Tammy Drezner

Optimal continuous location of a retail facility, facility attractiveness, and market share: An interactive model

Abstract In this paper a model for the location of a retail facility anywhere in the plane is presented. Existing location papers suggest that marketers can evaluate a set of potential sites for the location of a new facility. The site that maximizes the market share captured is selected. However, the best site for the new facility may not be included in the user provided set of potential sites. Finding the best location anywhere in the plane requires the analysis of the market share function which is addressed in this paper. In addition, a sensitivity analysis of both the best location and the market share captured is provided. Computational experiments illustrate the properties of this function and its sensitivity to the data parameters. The analysis shows that the market share captured by the facility (existing or new) is sensitive to both facility location and attractiveness.

Solving the multiple competitive facilities location problem

In this paper we propose five heuristic procedures for the solution of the multiple competitive facilities location problem. A franchise of several facilities is to be located in a trade area where competing facilities already exist. The objective is to maximize the market share captured by the franchise as a whole. We perform extensive computational tests and conclude that a two-step heuristic procedure combining simulated annealing and an ascent algorithm provides the best solutions.

Equitable service by a facility: Minimizing the Gini coefficient

In this paper, we investigate the location of facilities with equity considerations, namely, minimizing the Gini coefficient of the Lorenz curve based on service distances. Properties of the Gini coefficient in the context of location analysis are investigated both for demand originating at points and demand generated in an area. An algorithm that finds the optimal location of one facility in a bounded area in the plane when demand is generated at a set of demand points, is constructed. Randomly generated problems with up to 10,000 demand points are successfully solved in a reasonable computer time.

Finding the optimal solution to the Huff based competitive location model

Abstract.In this paper we solve the gravity (Huff) model for the competitive facility location problem. We show that the generalized Weiszfeld procedure converges to a local maximum or a saddle point. We also devise a global optimization procedure that finds the optimal solution within a given accuracy. This procedure is very efficient and finds the optimal solution for 10,000 demand points in less than six minutes of computer time. We also experimented with the generalized Weiszfeld algorithm on the same set of randomly generated problems. We repeated the algorithm from 1,000 different starting solutions and the optimum was obtained at least 17 times for all problems.

Replacing continuous demand with discrete demand in a competitive location model

Location models commonly represent demand as discrete points rather than as continuously spread over an area. This modeling technique introduces inaccuracies to the objective function and consequently to the optimal location solution. In this article this inaccuracy is investigated by the study of a particular competitive facility location problem. First, the location problem is formulated over a continuous demand area. The optimal location for a new facility that optimizes the objective function is obtained. This optimal location solution is then compared with the optimal location obtained for a discrete set of demand points. Second, a simple approximation approach to the continuous demand formulation is proposed. The location problem can be solved by using the discrete demand algorithm while significantly reducing the inaccuracies. This way the simplicity of the discrete approach is combined with the approximated accuracy of the continuous-demand location solution. Extensive analysis and computations of the test problem are reported. It is recommended that this approximation approach be considered for implementation in other location models.

The gravity p-median model

Abstract In this paper we propose a new model for the p -median problem. In the standard p -median problem it is assumed that each demand point is served by the closest facility. In many situations (for example, when demand points are communities of customers and each customer makes his own selection of the facility) demand is divided among the facilities. Each customer selects a facility which is not necessarily the closest one. In the gravity p -median problem it is assumed that customers divide their patronage among the facilities with the probability that a customer patronizes a facility being proportional to the attractiveness of that facility and to a decreasing utility function of the distance to the facility. The model is analyzed and heuristic solution procedures are proposed. Computational experiments using a set of test problems, provide excellent results.

FACILITY LOCATION IN ANTICIPATION OF FUTURE COMPETITION.

Abstract In this paper, we consider locating a new facility in a competitive environment. A future competitor is expected to enter the market and locate his facility at its best site. The best location for ones own facility is to be found such that the market share captured following the competitors entry is maximized. The problem is complicated because the best location for the competitor depends on the selected location for ones own facility. The problem is formulated using the gravity model for the estimation of market share. Three heuristic solution procedures are proposed. Computational experiments with these heuristics are presented.

Location of multiple retail facilities with limited budget constraints — in continuous space

Abstract The location of multiple competing facilities in an area where other facilities already exist is investigated. The objective is to maximize the total market share captured by the entire franchise chain, both new franchise facilities and existing franchise facilities. The budget for constructing new facilities is given and it is up to the planners discretion to allocate that budget among them. Market share is calculated using gravity type models in a continuous space. Both the optimal allocation of the budget among the new facilities and the best locations for them are found. We conclude that new franchises should invest the total budget in one new facility, while established franchises should consider equally dividing the budget among several new facilities. The model is analyzed and computational experiments are reported.

A multi-objective heuristic approach for the casualty collection points location problem

In this paper, we formulate the casualty collection points (CCPs) location problem as a multi-objective model. We propose a minimax regret multi-objective (MRMO) formulation that follows the idea of the minimax regret concept in decision analysis. The proposed multi-objective model is to minimize the maximum per cent deviation of individual objectives from their best possible objective function value. This new multi-objective formulation can be used in other multi-objective models as well. Our specific CCP model consists of five objectives. A descent heuristic and a tabu search procedure are proposed for its solution. The procedure is illustrated on Orange County, California.

Location of casualty collection points

In this paper I find the best location of casualty collection points (CCPs). CCPs are expected to become operational in case of a human-made or natural disaster with mass casualties, such as a high-magnitude earthquake. Five objective functions are suggested and analyzed: p-median, p-center, p-maxcover, min-variance, and Lorenz curve. Multiobjective models are also analyzed. To illustrate the location problem, the models are applied to a scenario based on a large earthquake hitting Orange County, CA as a case study. The optimal locations for the CCPs using the objective functions are found, analyzed, and compared.