Management Science

Brans, J. P.; Vincke, Ph.

doi: 10.1287/mnsc.31.6.647pmid: N/A

Principles for a new family of outranking methods are given. The main aim of the proposed PROMETHEE approach is to be as easily understood as possible by the decision-maker. It is based on extensions of the notion of criterion. Six possible extensions are considered. These extensions can easily be identified by the decision-maker because the parameters to be defined (at most 2) have an economic significance. A valued outranking graph is constructed by using a preference index. Two possibilities are considered to solve the ranking problem by using this valued graph. PROMETHEE I provides a partial preorder and PROMETHEE II a total preorder on the set of the possible actions.

Krasker, William S.

doi: 10.1287/mnsc.31.6.657pmid: N/A

This paper addresses a problem faced by the producer of a commodity for which futures are traded. The producer wishes to reduce his exposure to the random fluctuations in spot prices; however, the futures markets extend out for fewer time periods than the revenue stream that he wants to hedge. The main result of the paper is that under certain conditions on the relationship between the futures prices and past spot prices, it is still possible to hedge perfectly; in other words, there exists a sequence of futures positions that entirely eliminates the risk in the present value of the producer's revenues. Under those conditions—which are necessary as well as sufficient—the paper shows explicitly the futures positions that achieve the exact hedge.

Aronson, Jay E.; Morton, Thomas E.; Thompson, Gerald L.

doi: 10.1287/mnsc.31.6.664pmid: N/A

Modelling planning problems that extend over many time periods as linear programs leads to a special structure called a “staircase” or “dynamic” linear program. In this special structure, the nonzero coefficients of the linear program appear in blocks along the “main diagonal” of the coefficient matrix. Such problems are commonly found in economic planning, structural design, agricultural planning, dynamic traffic assignment, production planning, and scheduling models. Forward algorithms provide an approach to solving these dynamic problems by solving successively longer finite horizon subproblems, terminating when a stopping rule can be invoked (or a decision horizon found). Such algorithms are available for a large number of specific models. Here we discuss the implementation and testing of a forward algorithm for solving general dynamic (staircase) linear programs. Tests reported indicate that the solution time is linear in the number of periods of the staircase problem, as compared to a quadratic or cubic relationship for standard linear programming codes. Computational decision horizons are often found, and are responsible for the good performance of the algorithm.

Kleinmuntz, Don N.

doi: 10.1287/mnsc.31.6.680pmid: N/A

Research on cognitive processes in decision making has identified heuristics that often work well but sometimes lead to serious errors. This paper presents an investigation of the performance of heuristics in a complex dynamic setting, characterized by repeated decisions with feedback. There are three components: (1) A simulated task resembling medical decision problems (diagnosis and treatment) is described. (2) Computer models of decision strategies are developed. These include models based on cognitive heuristics as well as benchmark strategies that indicate the limit of the heuristic strategies' performance. The upper benchmark is based on statistical decision theory, the lower one on random trial and error. (3) Selected task characteristics are systematically varied and their influence on performance evaluated in simulation experiments. Results indicate that task characteristics often studied in past research (e.g., symptom diagonosticity, disease base-rates) have less influence on performance relative to feedback-related aspects of the task. These dynamic characteristics are a major determinant of when heuristics perform well or badly. The results also provide insights about the costs and benefits of various cognitive heuristics. In addition, the possible contribution of this research to the design and evaluation of decision aids is considered.

Mamer, John W.; Smith, Stephen A.

doi: 10.1287/mnsc.31.6.703pmid: N/A

In this paper, we consider multi-item inventory systems that contain repair kits of spare parts and tools and may include an inventory of spare machines as well. Demands occur in the form of field repair jobs, each requiring some collection of parts and tools for completion. If any required part or tool is not in the repair kit, the repair job is “broken.” The penalty or inconvenience cost is assumed to be proportional to the number of broken jobs, regardless of the number of items short. Previous work on job completion based systems is summarized and new results for the optimal solutions are derived. A more general job completion based system is also analyzed, which allows a pool of spare machines to be used to satisfy demands which cannot be met with the repair kits. Techniques are presented for optimizing the trade-off between the inventory cost of repair kits plus spare machines and the overall level of service.

Schmidt, Charles P.; Nahmias, Steven

doi: 10.1287/mnsc.31.6.719pmid: N/A

We consider (S − 1, S) policies for a single item whose lifetime is fixed and known with certainty. Demands are generated by a stationary Poisson process and there is a positive leadtime for replenishment. We believe this study gives the only analysis for perishables with a positive order leadtime. The analysis involves the derivation of the stationary distribution of the S-dimensional stochastic process corresponding to the time elapsed since the last S orders were placed. This distribution is then used to obtain an expression for the expected cost rate of operating the system in steady state as a function of S. A computer program has been developed to compute optimal S values and expected annual costs. We report a computation for a variety of system parameters which show some of the unusual features of the problem. Finally, we show how this model can be used in the context of a problem of optimizing availability of operating equipment subject to scheduled maintenance as well as random failure.

de Kok, A. G.

doi: 10.1287/mnsc.31.6.729pmid: N/A

This paper deals with a one-product production/inventory model, where the production rate can be dynamically adjusted in order to cope with random fluctuations in demand. The inventory level is controlled by using one of two possible production rates where under each production rate the production is continually added to the inventory. The demand process for the product is described by a compound Poisson process. Also, excess demand is lost. In accordance with common practice we consider service measures as the average number of lost-sales occurrences per unit time and the fraction of demand that is lost. For a two-critical-number control rule we derive practically useful approximations for the switch-over level in order to achieve a prespecified service level. Numerical experiments reveal that the approximations are quite accurate.

Keller, L. Robin

doi: 10.1287/mnsc.31.6.738pmid: N/A

This paper reports an experimental investigation of the effects of three forms of problem representation on compliance with the Sure-Thing and Substitution Principles. The most common form of representation, written problem statements, was compared with two visual representations: decision matrices with each column proportional in size to the probability of the corresponding event and tubes containing 100 labeled balls. The proportional matrices led to fewer violations of both principles. Moreover, when subjects were trained to construct proportional matrices from written problem statements, they exhibited even fewer violations.

Lee, Hau Leung; Cohen, Morris A.

doi: 10.1287/mnsc.31.6.752pmid: N/A

In many service systems, customers interact with an agent who directs customers to specific service facilities. Each agent, as a decision maker, seeks to allocate his/her customers to the service centers so as to optimize a measure of performance based on the customers’ expected waiting time and the expected number of customers in service. In this paper, the problem of multiple agents, each optimizing his/her customer allocation decision in a stochastic service system, is analyzed as a noncooperative game. It is shown that an equilibrium point to such a game exists and sufficient conditions for which this equilibrium point is unique are also given. Finally, the relative efficiency of the multi-agent system is examined by comparing the customers’ average waiting time in the multi-agent system to the one-agent case. It is shown that, in general, the multi-agent system is not as efficient as the one-agent one in terms of customer welfare.

Chiu, Samuel S.; Berman, Oded; Larson, Richard C.

doi: 10.1287/mnsc.31.6.764pmid: N/A

This paper extends recent work on finding the stochastic queue median (SQM) on a network. The SQM is the optimal location of a single mobile server, when idle, who travels to customers in response to requests for service. Customer demands are limited to the nodes of the network and their requests for service arrive according to a time homogeneous Poisson process, independently from each node. When a service request finds the server busy with a previous customer, it is entered into an M/G/1 queue that is depleted in a first-in, first-out (FIFO) manner. The SQM is the point on the network at which the sum of mean queueing delay and mean travel time is minimized. In this paper the transportation network is restricted to be a tree. By discovering and exploiting convex properties of the objective function and related functions, an efficient finite-step algorithm is found for locating the SQM on a tree.