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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematical and Computing Science, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-ku, Tokyo, 152-8552, Japan

    Masaki Kimizuka & Makoto Yamashita

  2. Department of Mathematics, Ewha W. University, 52 Ewhayeodae-gil, Sudaemoon-gu, Seoul, 03760, Korea

    Sunyoung Kim

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  1. Masaki Kimizuka
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  2. Sunyoung Kim
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  3. Makoto Yamashita
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Correspondence to Sunyoung Kim.

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S. Kim: The research was supported by NRF 2017-R1A2B2005119. M. Yamashita: This research was partially supported by JSPS KAKENHI (Grant Number: 15K00032, 18K11176).

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Kimizuka, M., Kim, S. & Yamashita, M. Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods. J Glob Optim 75, 631–654 (2019). https://doi.org/10.1007/s10898-019-00795-w

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  • DOI: https://doi.org/10.1007/s10898-019-00795-w

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