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

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Abstract

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.

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Source: Reproduced with permission from Akyüz et al. (2013)

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Acknowledgements

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.

Author information

Correspondence to M. Hakan Akyüz.

Appendix

Appendix

Table 2 The performance of the ABB algorithm with RLT based lower bounding procedure
Table 3 The performance of the ABB algorithm with with block norm based lower bounding procedure
Table 4 The performance of the LBB algorithms

See Tables 2, 3 and 4.

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Akyüz, M.H., Öncan, T. & Altınel, İ.K. Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem. Ann Oper Res 279, 1–42 (2019). https://doi.org/10.1007/s10479-018-3026-5

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Keywords

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

Mathematics Subject Classification

  • 90B06
  • 90B85
  • 90C26