Abstract
The pooling problem, also called the blending problem, is fundamental in production planning of petroleum. It can be formulated as an optimization problem similar with the minimum-cost flow problem. However, Alfaki and Haugland (J Glob Optim 56:897–916, 2013) proved the strong NP-hardness of the pooling problem in general case. They also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of qualities. In this paper, we prove that the pooling problem is still strongly NP-hard even with only one quality. This means the quality is an essential difference between minimum-cost flow problem and the pooling problem. For solving large-scale pooling problems in real applications, we adopt the non-monotone strategy to improve the traditional successive linear programming method. Global convergence of the algorithm is established. The numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local minimizer. Our results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.
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This research is supported by the National Natural Science Foundation of China (Nos. 11631013, 71331001, 11331012) and the National 973 Program of China (No. 2015CB856002).
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Dai, YH., Diao, R. & Fu, K. Complexity Analysis and Algorithm Design of Pooling Problem. J. Oper. Res. Soc. China 6, 249–266 (2018). https://doi.org/10.1007/s40305-018-0193-7
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DOI: https://doi.org/10.1007/s40305-018-0193-7