A bi-level capacitated P-median facility location problem with the most likely allocation solution

Abstract

In this paper, a bi-level model is introduced to evaluate the capacitated p-median facility location problem with the most likely allocation solution. The classical capacitated p-median problem is considered in the upper-level to minimize the cost of locating facilities and serving demands while a log-based model resulting from the minimum information approach is used in the lower-level to determine the most likely allocation solution based on the available information. Using Lagrangian dual theory, the proposed bi-level problem is reduced to a new one-level nonlinear mixed-integer problem whose solution is obtained by comparing two mixed-integer linear problems. Some numerical examples are provided to illustrate the added value of the proposed model.