Solution Approach To P-Median Facility Location Problem With Integer Programming And Genetic Algorithm

Abstract

In the study, the P-median problem that Hakimi brought to science was discussed. With this problem, in short, it is ensured that the locations for the supply of n demand points of p facilities with the lowest cost are determined and the demand points to be served are allocated to these locations. The solution of the p-median problem with the integer programming approach is in the NP (Non-Polynominal) difficult class, and the solution time increases exponentially as the size of the problem increases. For this, the use of heuristic approaches in the P-median problem significantly shortens the solution time of large-sized problems. The data used in the application were taken from the Operation Research-Library site. In practice, the P-median is considered as capacity-constrained and unconstrained. Euclidean distances were calculated in Excel. The solution of mixed integer programming is obtained by using the CPLEX program. In addition to mixed integer programming, genetic algorithm, which is a meta-heuristic method, is applied to the capacity-constrained P-median problem. Different solutions were obtained by changing the population size, maximum number of iterations, crossover and mutation probability values. It has been observed that there is more than one optimum solution in repeated studies. When working with larger data sets, this algorithm will be less likely to find the global optimum. However, when compared to mixed integer programming, the genetic algorithm gave results very close to the optimum result. The use of heuristic algorithms in real-world complex problems will both shorten the solution time considerably compared to the integer programming method and provide results that are very close to the optimum result.