Efficient MILP formulations and valid cuts for multiproduct pipeline scheduling

Companies are faced with an ever-increasing competitive environment, larger commodity requirements and the need for rapid response to several uncertainties related to distribution and transportation scheduling. The problem addressed in this paper is composed by the short-term scheduling of a real world logistic complex that comprises the distribution of several petroleum derivatives from a single oil refinery to several depots through a single pipeline. The objective of this work is to generalize and to improve the efficiency of the MILP formulation proposed by Rejowski Jr. and Pinto [Comput. Chem. Eng. 27 (2003) 1229]. The model satisfies all operational constraints, such as mass balances, distribution constraints, product demands, sequencing constraints and logical constraints for pipeline operation. Firstly, the original formulation proposed by the authors is stated in a generalized form. Then, special and non-intuitive practical constraints, which minimizes product contamination inside the pipeline segments, are added to the original MILP and the resulting model is analyzed in terms of computational performance and solution quality. Finally, a set of integer cuts that are based on demands and pipeline segment initial inventories is included in the original formulation. All proposed examples are tested in three different demand scenarios. Results show that the formulations with the special constraints find the optimal solution with a higher value when compared to a feasible one of the respective problems without this assumption. When the delivery cuts were considered on the formulation with the special constraints for high demand scenario cases, they improved the CPU time in at least almost 70% when compared to the formulations that did not considered this set of valid cuts.