A bi-level capacitated P-median facility location problem with the most likely allocation solution. (May 2019) - Abareshi, Maryam
Highlights: A bi-level model is proposed to investigate the p -median problem on a minimum information approach. The most likely allocation solution is determined while the costumers' demands are provided. The Lagrangian dual approach is applied to reduce the bi-level capacitated p-median to a one level problem. Some mixed integer linear problems are applied to increase the efficiency of the problem. 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.