A Squared-Euclidean distance location-allocation problem

Abstract

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This thesis is concerned with the analysis of a squared-Euclidean distance location-allocation problem with balanced transportation constraints, where the costs are directly proportional to distances and the amount shipped. The problem is shown to be equivalent to maximizing a convex, quadratic function subject to transportation constraints. A branch and bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds. These bounds are shown to substantially dominate several other upper bounds that are derived using standard techniques, to an extent which significantly increases the size of problems solvable within a reasonable effort. The special structure of the transportation constraints is used to derive a partitioning scheme, and this structure is further exploited via suitable logical tests which tighten the bounds implied on the transportation flows by the branching restrictions. The transportation structure is also used to generate additional cut-set inequalities based on a cycle prevention method which preserves a forest graph for any partial solution. Results of the computational experiments, and a discussion of possible extensions are also presented.