and Goal Programming Models in the
Downstream Oil Industry ......................................... 346
M. Tamiz, S. J. Mardle, D. F. Jones
Introduction
Mehrdad Tamiz,
University of Portsmouth, UK.
This book contains a collection of some of the most important and in
teresting papers that were presented at the first international conference in
Multi-objective programming and Goal programming theories and applications
(MOPGP94). It is aimed to present some of the latest theoretical and algo
rithmic developments in the field as well as presenting a very useful selection of
application papers.
MOPGP94 was held at the University of Portsmouth, United Kingdom, from
1 to 3 June 1994. The international organising committee consisted of Professors
S. Gass, J. Ignizio, G. Mitra, C. Romero, R. Steuer, and myself (Chairman).
This conference was initiated and organised by me and some of my research
students (Miss R. Hasham, Mr D. Jones, Mr S. Mardle, and Mr K Mirrazavi)
who formed the members of the local organising committee. I am grateful for
their help in organising and running the conference. We identified the need
for such a specialised conference and believe to date that MOPGP94 was the
very first international conference solely devoted to multi-objective and goal
programming.
The main aim of MOPGP94 was, therefore, to bring together researchers and
practitioners from different disciplines of Optimisation, Operational Research,
Mathematical Programming, and Multi Criteria Decision M:aking, whose com
mon interest was in multi-objective analysis. During the conference delegates
unanimously decided that MOPGP should become a regular bi-annual event.
This book is appropriately divided into two parts: 'Multi-Objective Pro
gramming and Multi-Criteria Decision Making', and 'Goal Programming'.
Part 1: Multi-Objective Programming and
M ulti-Criteria Decision Making
Ralph Steuer presented a very interesting plenary talk on Multi-Objective pro
gramming which generated a lot of discussions amongst the delegates. Here is
a short summary of his talk.
Although most new operational research textbooks contain a chapter on pro
gramming with multiple objectives, usually little more than goal programming
2
is discussed. Typically, the concept of nondominance is not mentioned. One rea
son a more advanced treatment of multiple objective programming is avoided is
because of space. Efficient points, criterion space, the size of the non dominated
set, payoff tables, aspiration criterion vectors, quasi concave utility functions,
Tchebycheff metrics, etc. would have to be discussed. However, by carefully
crafting the presentation of these topics, standardizing notation, and exploit
ing similarities among the procedures of multiple objective programming, one
can develop a self-contained, technically rigorous, chapter-length presentation
of multiple objective programming problem.
The first paper in this part is on "Dynamic Choices in Economics: A Com
promise Approach". The authors formulate a dynamic compromise model where
criteria are state variables evolving in time. Motion equations are determined
under a few widely accepted assumptions in decision theory. This can apply
to several fields such as economics, sociology, ecology, etc. They highlight two
applications: a) the choice of consumer goods aggregates and b) the Pigovian
Coasian reparation of negative externality through a negotiation process.
The next paper is on " Application of Multicriteria Analysis to Ranking and
Evaluation of Water Development Project (The Case of Jordan). In this paper
the authors discuss the water shortage in Jordan. They formulate the prob
lem, present and quantify criteria, and obtain partial and complete ranking of
projects by applying the PROMETHEE method to rank a sample of 13 water
development projects. They present and discuss some interesting computational
results.
The next paper is on "Multi-Criteria Efficiency Profiling". Given a set of
organizational units or branches which use multiple inputs (e.g. staff, machinery,
materials, money) to generate multiple outputs, the author aims to estimate the
relative efficiency with which each input is being utilised at each branch. The
techniques presented should be of use in the public sector (e.g. education, health
etc.) as well as the private sector. The methods are applied to a benchmark data
set and the results are found to be superior to those of the widely investigated
technique of data envelopment analysis.
The next paper is on "Nimbus - Interactive Method for Nondifferentiable
Multiobjective Optimization Problems". An interactive method, NIMBUS,
for non differentiable multiobjective optimization problems is introduced. The
method starts by moving as far as possible from the starting point into a direc
tion where the values of all the objective functions improve. The decision maker
is asked to classify the objectives into five different classes and according to this
classification a new problem is formed. The resulting solutions are presented to
the decision maker to select the most desirable alternative for continuation. It
is guaranteed that only (weakly) Pareto optimal solutions are presented to the
decision maker in the selection phase. Then the objective functions are classified
at this new solution and so on. Some numerical experiments with test problems
are reported.
The next paper is on "A Graphic Search Based on Active Sets For Nonlin-
3
ear Convex Multiple Objective Programming with Linear Constraints". The
authors present an algorithm which makes possible the determination or ap
proximation of the efficient set for a nonlinear convex multiple objective pro
gramming problem with linear constraints. The algorithm is based on the idea
of the active set methods in nonlinear programming problems.
The next paper is on " A Sequential Network-Based Approach for the Mul
tiobjective Network Flow Problem with Preemptive Priorities". Network flow
optimisation is probably one of the most widespread techniques used to model
real systems. In many practical problems, where there exist multiple measures
of the quality of feasible alternatives, a multiple criteria (associated with pre
emptive priorities) network flow formulation of the problem is appropriate. A
sequential approach for obtaining an optimal solution for this class of problems
is given in this paper.
The next paper is on "MOLP Formulation Assistance Using LP Infeasibility
Analysis". The correct formulation of a large multiple objective linear program
can be very difficult. The problem formulator faces the usual difficulties posed
by single objective linear programs, such as isolating and analyzing infeasibil
ity among the constraints. In addition, MOLP problems may raise questions
about whether certain relationships should be cast as objectives or constraints,
and about how the different objectives interact and interfere with each other.
Automated or semi-automated assistance is needed to handle problems of prac
tical scale effectively. The authors demonstrate how the techniques recently
developed for the analysis of infeasible LPs can be extended to assist in the
formulation of MOLPs.
The next paper is on "Optimizing the Yield of an Extrusion Process in the
Aluminum Industry". Aluminum extrusion is a common metallurgical process
used to produce elongated components of variable lengths and uniform cross
section. The most common application of extrusion is in the application of
aluminum siding. Due to the competitive nature of the industry as well as the
variable nature of the price of aluminum, it is important to a manufacturer to
operate an efficient extrusion operation. The authors describe a multiple ob
jective model for optimising the efficiency of an aluminum extrusion operation.
The model has been successfully applied at Alcan Aluminum's Vancouver Works
where it has resulted in annual savings of over one million dollars.
The next paper is on "Projective and Symbolic Degeneracy-reducing Tech
niques for Multiple Objective Linear Programming". Multiple objective linear
programming is typically designed for iterative user assessment that can be
crucially enhanced by post-optimal analysis. Generally implemented within a
simplex algorithm, post-optimal (sensitivity) analysis is affected by degeneracy.
Alternative linear programming methods such as the projective method need
not use bases, and are therefore affected differently. Yet, their most common
approach to post-optimal analysis has been conservative, e.g. reconstructing a
basis in order to use the classical framework. A second, much less investigated
approach, is to define post-optimal analysis without bases. Even so, the new
4
methods can be affected by degeneracy, caused by numerical difficulties both in
the data representation and the solution process. Symbolic solvers can avoid
such difficulties. Viewing MOLP as disjunctive programming, related to discrete
optimization and thereby to logic programming, the constraint logic program is
selected for its symbolic treatment of algebraic constraints seamlessly embedded
in a Prolog syntax.
The next paper is on "Interactive Multiple Criteria Optimization for Capi
tal Budgeting in a Canadian Telecommunications Company". The authors de
scribe DSSORA (Decision Support System Optimal Resource Allocation) which
is an interactive system for optimal resource allocation developed to support
decisions of investment in capital intensive telecommunications projects. Each
manager makes an annual funding recommendation to the budget committee
which, through discussions and negotiations, decides what level of funding each
program will receive. An analysis of the financial and institutional imperatives,
the corporate aspirations and the decision procedures has led to the development
of DSSORA. It has been tested by several groups of managers responsible for
the management and the implementation of project portfolios with significantly
consistent results. The flexibility, user friendliness and quick time response of
DSSORA make it an effective negotiation tool in a group setting.
The next paper is on "The Ekeland's Principle and the Pareto f-efficiency".
Using a variant of Caristi's fixed point theorem in locally convex spaces. It is
well known that the Caristi's fixed point theorem is equivalent to the Ekeland's
principle. The author presents a new and interesting variant of Ekeland's prin
ciple for vector valued mappings with applications to the study of both, Pareto
efficiency and Pareto f-efficiency.
The last, but not least, paper in this part is on "Generation of Pareto So
lutions By Entropy-Based Methods". In recent years the Maximum Entropy
Principle has been used to develop radically new approaches to various classes
of optimisation problems such as those of scaler non-linear constrained optimisa
tion, vector and minimax optimisation. The authors develop two new entropy
based approaches and apply them to the problem of generating Pareto optimal
solution sets for general multi-criteria optimisation problems. The algorithms
are tested on several test problems and the solutions are reported.
Part 2: Goal Programming
In the light of the recent developments in G P (see the first paper in this part),
We believe that it is now becoming a very powerful tool for modelling and solv
ing a wide class of optimisation problems with multiple objectives. We have in
recent years identified and addressed various shortcomings in G P. Among these
are: normalisation of the objectives prior to optimisation, identifying and gen
erating pareto efficient solutions, and effective modelling of the decision maker's
preferences. These ideas as well as various solution speed up techniques are