Capacitated set-covering model considering the distance objective and dependency of alternative facilities

Abstract

We propose a new model of facility location to solve a kind of problem that belong to a class of set-covering problem using an integer programming formulation. Our model contains a single objective function, but it represents two goals. The first is to minimize the number of facilities, and the other is to minimize the total distance of customers to facilities. The first goal is a mandatory goal, and the second is an improvement goal that is very useful when alternate optimum solutions for the first goal exist. We use a big number as a weight on the first goal to force the solution algorithm to give first priority to the first goal. Besides considering capacity constraints, our model accommodates a kind of either-or constraints representing facilities dependency. The either-or constraints will prevent the solution algorithm to select two or more facilities from the same set of facility with mutually exclusive properties. A real location selection problem to locate a set of wastewater treatment facility (IPAL) in Surakarta city, Indonesia, will describe the implementation of our model. A numerical example is given using the data of that real problem.