This paper examines the effects of hospital closures on geographical access by potential patients, using data from four southeastern U.S. states. Using optimization models designed to minimize the adverse effects of hospital closures, extensive computations are performed and the results are discussed. The effects of the closures on the rural areas is also investigated. Finally, the paper determines which hospitals are most likely among those to be closed assuming that up to 10% of the existing hospitals in each of the four states were to be shut down. The overall conclusion of the empirical findings is that while differences exist among the states, efficiency, coverage, and equality measures for geographical access do not suffer significantly if only a few hospitals are closed in each state, provided these closures are done optimally to minimize impact. Further, for efficiency objectives, decision makers can follow a sequential strategy for closures and still be guaranteed optimality. The paper also discusses the effects of hospital closures on equity and it examines whether or not rural areas are disproportionately affected by closures.

This concept paper investigates possibilities to detect terrorist cells based on communications between individuals without the need for wiretapping. The advantages of such procedure are apparent: fewer (if any) legal requirements, and, most importantly, the possibility to automate the surveillance. After a brief review of the pertinent literature, we offer three approaches that are designed to aid in the detection of not only terrorist cells, but also the command structures within the cells. The techniques are demonstrated by using a small illustration. The paper concludes by outlining limitations of the procedures described here.

This paper examines the efficiency and equality in geographic accessibility provided by hospitals. We use the criteria efficiency, availability of the service, and equality. Quantitative measures are defined for all criteria, and are measured using a geographical information system. We then compare existing locations with optimal locations satisfying two objectives, one that minimizes hospital–patient distance, and another that captures as many patients as possible within a pre-specified time or distance. The results of our study indicate that the existing locations provide near-optimal geographic access to health care. Some potential for improvement is indicated.

This paper addresses the current gap in the literature on quantitative tools that enable a manager to build schedules which incorporate job rotation by employees. This is done within the framework of the well-known Assignment Model recast in a multi-period setting. In addition to the usual objective of minimizing the total cost of assignment, we also consider a requirement to minimize the boredom felt by employees due to continued repetition of the same task over consecutive periods. Depending on alternative definitions of 'boredom', different bi-objective optimization models are formulated and solved using polynomial time algorithms or simple heuristics. In the case of heuristics, their implementation is discussed and computational experience is also reported.

In this paper, we study a budget constrained location problem in which we simultaneously consider opening some new facilities and closing some existing facilities. Motivations for this problem stem from applications where, due to a change in the distribution of customer demand, the existing facility system no longer provides adequate service. The objective is to minimize the total weighted travel distance for customers subject to a constraint on the budget for opening and/or closing facilities and a constraint on the total number of open facilities desired. For this problem, we develop a mathematical programming model and examine its theoretical properties. We then develop three heuristic algorithms (greedy interchange, tabu search and Lagrangian relaxation approximation) for this NP-hard problem. Computational testing of these algorithms includes an analysis of the sensitivity of the solution to the budget and the desired number of facilities. The intended application in this testing is that of locating/relocating bank branches in a large-size town such as in our data set from Amherst, New York. We also discuss the situation where operating costs are part of the objective function.

This paper develops two heuristics for solving the centroid problem on a plane with discrete demand points. The methods are based on the alternating step well known in location methods. Extensive computational testing with the heuristics reveals that they converge rapidly, giving good solutions to problems that are up to twice as large as those reported in the literature. The testing also provides some managerial insight into the problem and its solution.

This paper considers the problem of selecting the most economical target mean and variance for a continuous production process, In earlier studies, many authors considered the problem of finding an optimal target mean assuming that the variance is known. The problem with this assumption is the difficulty or impossibility of setting a target variance. Taguchi suggested a two-step procedure: first, set the target mean; then, find the smallest variance through redesign or experiment (resetting the level of factors). In this study, three new approaches are suggested for the economic selection of a target variance integrated with a target mean. In the first approach, an expected profit maximization criterion is used to obtain the target mean and variance simultaneously. The example used to illustrate this approach is a filling process where the quality characteristic is assumed to be normally distributed. The containers that are underfilled can be sold in a secondary market at a price of $P-L per can, those within specification can be sold at a price of $P-0 per can, and those over the upper specification limit can be sold at a price of $P-U per can. In the second approach, a minimum cost criterion based on the Taguchi loss function is used: first, the processes optimized for the variance; then, an optimal process mean is obtained. In the third approach, an economic model for the selection of the target variance is developed, using both customer and producer costs to minimize societal loss independent of the product quality characteristic distribution.

This paper seeks to evaluate the performance of genetic algorithms (GA) as an alternative procedure for generating optimal or near-optimal solutions for location problems. The specific problems considered are the uncapacitated and capacitated fixed charge problems, the maximum covering problem, and competitive location models. We compare the performance of the GA-based heuristics developed against well-known heuristics from the literature, using a test base of publicly available data sets.

This paper studies a facility location model in which two-dimensional Euclidean space represents the layout of a shop floor. The demand is generated by fixed rectangular-shaped user sites and served by a single supply facility. It is assumed that (i) communication between the supply point and a demand facility occurs at an input/output (I/O) point on the demand facility itself, (ii) the facilities themselves pose barriers to travel and (iii) distance measurement is as per the L-1-metric. The objective is to determine optimal locations of the supply facility as well as I/O points on the demand facilities, in order to minimize total transportation costs. Several, increasingly more complex, versions of the model are formulated and polynomial time algorithms are developed to find the optimal locations in each case.

Several social, economic and political factors have contributed to the increasing diversity of today's workforce. In addition, in an era when organizations are continuously redesigning their work and restructuring their operations to achieve their goals with fewer resources, performing work in teams has become commonplace. These trends have increased the need for managing diverse work teams effectively. There are several existing models in the management science literature that help managers to assign employees to work groups in order to maximize the groups' diversity and hence, facilitate their effectiveness. This paper introduces a new model that recasts the problem of managing diversity in a different way: it is assumed that the population comes partitioned into 'families' with a high degree of intra-familial similarity and inter-familial dissimilarity. The objective of the assignment then is to disperse these family members as evenly into the workgroups as possible. A little known network flow problem, known as the dining problem, is used to develop an efficient algorithm to produce solutions to this new model. This is followed by a report on an experimental application of the developed model to assign Master of Business Administration students in a business school to different projects in a course. As a part of this empirical report, an attractive feature of this model is also demonstrated; namely, how to conduct sensitivity analysis to determine the optimal levels of diversity in the presence of resource constraints. Finally, the paper concludes by discussing limitations of this new model and how they may be addressed in future research on this topic.

This paper discusses a brand positioning model in which two brands of a product are to be positioned in a price-quality space under a new behavioral assumption. This assumption asserts that customers determine the highest-quality product within their reservation price and purchase it, provided its quality does not fall short of a minimum standard. The model also includes producers' costs that are incurred for delivering a certain quality. We first delineate reaction functions for the optimal location of one brand, give a location of its competitor. We then show that Nash equilibria do not exist as long as price and quality are both variable. Finally, we consider a two phase model: in the first phase, the duopolists sequentially choose their quality levels under the assumption that both competitors know that in the second phase, a Nash equilibrium in prices follows. Single-variable mathematical programming formulations are presented to solve the problem. A numerical example is also given to illustrate the working of the model.

The design approximation problem is a well known problem in stock cutting, where, in order to facilitate the optimization techniques used in the cutting process, it is required to approximate complex designs by simpler ones. Although there are algorithms available to solve this problem, they all suffer from an undesirable feature that they only produce one optimal solution to the problem, and do not identify the complete set of all optimal solutions. The focus of this paper is to study this hitherto unexplored aspect of the problem: specifically, the case is considered in which both the design and the parent material are convex shapes, and some essential properties of all optimal solutions to the design approximation problem are ascertained. These properties are then used to devise two efficient schemes to identify the set of all optimal solutions to the problem. Finally, the recovery of a desired optimal approximation from the identified sets of optimal solutions, is discussed.

This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.

This paper describes a project undertaken at the New Brunswick Power Corporation (NB Power) the utility corporation of the Canadian province, in a cost-cutting effort through the use of improved time management. The focus of the project was to investigate if the time estimates in use at the corporation for work completion were accurate. We begin with a description of how the data was gathered from two sets of time measurement and was validated—the first set represents the current times in use at NB Power while the second set represents estimates obtained from experts. This is followed by a discussion of the methodology. Finally, this paper summarizes the conclusions and recommendations that are made to serve as the basis for improvement of performance and quality measurement.

The import of cost allocation procedures are through their ex ante important decision making. Hence, it is important that the allocation issue be placed squarely within the context of those firm's objectives which gave rise to the need for the specific allocation. To that effect, this paper focuses the debate on the identification of the indirect cost allocation method that is best suited to the specific reasons for requiring the cost information. First, it is shown that all existing allocation schemes (i) may be expressed in a common equation, flexible enough to be adapted to whatever decision-making purpose the firm desires; and (ii) fulfil the individual rationality conditions of game theory. Then, in light of the controversy as to whether the US Defense Department indirectly subsidizes the commercial side of its suppliers' operations, necessary and sufficient conditions are provided for allocations which do and do not subsidize. Non-subsidized allocations are shown to belong to the core. Subsidized allocations occur when the players (divisions') rational objectives are superseded by higher priority coordinating objectives of non-players (the firm).

In this paper we investigate the following problem: Given two convex Pin, and Pout where Pin is completely contained in Pout, we wish to find a sequence of ‘guillotine cuts’ to cut out Pin from Pout such that the total length of the cutting sequence is minimized. This problem has applications in stock cutting where a particular shape or design (in this case the polygon Pin) needs to be cut out of a given piece of parent material (the polygon Pout) using only guillotine cuts and where it is desired to minimize the cutting sequence length to improve the cutting time required per piece. We first prove some properties of the optimal solution to the problem and then give an approximation scheme for the problem that, given an error range δ, produces a cutting sequence whose total length is atmost δ more than that of the optimal cutting sequence. Then it is shown that this problem has optimal solutions that lie in the algebraic extension of the field that the input data belongs to — hence due to this algebraic nature of the problem, an approximation scheme is the best that can be achieved. Extensions of these results are also studied in the case where the polygons Pin and Pout are non-convex.

This paper describes a project that was done for the Shad Valley Program, where it was required to assign students to seminars so as to maximize the satisfaction of the students with their assignments. We begin by describing the problem, its inputs and constraints. Two models are proposed to determine optimal assignments. The first model is based on the Capacitated Transportation Problem and a network formulation is proposed to solve it. The second model is a two phase model whose first phase involves solving a Bottleneck Capacitated Transportation Problem and the second phase solving a Capacitated Transportation Problem. A simple search algorithm is proposed that solves the second model. Implementation of these models is described and the results obtained are discussed. Extensions to the two models are also proposed.

Consider a locational game on a network in which two competing facilities charge fixed, but not necessarily equal, prices and the decision variables are their respective locations. Rather than deciding in a given situation whether or not an equilibrium exists, we devise a stability index that measures the stability or instability of a given situation. In other words, given that an equilibrium exists, our index indicates how much external effort (or subsidy) is required to destroy that equilibrium; if equilibria do not exist, the index shows how much external effort (or tax) is needed to ''generate'' an equilibrium. Computational evidence for randomly generated problems is presented.

This paper studies the following problem in stock cutting: when it is required to cut out complicated designs from parent material, it is cumbersome to cut out the exact design or shape, especially if the cutting process involves optimization. In such cases, it is desired that, as a first step, the machine cut out a relatively simpler approximation of the original design, in order to facilitate the optimization techniques that are then used to cut out the actual design. This paper studies this problem of approximating complicated designs or shapes. The problem is defined formally first and then it is shown that this problem is equivalent to the Minimal Nested Polygon problem in geometry. Some properties of the problem are then shown and it is demonstrated that the problem is related to the Minimal Turns Path problem in geometry. With these results, an efficient approximate algorithm is obtained for the original stock cutting problem. Numerical examples are provided to illustrate the working of the algorithm in different cases.

In this paper we present a competitive location model. Models of this type have been used since Hotelling (1929) in his seminal paper “Stability in Competition” suggested a scenario in which duopolists compete on a linear market, i.e. a line segment, in prices and locations. His conclusion was that an equilibrium exists in which both competitors locate at the center of the market. This result was dubbed the “principle of minimum differentiation” and has been used by various authors to explain why existing products and political platforms are so similar to each other.