Complexity Analysis and Algorithm Design of Pooling Problem

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 po...

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Veröffentlicht in:Journal of the Operations Research Society of China (Internet) Jg. 6; H. 2; S. 249 - 266
Hauptverfasser: Dai, Yu-Hong, Diao, Rui, Fu, Kai
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Beijing Operations Research Society of China 01.06.2018
Springer Nature B.V
Schlagworte:
Algorithms
Boolean
Complexity
Integer programming
Linear programming
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Optimization
Production planning
Strategy
Variables
Pooling problem
90C90
Complexity analysis
Successive linear programming
90C60
Non-monotone
ISSN:2194-668X, 2194-6698
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Zusammenfassung: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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ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-018-0193-7