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BEAMR M2 – A spatially informed model for faster performance when solving the p-Median problem

Authors: F. Antonio Medrano*, Texas A&M University Corpus Christi, TX
Topics: Spatial Analysis & Modeling, Urban and Regional Planning
Keywords: spatial optimization, p-median, location analysis
Session Type: Paper
Presentation File: No File Uploaded

The p-Median location-allocation problem is a fundamental problem in the location science literature. It locates p facilities on a network in order to minimize the total weighted distance of serving all demand, and is commonly used for locating a set of warehouses or transportation hubs that serve numerous spatially distributed demands. The classic IP formulation has O(n^2) variables and constraints, and is one of the more challenging models to solve to optimality for problems of reasonable size. In 2008 the BEAMR model was developed, a frugal exact approximate formulation that for p-Median problem eliminates distant allocation variables while still maintaining optimality. It maintains optimality with a reduced problem definition by introducing allocation variables that if selected, indicate the current solution is not optimal and requires another iteration with an expanded (yet still reduced) problem definition. While this approach requires multiple solver iterations for one problem, each reduced iteration runs significantly faster than the complete model, and can still solve much more quickly than the full model alone. The original BEAMR algorithm uses a fixed variable increment procedure to expand the model when the current solution is not optimal, we introduce a spatially informed incrementing methodology called BEAMR M2. This new approach reduces the number of iterations by focusing the problem expansion only to where the optimal solution is more likely to be. Computational results show improved performance over the standard BEAMR model.

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