The pooling problem plays an important role in industrial production planning. The optimization model of this problem is similar to the minimum cost problem. However, due to the complexity of the problem, the pooling problem is strong NP-hard even with only one quality. In this paper, based on the optimization model proposed by Dai, we reformulate the model step by step. First, we reformulated the primal model into a quadratic non-convex optimization model equivalently. Then, we relaxed and inner approximate quadratic non-convex optimization model into both second-order cone programming problem, respectively. To solve both second-order cone programming problem, we used the branch and bound method to approximate the optimal solution of the original problem by solving the upper and lower bounds. Finally, we carried out the numerical experiments by using seven examples to demonstrate the effectiveness of our models and the algorithm.
REN Yequan, BAI Yanqin, LI Qian, YU Changjun, ZHANG Liansheng
. A second-order cone programming algorithm for pooling problem[J]. Operations Research Transactions, 2020
, 24(2)
: 61
-72
.
DOI: 10.15960/j.cnki.issn.1007-6093.2020.02.005
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