Optimal Scheduling of Refinery Crude-Oil Operations

This thesis deals with the development of mathematical models and algorithms for optimizing refinery crude-oil operations schedules. The problem can be posed as a mixed-integer nonlinear program (MINLP), thus combining two major challenges of operations research: combinatorial search and global optimization. First, we propose a unified modeling approach for scheduling problems that aims at bridging the gaps between four different time representations using the general concept of priority-slots. For each time representation, an MILP formulation is derived and strengthened using the maximal cliques and bicliques of the non-overlapping graph. Additionally, we present three solution methods to obtain global optimal or near-optimal solutions. The scheduling approach is applied to single-stage and multi-stage batch scheduling problems as well as a crude-oil operations scheduling problem maximizing the gross margin of the distilled crude-oils. In order to solve the crude-oil scheduling MINLP, we introduce a two-step MILP-NLP procedure. The solution approach benefits from a very tight upper bound provided by the first stage MILP while the second stage NLP is used to obtain a feasible solution. Next, we detail the application of the single-operation sequencing time representation to the crude-oil operations scheduling problem. As this time representation displays many symmetric solutions, we introduce a symmetry-breaking sequencing rule expressed as a deterministic finite automaton in order to efficiently restrict the set of feasible solutions. Furthermore, we propose to integrate constraint programming (CP) techniques to the branch & cut search to dynamically improve the linear relaxation of a crude-oil operations scheduling problem minimizing the total logistics costs expressed as a bilinear objective. CP is used to derived tight McCormick convex envelopes for each node subproblem thus reducing the optimality gap for the MINLP.