, Volume 16, Issue 4, pp 343–377 | Cite as

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

  • S. Nobakhtian
  • A. Raeisi Dehkordi
Research Paper


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 



The first-named author was partially supported by a grant from IPM (No. 96900422).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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