An algorithm for generalized constrained multi-source Weber problem with demand substations

In this paper, we consider a multi-source Weber problem of m new facilities with respect to n demand regions in order to minimize the sum of the transportation costs between these facilities and the demand regions. We find a point on the border of each demand region from which the facilities serve the demand regions at these points. We present an algorithm including a location phase and an allocation phase in each iteration for solving this problem. An algorithm is also proposed for carrying out the location phase. Moreover, global convergence of the new algorithm is proved under mild assumptions, and some numerical results are presented.