Relax-and-fix decomposition technique for solving large scale grid-based location problems

Authors:
Md. Noor-E-Alam;John Doucette
Affiliations:
Department of Mechanical Engineering, 4-9 Mechanical Engineering Bldg., University of Alberta, Edmonton, AB, Canada T6G 2G8;Department of Mechanical Engineering, 4-9 Mechanical Engineering Bldg., University of Alberta, Edmonton, AB, Canada T6G 2G8 and TRLabs, Edmonton, AB, Canada
Venue:
Computers and Industrial Engineering
Year:
2012

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Abstract

Many problems in business, engineering, defence, resource exploitation, and even the medical sciences with location aspects can be expressed as grid-based location problems (GBLPs), modeled as integer linear programming problems. Such problems are often very computationally complex to solve. We develop a relax-and-fix-based decomposition approach to solve large-scale GBLPs, which we demonstrate will significantly reduce solution runtimes while not severely impacting optimality. We also introduce problem-specific logical restrictions, constraints that reduce the feasible region and the resulting branch-and-bound tree with minimal reductions in optimality.