Journal of Global Optimization

, Volume 75, Issue 3, pp 631–654 | Cite as

Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods

  • Masaki Kimizuka
  • Sunyoung KimEmail author
  • Makoto Yamashita


The pooling problem is an important industrial problem in the class of network flow problems for allocating gas flow in pipeline transportation networks. For the pooling problem with time discretization, we propose second order cone programming (SOCP) and linear programming (LP) relaxations and prove that they obtain the same optimal value as the semidefinite programming relaxation. Moreover, a rescheduling method is proposed to efficiently refine the solution obtained by the SOCP or LP relaxation. The efficiency of the SOCP and the LP relaxation and the proposed rescheduling method is illustrated with numerical results on the test instances from the work of Nishi in 2010, some large instances and Foulds 3, 4 and 5 test problems.


Pooling problem Semidefinite relaxation Second order cone relaxation Linear programming relaxation Rescheduling method Computational efficiency 

Mathematics Subject Classification

90C20 90C22 90C25 90C26 



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Copyright information

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

Authors and Affiliations

  • Masaki Kimizuka
    • 1
  • Sunyoung Kim
    • 2
    Email author
  • Makoto Yamashita
    • 1
  1. 1.Department of Mathematical and Computing ScienceTokyo Institute of TechnologyMeguro-kuJapan
  2. 2.Department of MathematicsEwha W. UniversitySudaemoon-guKorea

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