IEOR153_paper on Capacitated Facility location model

IEOR153_paper on Capacitated Facility location model - WP...

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WP # 04 – 03 Modeling Data Envelopment Analysis (DEA) Efficient Location/Allocation Decisions Ronald K. Klimberg Haub School of Business Saint Joseph’s University Philadelphia, PA 19131 610-660-1625 Samuel J. Ratick The George Perkins Marsh Research Institute Clark University Worcester, MA 01610. Saint Joseph’s University Haub School of Business Division: Decision & System Sciences
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Klimberg & Ratick 3/3/2004 Modeling Data Envelopment Analysis (DEA) Efficient Location/Allocation Decisions ABSTRACT Many types of facility location/allocation models have been developed to find optimal spatial patterns with respect to location criteria such as: cost, time, coverage, and access. In this paper we develop and test location modeling formulations that utilize aspects of the data envelopment analysis (DEA) efficiency measure to find optimal and efficient facility location/allocation patterns. Solving for the DEA efficiency measure, together with location modeling objectives, provides a promising rich approach to multiobjective location problems. 2
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Klimberg & Ratick 3/3/2004 INTRODUCTION Many types of facility location/allocation models have been developed to find optimal patterns with respect to different location objectives such as: costs, time, coverage, and access among others. Some of these models have been formulated in a multiobjective programming framework to elicit trade-offs among different and conflicting objectives. In this paper we use the concept of efficiency as defined by data envelopment analysis (DEA) as another objective for location modeling. DEA determines the relative efficiencies of comparable decision making units (DMUs) measured by the ratio of the sum of weighted outputs to the sum of weighted inputs, in which inputs and outputs can be measured in their natural units. Two types of efficiencies can be optimized in this way; spatial efficiency - measured the least cost location and allocation patterns for facilities, and the facility efficiencies in serving demands - measured by the DEA efficiency score for “opened” facilities (those that are chosen to operate in the optimal solution). In the next section, we provide a brief introduction to facility location/allocation and DEA models. Next, we develop and present formulations combining the uncapacitated and capacitated facility location models with the DEA model. Subsequently, we apply these models to a small hypothetical data set and present the results. Finally, the conclusions and future extensions are discussed. BACKGROUND Facility Location Models The classical transportation problem satisfies demands from supply nodes at minimum transportation cost. The uncapacitated facility location problem (UPLP) model extends this by choosing among a number of potential sites for locating supply facilities, those that minimize costs – defined here as the sum of transportation costs and the fixed costs of opening facilities (see Daskin, 1995 pp. 247 – 303, for a comprehensive and cogent review of formulations and solution algorithms for fixed charge location problems) (Balinski 1965).
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