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.
Location Location-allocation Heuristic algorithm Global convergence Distance function
Mathematics Subject Classification
Primary 90B85 49J52 Secondary 90B06 90C26 90C90
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The first-named author was partially supported by a grant from IPM (No. 96900422).
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