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

0360-8352/$ see front matter 2012 Elsevier Ltd. A http://dx.doi.org/10.1016/j.cie.2012.07.006 ⇑ Corresponding author at: Department of Mechanica Engineering Bldg., University of Alberta, Edmonton, AB, 492 2651. E-mail address: [email protected] (J. Dou 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. 2012 Elsevier Ltd. All rights reserved.