Annals of Operations Research

, Volume 279, Issue 1–2, pp 1–42 | Cite as

Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem

  • M. Hakan AkyüzEmail author
  • Temel Öncan
  • İ. Kuban Altınel
Original Research


The Multi-commodity Capacitated Multi-facility Weber Problem is concerned with locating I capacitated facilities in the plane in order to satisfy the demands of J customers for K commodities such that the total transportation cost is minimized. This is a multi-commodity extension of the well-known Capacitated Multi-facility Weber Problem and difficult to solve. In this work, we propose two branch-and-bound algorithms for exactly solving this nonconvex optimization problem. One of them considers partitioning of the allocation space while the other one considers partitioning of the location space. We have implemented two lower bounding schemes for both algorithms and tested several branching strategies. The results of an extensive computational study are also included.


Facility location–allocation Branch-and-bound algorithm Multi-commodity transportation 

Mathematics Subject Classification

90B06 90B85 90C26 



This research is supported by the Turkish Scientific and Technological Research Council (TÜBİTAK) Research Grant No: 107M462, and Galatasaray University Scientific Research Projects Grant Nos: 07.402.014, 10.402.001 and 10.402.019. The first author acknowledges the partial support of National Graduate Scholarship Program for PhD Students awarded by TÜBİTAK.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • M. Hakan Akyüz
    • 1
    Email author
  • Temel Öncan
    • 1
  • İ. Kuban Altınel
    • 2
  1. 1.Department of Industrial EngineeringGalatasaray UniversityOrtaköy, İstanbulTurkey
  2. 2.Department of Industrial EngineeringBoğaziçi UniversityBebek, İstanbulTurkey

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