The normative solution concepts of game theory try to provide a clear mathematical characterization of what it means to act rationally in a game where all players expect each other to act rationally. Kadane and Larkey reject the use of these normative solution concepts. Yet, this amounts to throwing away an important piece of information to the effect that the players are rational and expect each other to be rational. Even in situations where the players do not expect each other to act with complete rationality, normative game theory can help them heuristically to formulate reasonable expectations about the other players' behavior.

Most office equipment is maintained by service organizations consisting of teams of service representatives. An important problem for the service organizations is the determination of the spare parts inventory to be carried by each service representative. This note presents a model for finding the spare parts kit that has the minimum inventory investment for a specified job completion criterion. The model is shown to be equivalent to a binary knapsack problem. The model is contrasted with the model developed by Smith, Chambers and Shlifer for a similar problem.

This paper develops two distinct models for studying inventory systems with continuous production and perishable items. The perishable items have a deterministic usable life after which they must be outdated. For each of the models, analytical expressions derived from queueing theory, are found for the steady-state distribution of system inventory. Knowledge of this steady-state behavior may be used for evaluation of system performance, and for consideration of alternatives for improving system performance. Both models assume that inventory is replenished by a continuous production process. The first model, assuming continuous inventory units, has Poisson demand requests with the size of each request distributed as an exponential random variable. The second model has Poisson demand requests with all demands being for a single unit. The analysis for both models exploits the similarity of the inventory system with a single-server queueing system.

John C. Harsanyi's rejoinder to comments and replies to Kadane, J. B., P. D. Larkey. 1982. Subjective probability and the theory of games. Management Sci. 28 (2) 113–120 and Kadane, J. B., P. D. Larkey. 1982. Reply to Professor Harsanyi. Management Sci. 28 (2) 124.

This paper proposes and tests a procedure for decomposing a large scale production planning problem modeled as a mixed-integer linear program. We interpret this decomposition in the context of Hax and Meal's hierarchical framework for production planning. The procedure decomposes the production planning problem into two subproblems which correspond to the aggregate planning subproblem and a disaggregation subproblem in the Hax-Meal framework. The linking mechanism for these two subproblems is an inventory consistency relationship which is priced out by a set of Lagrange multipliers. The best values for the multipliers are found by an iterative procedure which may be interpreted as a feedback mechanism in the Hax-Meal framework. At each iteration, the procedure finds both a lower bound on the optimal value to the production planning problem and a feasible solution from which an upper bound is obtained. Our computational tests show that the best feasible solution found from this procedure is very close to optimal. For thirty-six test problems the percentage deviation from optimality never exceeds 4.4%, and the average percentage deviation is 2.2%. In addition, these best feasible solutions dominate the corresponding solutions obtained by a hierarchical procedure.

A location problem with a hierarchy of facilities and services is proposed and solved. The formulation defines a demand point to be covered for a given level of service if some member of the facility hierarchy eligible to provide that service is present within an appropriate distance. Furthermore, the absence of coverage at any one service level for a demand point is taken to imply lack of coverage in the grand measure of coverage. The problem's objective is the maximum coverage of population given specific limits on either the number of each type of facility or on the total investment that can be made in all facility types. Relaxed linear programming, supplemented by branch and bound where necessary, is used to solve the resulting integer programming problem. An application is described that uses distance and population data developed for a region of Honduras. Honduran nationals are currently being trained in the use of this and related location methodologies under a contract with the Agency for International Development. This effort is in support of work being undertaken by the Honduran National Planning Council to develop a nationwide data set of populated places in Honduras to which location methodologies will be applied.

Utility functions are an important component of normative decision analysis, in that they characterize the nature of people's risk-taking attitudes. In this paper we examine various factors that make it difficult to speak of the utility function for a given person. Similarly we show that it is questionable to pool risk-propensity data across studies (for descriptive purposes) that differ in the elicitation methods employed. The following five sources of bias or indeterminacy are hypothesized and demonstrated. First, certainty equivalence methods generally yield greater risk-seeking than probability equivalence methods. Second, the probability and outcome levels used in reference lotteries induce systematic bias. Third, combining gain and loss domains yields different utility measures than separate examinations of the two domains. Fourth, whether a risk is assumed or transferred away exerts a significant influence on people's preferences in ways counter to expected utility theory. Finally, context or framing differences strongly affect choice in a nonnormative manner. The above five factors are first discussed as essential choices to be made by the decision scientist in constructing Von Neumann-Morgenstern utility functions. Next, each is examined separately in view of existing literature, and demonstrated via experiments. The emerging picture is that basic preferences under uncertainty exhibit serious incompatibilities with traditional expected utility theory. An important implication of this paper is to commence development of a systematic theory of utility encoding which incorporates the many information processing effects that influence people's expressed risk preferences.

This paper considers the question: How should a firm allocate a resource among divisions when the productivity of the resource in each division is known only to the division manager? Obviously if the divisions (as represented by their managers) are indifferent among various allocations of the resource, the headquarters can simply request the division managers to reveal their private information on productivity knowing that the managers have no incentive to lie. The resource allocation problem can then be solved under complete (or at least symmetric) information. This aspect is a flaw in much of the recent literature on this topic, i.e., there is nothing in the models considered which makes divisions prefer one allocation over another. Thus, although in some cases elaborate allocation schemes are proposed and analyzed, they are really unnecessary. In the model we develop, a division can produce the same output with less managerial effort if it is allocated more resources, and effort is costly to the manager. We further assume that this effort is unobservable by the headquarters, so that it cannot infer divisional productivity from data on divisional output and managerial effort. Given these assumptions, we seek an optimal resource allocation process. Our results show that certain types of transfer pricing schemes are optimal. In particular, if there are no potentially binding capacity constraints on production of the resource, then an optimal process is for each division to choose a transfer price from a schedule announced by the headquarters. Division managers receive a fixed compensation minus the cost of the resource allocated to them at the chosen transfer price. Resources are allocated on the basis of the chosen transfer prices. If there is a potentially binding constraint on resource production, a somewhat more complicated, but similar, scheme is required.

Officers in police patrol cars operate in a complex stochastic environment. In addition to handling dispatcher-assigned calls for service from the public, they patrol to pose a threat of apprehension to would-be offenders and undertake certain on-site interventions to help improve general public safety. The on-site work, often highly discretionary, is called patrol-initiated activity. It includes issuing tickets for traffic violations, building checks, car checks, pedestrian checks and assisting motorists. In many cities patrol-initiated activities and calls for service consume comparable amounts of officers' time. In this paper we develop a spatially-oriented queueing-type model of a police patrol force that allows each of N patrol cars to be in one of three states: (1) busy, on a call for service; (2) busy, on a patrol-initiated activity; (3) free, on patrol. Designed for computer solution, the model yields N nonlinear equations whose unknowns are the workloads of the N patrol cars. Other performance measures of patrol can be computed easily in terms of the workloads. The incorporation of patrol-initiated activities represents an improvement over previous OR/MS models, and could result in more informed police management decisions regarding patrol beat design, workload smoothing among officers, and reduction of neighborhood-specific inequities in police accessibility. The methods of this paper are potentially applicable to other urban services, including taxi and maintenance operations.

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 (Keeney, R. L., H. Raiffa. 1977. Decisions with Multiple Objectives. Wiley, New York.), (3) a recent eigen-vector technique of Saaty (Saaty, T. L. 1977. A scaling method for priorities in hierarchical structures. J. Math. Psych. 15 (3) 234–281.) 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.