A Benders’ Decomposition Method to Solve a Multi-period, Multi-echelon, and Multi-product Integrated Petroleum Supply Chain

Abstract

Problems of large dimensions (linear, non-linear, integer, and continuous) are the major principles in the modeling of important natural and social phenomena. The larger are the extent and scope of the application of the phenomenon or the vastness of its applications; the larger is the dimension confronted in modeling. Integrated Petroleum Supply Chain (IPSC), which has been proposed by Nasab and Amin-Naseri (Energy 114:708–733, 2016), is one such problem. Specific solutions have been proposed over the years for problems of this kind. One of the most important methods in this regard is Benders’ decomposition method, proposed in 1962 by Benders for combinatorial optimization problems. In this paper, Benders’ decomposition method has been used to solve the IPSC model and the gap criteria are then used to evaluate the performance of this method. Here, for analyzing the performance of Benders’ decomposition method, the results of this method and those of Branch & Bound algorithm, which has been proposed by Nasab and Amin-Naseri (Energy 114:708–733, 2016), have been compared. Based on the results, while Branch & Bound algorithm method is not able to solve large size problems, the generated gap in Benders’ method is very small. This indicates the capability of Benders’ method to achieve a response close to the optimal response. Therefore, Benders’ method possesses appropriate efficiency.