Three problems in discrete network facility location
Berglund, Paul Gordon
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This thesis considers three separate but related problems in the area of locational analysis, more specifically discrete facility location on networks. The first part of the thesis considers a manufacturing facility location problem under competition on a network. The decision maker must choose the set of locations which will maximize net profits at the equilibrium reached after competitors react to maximize their own profits. This problem is formulated as a discretely-constrained mathematical program with equilibrium constraints (DC-MPEC). An MPEC is in and of itself typically very hard to solve due in part to non-convexity; the addition of integer variables increases the difficulty level further. A branch and bound technique is attempted, but this is only practical for small problems. For larger problems a heuristic based on simulated annealing is used. The second part of the thesis examines robust solutions to uncapacitated single-allocation hub network design problems. It is shown that the p- hub center problem and the hub covering problem may be solved by the same heuristics as are used for the corresponding nominal problems. For the p- hub median problem, a heuristic based on variable neighborhood search is used. A number of example problems are solved. The resulting networks are analyzed and compared with the solutions to the corresponding nominal problems. The third part solves a robust hazardous waste facility problem. The problem is to locate facilities for the disposal or storage of hazardous waste so as to minimize a linear combination of facility construction cost and exposure risk due to the transportation of the hazardous waste. A formulation for the exact solution to the problem is developed and some small examples are solved using CPLEX. A genetic algorithm is used to solve examples too large to be solved by CPLEX. The resulting robust solutions are discussed and compared with the solutions to the corresponding nominal problems.