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 unied 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. Finally, the refinery planning and crude-oil scheduling problems are simultaneously solved using a Lagrangian decomposition procedure based on dualizing the constraint linking crude distillation feedstocks in each subproblem. A new hybrid dual problem is proposed to update the Lagrange multipliers, while a simple heuristic strategy is presented in order to obtain feasible solutions to the full-space MINLP. The approach is successfully applied to a small case study and a larger refinery problem

Time representations and mathematical models for process scheduling problems

During the last 15 years, many mathematical models have been developed in order to solve process operation scheduling problems, using discrete or continuous-time representations. In this paper, we present a unified representation and modeling approach for process scheduling problems. Four different time representations are presented with corresponding strengthened formulations that rely on exploiting the non-overlapping graph structure of these problems through maximum cliques and bicliques. These formulations are compared, and applied to single-stage and multi-stage batch scheduling problems, as well as crude-oil operations scheduling problems. We introduce three solution methods that can be used to achieve global optimality or obtain near-optimal solutions depending on the stopping criterion used. Computational results show that the multi-operation sequencing time representation is superior to the others as it allows efficient symmetry-breaking and requires fewer priority-slots, thus leading to smaller model sizes.</p

Integration of Refinery Planning and Crude-Oil Scheduling using Lagrangian Decomposition

The aim of this paper is to introduce a methodology to solve a large-scale mixed-integer nonlinear program (MINLP) integrating the two main optimization problems appearing in the oil refining industry: refinery planning and crude-oil operations scheduling. The proposed approach consists of using Lagrangian decomposition to efficiently integrate both problems. The main advantage of this technique is to solve each problem separately. A new hybrid dual problem is introduced to update the Lagrange multipliers. It uses the classical concepts of cutting planes, subgradient, and boxstep. The proposed approach is compared to a basic sequential approach and to standard MINLP solvers. The results obtained on a case study and a larger refinery problem show that the new Lagrangian decomposition algorithm is more robust than the other approaches and produces better solutions in reasonable times.</p