Coverage location problems

Martin William Broin, Purdue University

Abstract

Coverage location problems utilize some form of maximum service distance or time criteria to determine if suitable service can be provided. The particular coverage location problem investigated is called the Maximal Covering problem, which attempts to minimize the costs of establishing facilities and the costs of not covering customer or client locations for a single service where there is an upper bound on the number of facilities that can be established. The major thrust of this thesis is two fold. First we develop some theoretical results for covering problems with matrices that exhibit a special structure called totally balanced. Second, we exploit totally balanced matrices to solve general covering problem. Covering problems on tree networks are intimately related to covering matrices with special structures called "balanced" and "totally balanced". We present some theoretical results that extend the known relationships between totally balanced matrices and tree covering problems. We also develop the first known efficient, O(p$\sp2$n min$\{$m$\sp2$,n$\sp2\}$), algorithm for the totally balanced maximal covering problem. A method is developed to find a "large" totally balanced submatrix within a general covering matrix. We also show, via simulation studies, that covering problems arising from planar location problems have significantly more structure than randomly generated covering matrices. Primal and dual heuristics for the general maximal coverage location problems are developed most of which are based on finding a totally balanced submatrix of the covering matrix. Several problem reduction methods are investigated in conjunction with the dual Lagrangian based heuristics. Extensive computational testing of these heuristics is reported.

Degree

Ph.D.

Advisors

Lowe, Purdue University.

Subject Area

Operations research

COinS