Multi-commodity capacitated multi-facility Weber problem with probabilistic customer locations

Abstract

This paper presents a rectilinear distance multi-commodity multi-facility Weber problem with capacity constraints and finds the location of facilities and assigns the amount of each commodity to each customer at minimum cost. Although this problem is Np- hard and has neither convex nor concave objective function, considering probabilistic customer points make the problem more difficult. An exact and an approximated expected distance function is applied in order to solve the problem. An Alternate location–allocation heuristic method which divides the problem into multi-commodity transportation subproblem and pure allocation subproblem is implemented until no improvement is observed. A typical example is illustrated and results are then reported.