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In this note we consider the validity of substituting a linear goal for a fractional goal in a mathematical program and provide a simple geometric interpretation that contrasts the essential differences between the two programs. [ABSTRACT FROM AUTHOR]

Commentary is presented for the article "Remarks on the Analytic Hierarchy Process," by James S. Dyer, published in the March 1, 1990 issue of "Management Science." The author discusses the merits of various theories of decision making. He notes one in particular, the analytic hierarchy process (AHP), which is a theory of measurement designed to aid decision makers in deconstructing complex problems into multiple levels of subproblems that have a hierarchical structure. According to the author, as a theory, AHP exists independently of utility theory.

This paper is an update of a paper that five of us published in 1992. The areas of multiple criteria decision making (MCDM) and multiattribute utility theory (MAUT) continue to be active areas of management science research and application. This paper extends the history of these areas and discusses topics we believe to be important for the future of these fields. [ABSTRACT FROM AUTHOR]

Decisions under risk are often multidimensional, where the preferences of the decision maker depend on several attributes. For example, an individual might be concerned about both her level of wealth and the condition of her health. Many times the signs of successive cross-derivatives of a utility function play an important role in these models. However, there has not been a simple and intuitive interpretation for the meaning of such derivatives. The purpose of this paper is to give such an interpretation. In particular, we provide an equivalence between the signs of these cross-derivatives and individual preference within a particular class of simple lotteries. [ABSTRACT FROM AUTHOR]

This note presents a description of a time-sharing computer program written to implement a man-machine interactive algorithm for the solution of the multiple criteria problem. The interactive algorithm was suggested in a recent paper by Geoffrion, "Vector Maximal Decomposition Programming," Working Paper No. 164, Western Management Science Institute, University of California, Los Angeles, September 1970. A unique feature of this program is the man-machine dialog which obtains information from the decision-maker through a series of simple, ordinal comparisons. [ABSTRACT FROM AUTHOR]

In this paper we consider linear multiple objective programs with coefficients of the criteria given by intervals. This class of problems is of practical interest since in many instances it is difficult to determine precisely the coefficients of the objective functions. A subproblem to test if a feasible extreme point is efficient in the problem considered is obtained. A branch and bound algorithm to solve the subproblem as well as computational results are provided. Extensions are discussed. [ABSTRACT FROM AUTHOR]

Methodologies developed in the last several years allow formal inclusion of two sources of complexity in the analysis of a decision problem--uncertainty and multiple conflicting objectives. Uncertainty can be handled by assessing the decision maker's attitude towards risk in the form of a von Neumann-Morgenstern utility function. Conflicting objectives may be handled by making the utility function multidimensional. A problem that then arises is in devising assessment protocols for these multidimensional (multiattribute) functions that make efficient use of the decision maker's time and effort. Mostly, such methods have concentrated on identifying structural properties of the function, such as separability, by asking questions of a general nature about the preferences and tradeoffs of the decision maker. These methods have been applied successfully on such problems as facilities siting, selection of appropriate medical treatment, optimal pest control and the evaluation of R & D proposals. The problem addressed in this paper is that of what to do about the assessment if no useful decomposition of the utility function can be identified. One possibility is to make use of some of the properties that were most nearly satisfied and then attempt to support the resulting recommendations with a sensitivity analysis. This paper provides the analyst with an efficient, routine method of approximating the utility function to any degree of accuracy that the decision maker or the problem requires. The idea is to assess the function exactly only on a multidimensional grid and then to interpolate other values of the utility function from those on the grid. Evidently, a finer grid will, in general, provide a better approximation. The resulting utility function is continuous. It is not anticipated that many of the problems in which conflicting objectives are a factor will need this level of sophistication. But just as there are problems that require a substantial modelling effort to identify feasible consequences, so, occasionally, an analysis would benefit from an accurate modelling of the objective functions. [ABSTRACT FROM AUTHOR]

This paper defines the components and characteristics of an important class of models called weighted assignment models and identifies these elements in a number of existing and potential applications. The weighted assignment model represents problems with the following characteristics: A set of tasks must be divided among a set of agents, and each task must be completed by only one agent. Tasks may be completed at one of several predetermined levels. When an agent completes a task at some levels, a resource possessed by the agent is consumed and a system disutility is incurred. The weighted assignment model may be used to determine the best assignment of tasks to agents and the task completion levels so as to minimize total system disutility while satisfying the agent resource constraints. In the first part of the paper, a general formulation is presented, and its relationship to assignment models, transportation models, knapsack models and various fixed charge models is established. In the second part of the paper, a number of applications are described which demonstrate the usefulness of weighted assignment models. These applications include machine loading problems, personnel assignment problems and districting problems. Computational results for several of the applications are presented to document the tractability of the models. [ABSTRACT FROM AUTHOR]

In a team decision problem there are two or more decision variables, and these different decisions can be made to depend upon different aspects of the environment, or information variables, the resulting payoff being a random variable. The choice of optimal rules for selecting information variables and for making decisions is the central problem of the economic theory of teams. This paper shows, by means of an example, how linear programming can be applied to obtain optimal team decision functions in the case in which the payoff to the team is a convex polyhedral function of the decision variables. [ABSTRACT FROM AUTHOR]

Multiattribute auctions extend traditional auction settings to allow negotiation over nonprice attributes such as weight, color, and terms of delivery, in addition to price and promise to improve market efficiency in markets with configurable goods. This paper provides an iterative auction design for an important special case of the multiattribute allocation problem with special (preferential independent) additive structure on the buyer value and seller costs. Auction Additive & Discrete provides a refined design for a price-based auction in which the price feedback decomposes to an additive part with a price for each attribute and an aggregate part that appears as a price discount for each supplier. In addition, this design also has excellent information revelation properties that are validated through computational experiments. The auction terminates with an outcome of a modified Vickrey- Clarke-Groves mechanism. This paper also develops Auction NonLinear & Discrete for the more general non-linear case--a particularly simple design that solves the general multiattribute allocation problem, but requires that the auctioneer maintains prices on bundles of attribute levels. [ABSTRACT FROM AUTHOR]

This paper studies the implications of the "zero-condition" for multiattribute utility theory. The zero-condition simplifies the measurement and derivation of the Quality Adjusted Life Year (QALY) measure commonly used in medical decision analysis. For general multiattribute utility theory, no simple condition has heretofore been found to characterize multiplicatively decomposable forms. When the zero-condition is satisfied, however, such a simple condition, "standard gamble invariance," becomes available. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Procedure. In the procedure, the decision maker articulates preference information over representative samples from the nondominated set either by assigning preference "values" to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Choo 1983). The computational results indicate that the Interactive FFANN Procedure produces good solutions and is robust with regard to the neural network architecture. [ABSTRACT FROM AUTHOR]

Management science and decision science have grown exponentially since midcentury. Two closely-related fields central to this growth are multiple criteria decision making (MCDM) and multiattribute utility theory (MAUT). This paper comments on the history of MCDM and MAUT and discusses topics we believe are important in their continued development and usefulness to management science over the next decade. Our aim is to identify exciting directions and promising areas for future research. [ABSTRACT FROM AUTHOR]

This paper proposes a brand choice model to aid in the prelaunch management of a new consumer durable entry in an existing category. The model contributes to theory by integrating the critical phenomena of multiattribute preference, risk, and dynamics in an individual level expected utility framework. The integration is based on established theoretical constructs in utility, Bayesian decision analysis, and discrete choice theory. Measurement and estimation procedures are presented, an application is described, and the managerial relevance of this work as a planning and forecasting tool is examined. [ABSTRACT FROM AUTHOR]

Mathematical programming models for nutrition planning in developing nations typically involve the optimization of a single criterion function subject to resource and nutritional constraints. The nutritional constraints specify that the amount available of each nutrient for human consumption should meet or exceed some prechosen nutrient requirement level. However, fixed nutrient requirement levels are difficult to prespecify. In this paper, a bicriteria mathematical programming model is proposed which does not require planners to prespecify nutrient requirement levels for several key nutrients. Instead, the model generates an entire set of efficient nutrition plans which supply various amounts of these nutrients. To demonstrate the use and potential benefits of this model, an illustrative application to Colombia, South America is included. [ABSTRACT FROM AUTHOR]

This paper explores the nature and extent of response error when direct multiattribute utility assessment procedures are used as a basis for modeling preferences for risky multiattribute alternatives. The analysis is based on an experimental study of preferences for alternative air pollution control policies whose consequences were characterized by three value attributes: cost to consumers, level of pollution related illness, and level of pollution related mortality. The study generated the following findings: (i) direct assessments of preferences for outcomes were quite reliable and stable over a two-week time period; (ii) parameter estimates for additive utility functions fitted to direct utility assessments were both precise and stable over a two-week time period; (iii) statistically fitted additive utility models provided very accurate predictions of directly assessed preferences two weeks later (or earlier); (iv) ranking outcomes before assigning utilities to them resulted in high levels of serial correlation of errors in direct assessments; and (v) using a parameter estimation procedure that adjusted for serial correlation of errors had little effect on the accuracy of the model's predictions of preferences in a different time period. [ABSTRACT FROM AUTHOR]

This paper presents multiperiod, multiple objective goal programming as an alternative to the more conventional hedge ratio approaches to financial futures hedging. The described model offers the potential benefits off (i) simultaneous achievement of multiple hedge-related objectives (i.e., minimization of transactions and margin opportunity costs; regulation of cash flow, and maximization of profits accruing from both the cash and futures positions); and (ii) periodic modification and updating of the futures position, as suggested by actual, observed prices and interest rates, throughout the hedging period. To assess its overall effectiveness, the model was applied to develop appropriate hedging strategies for three separate time periods, each representing a unique interest rate trend (i.e., upward movement, downward movement, and no change). Since real-world implementation of the model requires the use of forecast data, independent forecasts of both cash and futures prices were generated via (1) moving average, (2) exponential smoothing, and (3) random walk techniques. In progressing through each of the 13-week time periods, all forecasts were updated with the previous weeks' actual price data. Revised forecasts and actual price data were then incorporated into the model constraints on a weekly schedule. This approach, in essence, provided weekly futures activity recommendations based on the most recent price and interest rate developments observed at any point during the hedging period. The realized gains or losses were then compared to the previously-derived "perfect foresight" model results and to the traditional hedge ratio remits. This allowed for evaluation of the model's effectiveness under varying forecast methods and varying interest rate trends. The results show that the goal programming model outperformed other strategies in most cases. [ABSTRACT FROM AUTHOR]

A precise determination of a multiattribute utility function of a decision maker or a group of decision makers requires considerable information that may not be available in many decision situations. In this paper the method HOPIE, which allows one to determine a set of utility functions consistent with the incomplete information received from the decision maker, is proposed. The method is based on holistic judgments of hypothetical alternatives defined by a certain factorial design. It requires that the evaluation of the alternatives be given on an interval scale. The method can also accommodate other types of additional information such as pairwise comparisons. [ABSTRACT FROM AUTHOR]

In this paper we study the multiple objective linear programming problem with parametric criteria coefficients. This problem is of interest since in many situations the coefficients of the objective functions of a multiple objective linear program either represent estimates of the true data or are subject to systematic variations. Properties of this problem are developed, and an algorithm for generating the set of all weakly-efficient extreme points of this problem is described. To implement this algorithm, a nonconvex subproblem must be solved for each candidate extreme point encountered. This is accomplished by applying the Generalized Benders Decomposition method. Computational results concerning the solution of these subproblems are presented. [ABSTRACT FROM AUTHOR]

This paper proposes new concepts and new results which could lead to a more realistic preference modeling than in classical decision theory. &sect2;1-3 present four fundamental situations of preferences, their combinations and the concept of relational system of preferences. In §4, a particular case of relational system of preference is studied. It is associated with the concept of pseudo-criterion derived from the classical concept of criterion by adjunction of two thresholds. Some results are given, generalizing the properties of such well-known structures as complete preorders and semiorders. &sect2;5 and 6 emphasize the possibilities given by the preceding concepts to take the imprecisions, irresolutions and incomparabilities appearing in every concrete problem where several criteria must be considered into account. [ABSTRACT FROM AUTHOR]

In this paper, oil spills occurring near shore in semienclosed waterways are viewed as emergency events. A partial set covering model, similar to those developed for firehouse location analysis, is applied to the problem of locating oil spill response equipment. The model includes both assessments of the relative probability of occurrence and the impact after occurrence of various spill types. A multiple objective approach enables the decisionmaker to evaluate strategies without confounding the probability of occurrence with the impact of occurrence. The paper discusses how the model can be used to support the decisions of emergency response planners who must subjectively solve the problem of attaining the best overall protection with existing resources while minimizing the risk of being unprepared for politically and environmentally sensitive events. The model discussed in the paper, although employed in a resource constrained mode, can also be used in a budget-constrained mode. The model is applied to the problem of locating oil spill response equipment on Long Island Sound, and implications for public policy are discussed in this context. [ABSTRACT FROM AUTHOR]

In a decision-making problem where a group will receive an uncertain payoff which must be divided among the members of the group, the ultimate payoff of interest is the vector of individual payoffs received by the members of the group. In this paper, preferences are quantified in terms of cardinal utility functions for such vectors of payoffs. These utility functions can represent preferences concerning "equitable" and "inequitable" vectors of payoffs as well as attitudes toward risk. The individual utility functions are aggregated to form a group utility function for the vector of payoffs, and this latter function is, in turn, used to generate a group utility function for the overall group payoff and a sharing rule for dividing the group payoff into individual payoffs. The resulting group decisions are Pareto optimal in utility space. Properties of the sharing rule and the group utility function are investigated for additive and multilinear group utility functions. [ABSTRACT FROM AUTHOR]

The formal practice of forecasting and planning (F&P) has risen to prominence within a few decades and now receives considerable attention from both academics and practitioners. This paper explicitly recognizes the nature of F&P as future-oriented decision making activities and, as such, their dependence upon judgmental inputs. A review of the extensive psychological literature on human judgmental abilities is provided from this perspective. It is argued that many of the numerous information processing limitations and biases revealed in this literature apply to tasks performed in F&P. In particular, the "illusion of control," accumulation of redundant information, failure to seek possible disconfirming evidence, and overconfidence in judgment are liable to induce serious errors in F&P. In addition, insufficient attention has been given to the implications of numerous studies that show that the predictive judgment of humans is frequently less accurate than that of simple quantitative models. Applied studies of F&P are also reviewed and shown to mirror many of the findings from psychology. The paper subsequently draws implications from these reviews and suggests reconceptualizing F&P through use of decision-theoretic concepts. At the organizational level this involves recognizing that F&P may perform many, often conflicting, manifest and latent functions which should be identified and evaluated through a multi-attribute utility framework. Operationally, greater use should be made of sensitivity analysis and the concept of the value of information. [ABSTRACT FROM AUTHOR]

A fire department, in order to balance equitably its resources throughout a city, must consider several often conflicting objectives, This paper describes an allocation method that avoids the difficulty of choosing an objective in advance by allowing the decision-maker to enumerate a range of criteria by varying a trade-off parameter. The method uses travel time to fires as a measure of system performance and generates allocations satisfying criteria ranging from the minimization of city-wide travel time to the equalization of average travel times in different regions. A comparison of the allocations generated by the model to the current allocation of fire companies in New York City shows that one value of the trade-off parameter produces results that correspond closely to the current allocation policy. An example of how the model can be used as a policy tool is given. [ABSTRACT FROM AUTHOR]

In this paper a man-machine interactive mathematical programming method is presented for solving the multiple criteria problem involving a single decision maker. It is assumed that all decision-relevant criteria or objective functions are concave functions to be maximized, and that the constraint set is convex. The overall utility function is assumed to be unknown explicitly to the decision maker, but is assumed to be implicitly a linear function, and more generally a concave function of the objective functions. To solve a problem involving multiple objectives the decision maker is requested to provide answers to yes and no questions regarding certain trade offs that he likes or dislikes. Convergence of the method is proved; a numerical example is presented. Tests of the method as well as an extension of the method for solving integer linear programming problems are also described. [ABSTRACT FROM AUTHOR]

There are numerous situations in management and elsewhere in which an individual decision maker chooses subsets of multiattributed items. The specification of a measure of goodness for selecting subsets may differ from one situation to the next. In this paper, a model is developed for evaluating subsets where the choice criterion is one of balance among the attributes of items in the subset chosen. A method for determining the parameters of the model from a small number of judgments on subsets using linear programming is discussed, The model is applied to the problem of evaluating subsets of television shows and of choosing the most balanced subset of shows. Several extensions of the model and potential applications are also given. [ABSTRACT FROM AUTHOR]

A critical problem, continually faced by managers in developing "effective" resource allocation plans, is that only limited partial information is available about the system under consideration on which to base these plans. This is particularly true in planning involving the limited information typically available on the relevant behavior and characteristics of large human populations. This paper develops the insight that partial information--which at first scrutiny appears to contain only severely limited information about the system--in many important cases actually contains (or stores) a great deal of the relevant total system information needed for planning (or control). This insight leads to powerful methods for retrieving the needed information about the behavior and characteristics of the total system from the information contained in the partial information data. In the present paper, we illustrate these information retrieval methods by developing and applying them to partially specified media audience exposure systems to retrieve certain critical total system information needed for media planning. More specifically, partial information on the audience of a combination of advertising media vehicles consisting of only two information quantities--the sum of the individual audiences, and the sum of the audiences of all pairs of media vehicles in the combination--is shown, in fact, to contain a significant amount of the information about the audience exposure pattern of the combination that is needed for media planning evaluation. Theory and methods are developed which retrieve, from these two quantities, operationally useful information on the unduplicated audience, the average exposure frequency, and the frequency distribution of audience exposure of the combination. The retrieval methods developed in this paper have been successfully applied to evaluating and developing "effective" media selection programs. These retrieval methods... [ABSTRACT FROM AUTHOR]

In linear programming under uncertainty the two-stage problem is handled by assuming that one chooses a first set of constrained decision variables; this is followed by observations of certain random variables after which another set of decisions must be made to adjust for any constraint violations. The objective is to optimize an expected value functional defined relative to the indicated choices. This paper shows how such problems may always be replaced with either constrained generalized medians or hypermedians in which all random elements appear only in the functional. The resulting problem is called a deterministic equivalent for the original problem since (a) the originally defined objective replaces all random variables by corresponding expected values and (b) the remaining constraints do not contain any random terms. Significant classes of cases are singled out and special attention is devoted to the structure of the constraint matrices for these purposes. Numerical examples are supplied and related to the previous literature. Other properties of these models are also examined and related to types of problems which are often of interest. For instance the hypermedian and generalized median formulations involve minimizations over absolute value terms in the functional. These, in turn, are developed for their possible pertinence in problems where minimizations are to be over the maximum of a set of functions under inequality constraints. Utilizing Moore-Penrose (generalized) inverses, other characterizations are also secured in which all relevant weights and coefficients are stated explicitly in terms of original data. [ABSTRACT FROM AUTHOR]

To remedy challenges resulting from a high number of objectives in multiobjective programming and multicriteria decision making, this paper chooses to decompose the vector objective function and characterizes the relationships between solutions for the original problem and the collection of decomposed subproblems. In particular, it is shown how solutions that are found using this decomposition approach relate to solutions found by traditional scalarization techniques. For the selection of a final solution, two interactive coordination methods are proposed that allow to find any solution for the original problem by merely solving the smaller-sized subproblems, while integrating both preferences of the decision maker and trade-off information obtained from a sensitivity analysis. A theoretical foundation for the procedures is established, and their application is illustrated for portfolio optimization and a design selection problem. [ABSTRACT FROM AUTHOR]

This paper proposes a new analytical framework to quantify and correct for scale compatibility bias in the assessment of trade-off weights in multiattribute value analysis. The procedure is demonstrated with an application to a fisheries management problem. Trade-off judgments are elicited from a group of fisheries experts with management responsibility in the Lake Erie basin. Then we use a Bayesian method to compute posterior probability distributions of attribute weights. In computing the Bayesian weights, our measurement model assumes that the weight ratios produced by each respondent's judgments are subject to random error and an unknown scale compatibility bias. Ratios are log-transformed and analyzed by a Bayesian linear model with a noninformative prior distribution. Posterior distributions are then developed for the weights and the bias. We estimate the compatibility bias for each person and, in most cases, it is found to be large and in the predicted direction, suggesting the importance of its consideration in deriving trade-off weights. In addition, the Bayesian framework is shown to be useful for quantifying the value of additional information about multiattribute weights. Finally, a simple heuristic procedure for assessing the weights appears to be effective in eliminating the bias. [ABSTRACT FROM AUTHOR]

This paper proposes a new framework for the solution of interactive multiobjective group decision-making problems with interval parameters. Its novelty stems from a learning phase where decision makers (DMs) explore the structural characteristics of the specific Multiple Criteria Decision Making (MCDM) problem. This provides important and timely feedback to the DMs. Its core consists of four indices and their relationships. The solution framework consists of three stages. In the first, each DM provides the limits of variation for each problem parameter. These are subsequently combined mb a unique interval of variation. Then, the stochastic multiobjective problem is transformed into a deterministic one. In the second stage, DMs use the four MCDM characteristics to familiarize themselves with the problem before expressing their preferences for nondominated solutions. The DMs are then guided through an interactive procedure to find their best nondorninated solutions. In the last stage, all best nondominated solutions provided by the DMs are combined using a twofold approach to find the best-compromise nondominated solution. This final choice represents the opinion of the group of DMs, Our results show that the learning phase is beneficial to DMs in judging the quality of solutions, leading to better informed decisions. [ABSTRACT FROM AUTHOR]

This paper extends the behavioral results reported in Fischer et al. (2000) by developing a model addressing preference uncertainty in multiattribute evaluation. The model is motivated by two hypotheses regarding properties of multiattribute profiles that lead to greater preference uncertainty. Our attribute conflict hypothesis predicts that greater within-alternative conflict (discrepancy among the attributes of an alternative) leads to more preference uncertainty. Our attribute extremity hypothesis predicts that greater attribute extremity (very high or low attribute values) leads to less preference uncertainty. To provide a deeper explanation of attribute conflict and extremity effects, we develop RandMAU, a family of additive (RandAUF) and multiplicative (RandMUF) random weights multiattribute utility models. In RandMAU models, preference uncertainty is represented as random variation in both the weighting parameters governing trade-offs among attributes and the curvature parameters governing single-attribute evaluations. Simulation results show that RandMUF successfully predicts both the attribute conflict and attribute extremity effects exhibited by the experimental participants in Fischer et al. (2000). It also predicts an outcome value effect on error whose form depends on the shape of single-attribute functions and on the type of multiattribute combination rule. [ABSTRACT FROM AUTHOR]

This paper investigates the accuracy of an approximation procedure for evaluating alternatives under uncertainty with multiple evaluation attributes. This approximation uses only the first two moments of the probability distributions for the alternatives, and hence it can substantially reduce the amount of information which must be collected in order to evaluate alternatives when evaluation attributes are probabistically dependent. The accuracy of the approximation is investigated by comparing results from using it with exact calculations for a variety of situations representative of those found in decision analysis practice. This investigation shows that the approximation is accurate for situations representative of many decision analysis applications. However, caution is needed in applying the approximation in some situations where it may give inaccurate results. Characteristics of cases where the approximation is less accurate are presented. [ABSTRACT FROM AUTHOR]

The purpose of this short paper is to help clarify some questions which have arisen with respect to the suitability, or even the correctness, of the way Saaty's AHP method handles criteria weights, sometimes causing the rank reversal phenomenon. The position set forth in this paper is that this undesirable effect does not, per se, invalidate that method, but it does make it necessary to identify the kind of situations in which the method is suitable. [ABSTRACT FROM AUTHOR]

This paper considers the problem of evaluating the solution quality of multi-criteria heuristics. By assuming an additive multi-attribute value structure, efficient and heuristic solutions can be translated into value measures that depend only on the relative importance assigned to the criteria of interest. Approximation errors are then defined as the value penalty incurred by approximating an efficient solution with its heuristic alternative. Results are derived which can be used to eliminate solutions that cannot represent the best available alternative among the set of efficient and heuristic solutions. For the bicriterion case, a polynomial algorithm for determining the mean and maximum relative heuristic error for a given problem instance is presented. For more general multi-criteria problems, the maximum relative approximation error can be determined by solving a series of linear programming problems. [ABSTRACT FROM AUTHOR]

Several approaches exist to illuminate and clarify public values relevant for making public policy decisions. These include surveys, indirect and direct value elicitation, focus groups and public involvement. This paper describes a new approach, called the public value forum, which combines elements of focus groups and direct multiattribute value elicitation techniques. Two public value forums were conducted with selected members of the West German public to elicit values relevant for setting long term energy policies. The purposes of conducting the value forums were to examine the feasibility of eliciting values from laypeople and combining them with factual assessments of experts, to determine the extent to which values elicited formally conflict with values elicited informally, and to assess the advantages and disadvantages of the public value forum. The results indicate that the public value forum is feasible, that the participants felt comfortable with the procedure and that they were eager to resolve inconsistencies between their intuitive judgments and the multiattribute models. There was substantial conflict between the formally and informally elicited values. However, the participants were able to resolve those conflicts in the course of the value forum, tending towards more moderate alternatives in the process. The public value forum provided useful information for the policy process and education for the participants. However, because it is expensive and time consuming, its main application may involve small samples of opinion leaders and stakeholder representatives, rather than large representative samples of the general public. [ABSTRACT FROM AUTHOR]

This paper considers a bicriterion scheduling problem where a linear combination of two objective functions is considered, with weighting factors used to represent relative importance of the two criteria, i.e., total flowtime and range of lateness. A branch-and-bound solution procedure is designed for the problem. Computational results are also reported. [ABSTRACT FROM AUTHOR]

When designing systems, managers and engineers must often balance the desire for optimality with the need for analytic tractability. When new technologies are involved the problem may be further complicated by the need to conduct local tradeoffs among risk, cost, and time factors. In order to formally deal with these issues, this paper presents a decomposition scheme in which individual subsystems may be evaluated separately and a representative set of alternatives obtained for each. In the development, a set of multiple objectives is introduced to account for the range of organizational priorities underlying the decision making proof. Pareto-optimal solutions are then found with a general purpose parametric programming algorithm and ranked with the help of the Analytic Hierarchy Process. The methodology is demonstrated with an example centering on the selection of automation options for the upcoming Space Station, but is general enough to be applicable to the design of any complex system. [ABSTRACT FROM AUTHOR]

Payne, Laughhunn, and Crum (1984) 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. [ABSTRACT FROM AUTHOR]

In multivariate decisions under risk, assessing the complete utility function can be a major obstacle. Decision rules are investigated which characterize uniformly better alternatives with respect to a whole class of utility functions. In this paper independence assumptions are imposed on the preference structure while the levels of attributes may be stochastically dependent in an arbitrary way. The utilities considered are additive, multiplicative, or multilinear. Necessary and sufficient conditions are developed for uniform decisions over utilities with common substitutional structure and where the univariate conditional utilities show qualitative properties such as risk aversion. The rules are direct extensions of known univariate rules and easy to evaluate. [ABSTRACT FROM AUTHOR]

Multiobjective mathematical programming has been one of the fastest growing areas of OR/MS during the last 15 years. This paper presents: 1. some reasons for the rapidly growing increase in interest in multiobjective mathematical programming. 2. a discussion of the advantages and disadvantages of the three general approaches (articulation of the decision maker's preference structure over the multiple objectives prior to, during, or after the optimization) towards multiobjective mathematical programming, 3. a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming, and 4. a discussion of important areas for further research. The overview concentrates on those techniques which require an articulation of the decision maker's preference structure either during or after the optimization, since these are the areas where most of the recent research has been conducted. It differs from previous overviews in that, in addition to the timing of the elicited preference information, the techniques are also classified according to the types of decision variables contained in the model (i.e., only continuous decision variables, or at least some discrete decision variables). In addition, the types of preference information (e.g., a ranking of outcomes) required of the various techniques are also discussed. [ABSTRACT FROM AUTHOR]

Some people find decision making under uncertainty difficult because they fear making the "wrong decision", wrong in the sense that the outcome of their chosen alternative proves to be worse than could have been achieved with another alternative. These people may be willing to pay a premium to avoid consequences that produce this decision regret. This paper continues an earlier investigation into the normative implications of decision regret and looks at situations where the joint probability distribution of consequences between alternatives is not specified at the time of the decision. It includes a discussion of cases where the outcomes produced by alternatives not chosen are never resolved. A consequence of this model of preferences for risky situations is that two components of risk aversion may be identified, decreasing marginal value and regret aversion. [ABSTRACT FROM AUTHOR]

A number of recent research efforts in the area of research and development planning have indicated the necessity that the R&D project selection process be viewed as a multi-criteria decision-making problem. As a result, linear 0-1 goal programming, because of its ability to encompass multiple objectives, has been employed on several occasions as a project selection model. However, in these goal programming models the relationships between resource utilization and project outcomes or between various resource utilizations have been expressed linearly when, in reality, they are often non-linear. For example, as the resources allocated to a project are increased the probability of project success will also increase but at a decreasing rate. In this paper, a non-linear integer goal programming model is described via a case example. The case example encompasses a pool of thirty researchers available for allocation to seven possible R & D projects. As such, the model consists of integer decision variables for both the number of researchers allocated, and, project selection. Researcher allocation and project selection are subject to several linear and nonlinear goal constraints. Nonlinear goal constraints are constructed that relate the probability of project success to the number of researchers assigned to a project and to expected monetary return, and, that relate the number of researchers allocated to project completion time. Linear goal constraints are developed for budget limitations, computer capacity utilization and various strict conditions placed on the model. The model selects projects and allocates researchers to projects such that a prioritized goal structure is most satisfactorily achieved. The model solution of the case example indicated the selection of five of the seven projects and the number of researchers assigned to each project. Of the nine prioritized goals, six were achieved while three were only partially achieved. [ABSTRACT FROM AUTHOR]

Several studies this past decade have examined differences between holistic and decomposed approaches to determining weights in additive utility models. Some have argued that it matters little which procedure is used, whereas others strongly favored particular methods. In this paper we address this controversy experimentally by comparing five conceptually different approaches in terms of their weights and predictive ability. The five methods are (1) multiple linear and non-linear regression analyses of ten and fifteen holistic assessments, (2) direct decomposed tradeoffs as proposed by Keeney and Raiffa [19], (3) a recent eigen-vector technique of Saaty [28] involving redundant pairwise comparisons of attributes, (4) a straightforward allocation of hundred importance points, and (5) unit weighting (i.e., equal weighting after standardizing the attributes). The decision task involved college admissions. Subjects were asked to evaluate hypothetical college applicants on the basis of verbal SAT, quantitative SAT, high-school grade point average, and a measure of extra-curricular activity. Linear as well as nonlinear attribute utility functions were used in constructing the additive models. The nonlinear functions were specified graphically by the subjects through selection from five different shapes (i.e., one per attribute). To test the predictive ability of the various models, each subject made twenty separate pairwise comparisons of alternatives (including direction and strength of preference). The prediction criteria were percentage correct predictions as well as correlations (using these twenty pairs). Seventy subjects were tested, using an (order-controlled) within-subject design, in comparing the different methods of weight determination. Monetary incentives were used to enhance motivation. In terms of findings, the methods generally differed systematically concerning the weights given to the various attributes, as well as the variances of the resulting predictions. On average, however, the methods predicted about equally well, except for unit weighting which was clearly inferior. The findings differ in this regard from the general literature. Furthermore, nonlinear models were found to be inferior to linear ones. Finally, subjects judged the methods to differ significantly in difficulty and trustworthiness, which were found to correlate inversely. The overall results raise various applied and theoretical issues, which are discussed. [ABSTRACT FROM AUTHOR]

The modeling of preferences for multiattribute alternatives has received an increased attention in marketing (consumer behavior) and management science (decision analysis). The research in the two disciplines is closely related and can be applied to predicting consumer preferences for multiattribute options. The purpose of this paper is to illustrate and discuss several preference models and measurement techniques that have been used mainly by decision analysts and which are applicable in the consumer preference judgment context. A pilot application of the measurement techniques which provides some insight on their relative predictive accuracy and on the usefulness of empirically verifying the conditions necessary for the existence of the preference models is reported, too. [ABSTRACT FROM AUTHOR]

This paper addresses the office layout problem where existing offices vary considerably as to relevant criteria and yet permanent walls make it impractical to remodel existing spaces. The major objective of this study was the equitable reassignment of 144 offices to 289 faculty and staff members in 6 academic departments with the College of Administrative Science at The Ohio State University. Since the building contains 5 floors and a wide diversity of office quality, six conflicting objectives have been recognized. In order to adequately address these multiple objectives, a large mixed-integer goal programming model was formulated. A companion interactive computer program was also developed to evaluate the performance of each solution with respect to these objectives. The goal programming model served to evaluate several layout strategies and identify the tradeoffs implicit in the problem. The interactive computer program helped translate these insights into a final compromise solution. There are two interesting findings of the study. The first one is desirability of allowing the decision makers to be in command of the solution process. This may be particularly important when several decision makers must compete for the same resources. Another finding is that a linear programming code is sufficient for this particular formulation of a mixed-integer model. Although the model contains over 1700 integer variables, a very few non-integer values were generated. This avoided the computational burden of a mixed-integer code. The model presented here has its generic roots in the so-called "assignment problems", with the added feature of recognizing multiple objectives. It is felt that with the proper modifications, the ideas presented here may well be extended to location-distribution and other types of assignment problems. These models have been applied to the layout of the College, with the final implementation having occurred during the Summer Quarter, 1978. [ABSTRACT FROM AUTHOR]

In many decision problems, the consequences of an action may impact several individuals, and the decision may be based on the preferences of those who are affected. The rule for aggregating these individual preferences is called a group preference aggregation rule. In this paper we present a theory for group preference aggregation rules based on the concept of strength of preference. This concept is operationalized by asking an individual to order differences in his strength of preference between pairs of alternatives. A preference representation function that reproduces this ordering is called a measurable value function. In general we cannot expect a measurable value function and a utility function obtained from lottery questions to bear any particular relation to each other. A group preference aggregation rule based on the measurable value functions of individuals can be used under conditions of certainty without introducing lotteries into the preference assessment procedure. In addition, it facilitates the difficult problem of making interpersonal utility comparisons. We also establish several relationships between the group preference aggregation rules based on measurable value functions and previous work based on risky utility functions. These relationships allow either one of these preference aggregation rules to be transformed into the other after obtaining only a minimal amount of information from a group member. These relationships also raise several fundamental questions about the effects of the introduction of risk on the preferences of an individual and on the preferences of a group. We offer some preliminary comments and results retarding these issue. [ABSTRACT FROM AUTHOR]

This paper describes a multiobjective decision analysis performed to assist in selecting the conductor, tower size, and number of subconductors per bundle for a proposed 765 kV transmission line. Multiobjective decision analysis is shown to provide a systematic, logical framework for handling uncertainty and multiple objectives in this problem. [ABSTRACT FROM AUTHOR]

This paper proposes and illustrates by example a decision model for a resource allocation problem in urban management--the design of service areas for police mobile units. Estimates of the performance of alternative designs are given by existing analytic models of spatially distributed emergency service systems. Using multiattribute utility theory, alternatives are evaluated according to the preferences for efficiency and equality of service of three interest groups: citizens, police, and administrators. Meaningful measures of inequality are developed and an algorithm is created for generating improved sector designs. [ABSTRACT FROM AUTHOR]

This paper describes a dynamic programming model that has been developed to determine an optimal expansion plan for the generating capacity of an electric power system. The optimization model determines the least-cost mix of capacity between hydro, nuclear, thermal and peaking turbine plants, the size of the plants to add to the system, and the timing of these additions. We show how the computational requirements of this four-state-variable, four-decision-variable problem can be substantially reduced, resulting in a computationally feasible model. The techniques developed are applicable to a large class of capital budgeting problems under uncertainty. Reference is also made to the actual application of the model and an example is presented. [ABSTRACT FROM AUTHOR]