A Facility Location Problem with Tchebychev Distance in the Presence of a Probabilistic Line Barrier

This paper considers the Tchebychev distance for a facility location problem with a probabilistic line barrier in the plane. In particular, we develop a Mixed-Integer Nonlinear Programming (MINLP)model for this problem that minimizes the total Tchebychev distance between a new facility and theexisting facilities. A numerical example is solved to show the validity of the developed model. Becauseof difficulty in solving this problem, while increasing the number of existing facilities, we propose anefficient meta-heuristic algorithm and design it, namely differential evolution (DE), for the givenproblem. Finally, the associated results are compared with the exact solution and lower bound for the different-sized problems

Keywords:

Location problem , Tchebychev distance , Line barrier , Differential evolution