Optimizing the petroleum supply chain at petrobras

Abstract

The main objective of this study is to describe how mathematical programming is being used to solve the Petroleum Allocation Problem at Petrobras. We propose a Mixed Integer Linear Programming formulation of the problem which relies on a time/space discretization network. The formulation involves some inequalities which are redundant to the mixed integer model but no necessarily so to the Linear Programming relaxation of it. We also use some inequalities which are associated with polytopes that have been extensively studied in the literature. Furthermore, separation routines for strong valid inequalities associated with these polytope are readily available in some commercial solvers. Use of this feature allowed a substantial reinforcement of the underlying Linear Programming relaxation to be attained. Our formulation was tested on an industrial-size instance of the problem involving 11 crude oils, 6 tanker types, 5 maritime terminals involving 8 docks, 6 refineries, and 8 distillation units over a time horizon of 60 discretized intervals. The instance has 28,000 binary variables, 19,000 continuous variables, and 14,000 constraints and has been effectively solved under the proposed formulation. Feasible mixed integer solutions, guaranteed to be at no more than 5% of optimality, were obtained in less than 4000 CPU seconds under the mixed integer solver XPRESS-MP.