Computational Optimization and Applications

, Volume 72, Issue 3, pp 827–848 | Cite as

Two-phase semi-Lagrangian relaxation for solving the uncapacitated distribution centers location problem for B2C E-commerce

  • Huizhen ZhangEmail author
  • Cesar Beltran-Royo
  • Bo Wang
  • Ziying Zhang


This paper develops a mixed integer programming model for determining uncapacitated distribution centers location (UDCL) for B2C E-commerce. Based on the characteristics of distribution system for B2C E-commerce firms, the impact of supply cost of multi-commodity is considered in this model. Combining with the properties of the semi-Lagrangian relaxation (SLR) dual problem in the UDCL case, a two-phase SLR algorithm with good convergency property is furthermore developed for solving the UDCL problem. For the sake of contrastive analysis, this paper has performed computational experiments on 15 UDCL instances by the mixed integer programming solver, CPLEX, and the approach obtained by combining two-phase SLR algorithm with CPLEX, respectively. The numerical results show that the two-phase SLR algorithm not only can improve the solving speed of the CPLEX solver, but also can provide better results in reasonable time for most instances.


Uncapacitated distribution centers location B2C E-commerce Semi-Lagrangian relaxation Dual ascent method 



This work is supported by the National Natural Science Foundation of China (Grant No. 71401106), The Ministry of education of Humanities and Social Science Project (Grant No.16YJA630037), the Shanghai Natural Science Foundation (Grant No. 14ZR1418700), the Hujiang Foundation of China (Grant No. A14006).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Huizhen Zhang
    • 1
    Email author
  • Cesar Beltran-Royo
    • 2
  • Bo Wang
    • 3
  • Ziying Zhang
    • 4
  1. 1.School of ManagementUniversity of Shanghai for Science and TechnologyShanghaiChina
  2. 2.Department of Computer Science and StatisticsKing Juan Carlos UniversityMadridSpain
  3. 3.School of ManagementUniversity of Shanghai for Science and TechnologyShanghaiChina
  4. 4.School of Materials EngineeringShanghai University of Engineering ScienceShanghaiChina

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