Integer linear programming models for grid-based light post location problem

Selecting optimal location is a key decision problem in business and engineering. This research focuses to develop mathematical models for a special type of location problems called grid-based location problems. It uses a real-world problem of placing lights in a park to minimize the amount of darkness and excess supply. The non-linear nature of the supply function (arising from the light physics) and heterogeneous demand distribution make this decision problem truly intractable to solve. We develop ILP models that are designed to provide the optimal solution for the light post problem: the total number of light posts, the location of each light post, and their capacities (i.e., brightness). Finally, the ILP models are implemented within a standard modeling language and solved with the CPLEX solver. Results show that the ILP models are quite efficient in solving moderately sized problems with a very small optimality gap.