A multi-grid scheduling model for integrated gasoline blending operations

Abstract

Optimal scheduling of various operations in a refinery offers significant opportunities for saving costs and increasing profits. The overall refinery operations (Pinto et al. 2000) involve three main segments, namely crude oil storage and processing, intermediate processing, and product blending. Scheduling of crude oil operations has received the most attention so far, but limited work exists on the scheduling of product blending operations. Gasoline is one of the most profitable products of a refinery and can account for as much as 60-70% of total profit. A refinery typically blends several gasoline cuts or fractions from various processes to meet its customer orders of varying specifications. The large numbers of orders, delivery dates, blenders, blend components, tanks, quality specifications, etc. make this problem of blending and scheduling highly complex and nonlinear. A heuristic treatment of the nonlinear blending and complex combinatorics can lead to inferior schedules and costly quality give-aways. Thus, scheduling using advanced techniques of mixed-integer programming are imperative for avoiding ship demurrage, improving order delivery and customer satisfaction, minimizing quality give-aways, reducing transitions and slop generation, exploiting low-quality cuts, and reducing inventory costs. The early work on this problem focused mainly on gasoline-blending planning rather than scheduling. Some other work (Pinto et al., 2000) considered blending operations in general. Jia and Ierapetritou (2003) proposed a continuous-time event-based MILP formulation for scheduling gasoline-blending and distribution operations simultaneously for fixed recipes. Mendez et al. (2006) presented both discrete-time and continuous-time models for the simultaneous optimization of blending and short-term scheduling. However, most past work considered only select aspects of the full gasoline-blending problem. Recently, Li et al. (2009) developed a single-grid slot-based continuous-time formulation for the simultaneous treatment of recipe, blending, and scheduling. They incorporated several problem features such as multi-purpose product tanks, non-identical parallel blenders, one blender charging at most one tank at a time, etc. They also ensured the continuity of blending rate during a run and developed a schedule adjustment procedure to avoid solving nonconvex MINLP. However, their model proved inadequate for solving large-scale practical problems, as it needs large computation time just to obtain a feasible solution with large integrality gap. In addition, they assumed unlimited component inventories during the scheduling horizon. This paper presents a new model for the integrated treatment of recipe, blending, and scheduling of gasoline operations. Its main feature is the use of multiple partially independent time-grids with unit-slots instead of a single common grid with process-slots. While Susarla et al. (2008) have successfully demonstrated the use of multiple grids without any mass balance error for multi-purpose batch plants, the present problem involves continuous operations and changeovers in multi-purpose product tanks. Our proposed model addresses these additional complexities in a multi-grid framework and shows improved MILP relaxation. This allows us to solve the larger problems much quicker than the model of Li et al. (2009). In addition to all the problem features of Li et al. (2009), we also relax the assumption of unlimited component inventories during the scheduling horizon, and extend the schedule adjustment procedure of Li et al. (2009) to avoid solving nonconvex MINLP problem. Lastly, we use the fourteen examples from Li et al. (2009) to evaluate the performance of our new blending scheduling model.