Complexity Analysis and Algorithm Design of Pooling Problem

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.