Source-based discrete and continuous-time formulations for the crude oil pooling problem

The optimization of crude oil operations in refineries is a challenging scheduling problem due to the need to model tanks of varying composition with nonconvex bilinear terms, and complicating logistic constraints. Following recent work for multiperiod pooling problems of refined petroleum products, a source-based mixed-integer nonlinear programming formulation is proposed for discrete and continuous representations of time. Logistic constraints are modeled through Generalized Disjunctive Programming while a specialized algorithm featuring relaxations from multiparametric disaggregation handles the bilinear terms. Results over a set of test problems from the literature show that the discrete-time approach finds better solutions when minimizing cost (avoids source of bilinear terms). In contrast, solution quality is slightly better for the continuous-time formulation when maximizing gross margin. The results also show that the specialized global optimization algorithm can lead to lower optimality gaps for fixed CPU, but overall, the performance of commercial solvers BARON and GloMIQO are better.