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The pooling problem is an important industrial problem in the class ofnetwork flow problems for allocating gas flow in pipeline transportationnetworks. For P-formulation of the pooling problem with time discretization, wepropose second order cone programming (SOCP) and linear programming (LP)relaxations and prove that they obtain the same optimal value as thesemidefinite programming relaxation. The equivalence among the optimal valuesof the three relaxations is also computationally shown. Moreover, arescheduling method is proposed to efficiently refine the solution obtained bythe SOCP or LP relaxation. The efficiency of the SOCP and the LP relaxation andthe proposed rescheduling method is illustrated with numerical results on thetest instances from the work of Nishi in 2010, some large instances, and Foulds3, 4, 5 test problems.

Solving Pooling Problems by LP and SOCP Relaxations and Rescheduling Methods