Multiple Objective Decision Research Articles

A comparative evaluation of interactive solution methods for multiple objective decision models

This paper describes a laboratory experiment which compares the performance from the user's point of view of four different solution methods for multiple objective decision models with continuous variables. These are the method of Zionts and Wallenius, the surrogate worth tradeoff method, the method of Steuer and Choo and a simplistic ‘naive’ solution method. The users exhibited different preferences among the different solution methods with the method of Steuer and Choo favoured overall. The results highlight a need for solution methods to accommodate the decision making characteristics of the user.

A comparison of interactive multiple-objective decision making procedures

Many algorithms have been developed for the multiple objective decision making (MODM) problem. Unfortunately, there is a lack of empirical testing of these algorithms. From a managerial point of view, it is desirable to conduct a multi-model evaluation so that decision-makers can determine which method would be best in a given situation. This study compares the applicability of two computerized interactive MODM procedures: the Steuer Method and the Franz Method. Experimentation is designed to determine how effectively the two procedures arrive at a solution based upon interaction with a simulated decision-maker. Non-parametric statistical analysis is performed on the results of randomly generated problems. Both linear and nonlinear utility functions are examined. The experimentation also determines the efficiency by which the procedures derive solutions as measured by the number of iterations necessary for convergence. The results of the study recommend the use of the Steuer procedure when (1) the accuracy of the solution is the critical factor in selecting an interactive MODM algorithm, and/or (2) the objectives under consideration are of relatively equal importance to the decision maker. It is also recommended that the Franz procedure be used when (1) the number of iterations necessary for convergence is the critical factor in the algorithm selection, and/or (2) there is one main objective that the decision maker wishes to accomplish and the remaining objectives are of diminishing importance.

Multiple objective decision making on the microcomputer for production/operations management: An overview

This article presents an application of multiple objective decision making on the microcomputer for solving production/operations management (P/OM) decision problems. This article will, first, review multiple objective decision making literature in P/OM; then, the use of the microcomputer for P/OM with multiple objectives will be described.

Category-theoretic basis for social decision-making theory

The paper develops a basis for social welfare functions using mathematical general systems theory. Although research on social welfare functions has a long history, most of it has tried to devise a new condition for social welfare functions. This paper, on the contrary, views social welfare functions from a different angle, i.e. it applies to social decision-making a unified framework which the authors originally proposed for decision principles of decision-making under uncertainty or of multiple-objective decision-making. The framework claims basically that a ‘rational” decision principle should satisfy Pareto consistency and the similarity condition. Since the similarity condition requires recognition of the structural similarity explicitly among the social profiles, it naturally leads to a category-theoretic formulation of a social welfare function. Basic properties of social welfare functions are first represented in categorical terms, and then the validity of the framework is demonstrated by discussing Arrow's ‘impossible theorem” as well as Sen's ‘liberalism condition” in it. Furthermore, this categorical treatment reveals isomorphy among the ‘rational” decision principles of decision-making under uncertainty, of decision-making with multiple objectives and of social decision-making.

Integrated economic-environmental-energy policy and conflict analysis

The conventional theory of economic policy has usually taken for granted the paradigm of rational decision-making on the basis of full information. The majority of models designed for economic policy analysis presupposed rational behavior of clearly identifiable, individual decision-makers or of one (collective) decision agency. Given a set of axioms for rational actors confronted with a complex choice situation, these models for economic policy analysis were mainly normative in nature (see for instance, Harsanyi, 1979). In many cases, this traditional view of economic policy analysis (represented inter alia by unidimensional programming or a priori known utility models) was not very realistic, as important institutional and organizational aspects of decision-making were neglected, such as multilevel and multigroup processes, vote-trading, bargaining, power conflicts, impacts of informal pressure and interest groups, and strategic behavior. These shortcomings have in recent years caused the emergence of multiple objective (or multidimensional) decision analysis (Nijkamp, 1980). Multiple objective decision models take explicitly into account the existence of goal conflicts, while institutional and procedural aspects of economic planning can be included by means of interactive decision strategies (see Rietveld, 1981, and Spronk, 1981). Furthermore, in multiple objective decision analysis, usually a more modest satisficer principle instead of a strict optimizing behavior is assumed (cf. Simon, 1958), based on a compromise between different and usually conflicting objectives. In this sense the rationality paradigm receives

Risk Preferences for Gains and Losses in Multiple Objective Decision Making

Payne, Laughhunn, and Crum (Payne, J. W., D. J. Laughhunn, R. Crum. 1984. An experimental study of multiattribute risky choice. Management Sci. 30 1350–1361.) found that managers were multiattribute risk averse for gains, but multiattribute risk prone for losses, a pattern that is inconsistent with both the additive and the multiplicative multiattribute utility models. In this paper we develop the reference risk-value (RRV) model, which is simple in structure yet capable of representing the kinds of multiattribute reference effects observed by Payne et al. We also report the results of two experiments that compare the descriptive validity of the RRV model with that of the additive and multiplicative utility models. Experiment 1 involved choices between risky multiperiod cash flows; Experiment 2 choices between risky job alternatives described by change in salary and change in type of work. In Experiment 1, subjects were multiattribute risk averse for gains, but multiattribute risk neutral for losses. In Experiment 2, subjects were multiattribute risk averse for both gains and losses, but significantly more so for losses. Because both experiments produced significantly different multiattribute risk preferences for gains than losses, both favor the RRV model over the widely used additive and multiplicative models. However, because the patterns of multiattribute risk preferences for gains and losses were strikingly different in the two experiments, these results argue against any direct generalization of the “reflection effect” to a multiattribute context.

Conjoint measurement in multiple objective decision making: A new approach

A new methodology for estimating the objective function in a multiple objective mathematical programming model is presented. A decision maker is required to provide pairwise preferences, or rank orders, of a set of solutions to the multiple objective problem. Conjoint measurement is then applied to this preference information to estimate parameters of an assumed utility function. Simulation tests support the method as being mathematically tractable, while a laboratory study with human decision makers provides encouraging results for the practicality of the technique.

Multiple objective programming: An approach to planning and evaluation of agroforestry systems— Part 1: Model description and development

A conceptual framework for planning and evaluating agroforestry systems is described in this paper. The framework can accommodate the various features of agroforestry such as: (1) temporal and spatial dimensions, (2) multiple alternative uses of the land and (3) multiple and integrated production of forest and agricultural crops. The nature of agroforestry lends itself well to Multiple Objective Programming (MOP) formulation and decision making. The planning framework and MOP techniques outlined in this paper can be useful tools for the optimal allocation of land to a variety of alternative cropping systems.

Interactive multiple objective linear programming system implemented on a microcomputer

Linear programming is one of the most widely used Operations Research/Management Science techniques. Recently, multiple objective decision making has been well established as a practical approach to seek a satisfactory solution to a decision making problem. Much attention has been focused on a microcomputer as an economical management tool. In this paper we propose an interactive goal attainment method using the eigenvector algorithm for solving a multiple objective linear programming problem interactively on microcomputers. In the software package Micro-LPS based on the method proposed, we design a conversational and user-friendly system in which the user commands are involved.

Mathematical Programming for Highway Project Analysis

The development of a methodology to assist in the evaluation of alternative highway projects is described. The methodology selected is based on a multiple objective decision making approach and uses a goal programming technique as the evaluation mechanism. To examine the effectiveness of the technique, goal programming was compared to linear programming and to costbenefits analysis. Proposed improvements to the road system in the Acadian Peninsula of New Brunswick, New Brunswick, Canada were selected as the case study to demonstrate the effectiveness of the technique. Goal programming was considered to be the most suitable technique for evaluating sets of alternative highway projects with mutiple policies and objectives. The technique provides an easy method of assessing the impact of different policy structures on the selection of alternative highway improvement programs. The methodology is capable of multiyear analysis as used in programming of highway projects and accepts input from both the public and...

A Multiple objective shift allocation model

Abstract This paper is concerned with a production planning problem of allocating production items to production shifts on production lines in a multiple objective decision environment. The problem is modeled and solutions are generated using integer goal programming techniques. Objectives are formulated not only in terms of minimizing the sum of deviations from goal target levels, but also in terms of minimizing the maximum deviation. Test results indicate that the model structure and solution process utilized can provide decision makers with a good set of representative solutions in a rather complex multiple objective decision environment.

General multiple-objective decision functions and linguistically quantified statements

The concept of linguistically quantified propositions is used to develop a whole family of forms for the representation of multiple-objective decision functions.

A Goal Programming Example in Public Health Resource Allocation

A model developed to aid a state-level resource allocation process in the United States Department of Agriculture Special Supplement Food Program for Women, Infants, and Children (WIC) is presented. The model is formulated as a linear integer goal program, utilizing service levels for six categories of WIC participants as goals. The model employs a methodical, consistent approach to the allocation process, yet allows ample flexibility for consideration of state-specific issues. By allowing the user to adjust the relative importance of each goal, the model can incorporate subjective attitudes of state-level WIC administrators. This is extremely important as these attitudes are the result of the administrators' familiarity with the WIC program in their states, and the significance of input of this nature should not be neglected. An application of the model to the Indiana WIC program is presented. Sensitivity of the model to changes in the objective function weights and in the target values for the goals is explored. Although orginally developed to allocate budget increases, the model may be used in allocating budget cuts as well; this form of the model is also presented. The model can be extended hierarchically to incorporate resource allocation at the federal level. This modeling approach should be useful in all public sector programs characterized by multiple objective and hierarchical decisionmaking.

A comparative study of three methods of eliciting preference information

The study reported in this paper compared three methods of eliciting preference information from a decision maker and estimating weights with this information for use in a multiple objective decision making model. The design of the study included issues of implementing computerized interactive models vs more traditional question and answer techniques in the light of different decision models (in terms of level of complexity) and differing levels of decision maker experience. Results indicate that decision makers, regardless of prior exposure to computer terminals, are not intimidated by their use. Additionally, methods which required non-quantitative statements of preferences were preferred over techniques which requested numerical estimates of tradeoffs or marginal rates of substitution between objectives.

Multiple-objective decision analysis applied to chemical engineering

Chemical engineers are now being faced with new decisions involving multiple (and often conflicting) objectives as a result of increases in the scale and complexity of chemical plants and a re-evaluation of their performance criteria. Reliability and environmental impacts are now considered to be as important as economic efficiency, and this must be taken into account in process design, production planning and control. This paper describes methods for solving these multiple-objective optimization problems and gives an overview of the existing software. Selected applications of multiple-objective analysis are discussed—these include the design of a twin-screw extruder, the control of a film-hardening process and a production planning problem.

Quantifiers in the formulation of multiple objective decision functions

We discuss the interpretation of linguistically quantified statements using fuzzy sets. We indicate that there are two methods of interpreting these statements, the algebraic approach and the substitution approach. We then use quantified statements to express overall decision functions involving multiple objectives. These statements are of the type “A solution should satisfy many of the objectives”. Using the algebraic and substitution approach, we develop a whole family of forms for combining multiple objectives. We show that algebraic approach corresponds to situations in which we are unconcerned about the allocation of satisfaction amongst the objectives but just interested in getting much satisfaction. The substitution approach on the other hand leads to forms which are dependent upon the allocation of satisfaction between the objectives.

Conflict analysis and compromise strategies in integrated spatial systems

This paper aims at showing the potential of multiple objective analysis for analyzing conflicts in a spatial-economic-environmental system. After a brief introduction to interactive approaches to multiple objective decision models, a conceptual framework for an interregional system will be designed, while next an operational application will be given. Various empirical results of an interregional model for the Netherlands will be presented.

Fuzzy decision making with multiple objectives and discrete membership functions

A multiple objective decision making problem in which fuzzy sets are used to represent the decision maker's valuations of the objectives is addressed. A method presented by Yager is demonstrated to be inconsistent with a more general approach suggested by Baldwin & Guild. An alternative model which is consistent with the Baldwin & Guild model is presented. This model is shown to be consistent with the Standard non-fuzzy approach when the associated preferences are no longer vague.

A geometric averaging procedure for constructing supertransitive approximation to binary comparison matrices

Abstract The usefulness of encoding the fuzzy evaluations of alternatives and the importance weights of criteria, in a multiple objective decision problem through binary comparison matrices (or pairwise judgment matrices) is receiving considerable attention. The methodology for identifying the best alternative in a given decision problem involves the computation of the principal eigenvectors of the binary comparison matrices. The eigenvectors transform the fuzzy evaluations of the importance of the criteria and the ratings of the alternatives into a ratio scale. A difficulty that is often experienced in using this approach in practice, is the inconsistency of the binary evaluations. This paper proposes a simple averaging procedure to construct a supertransitive approximation to a binary comparison matrix, where inconsistency is a problem. It is further suggested that such an adjustment might be necessary to more closely reflect the inherent fuzziness of the evaluations contained in a binary comparison matrix. The procedure is illustrated by means of examples.

Regional multiple objective quantitative economic policy: a Belgian model

Already thirty years ago, L.R. Klein [10], R. Frisch [5], J. Tinbergen [16] and H. Theil [13] introduced the subject of quantitative economic policy. More recently, multiple objective decision making has been suggested for the quantitative determination of macro-economic policy. In this paper we present an application of multiple criteria interactive linear programming for policy analysis on the regional level. The multiregional economic model considered distinguishes the nine Belgian provinces and emphasizes on the interrelations between them.