Oil refinery operations involve three main segments, namely crude oil storage and processing, intermediate processing, and product blending and distribution [1-3]. While the first involves upstream operations from ship arrivals to crude distillation, the last involves downstream operations from the blending of hydrocarbon fractions to the storage and delivery of final products. Gasoline is one of the most profitable products of an oil refinery and can account for as much as 60-70% of total profit [4-6]. An oil 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 concept and techniques of mixed-integer optimization 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 blending recipe and scheduling decisions make this problem a non-convex mixed-integer nonlinear optimization model (MINLP).
Early work [7-8] on this problem focused mainly on optimal blending of various intermediate fractions and some additives to meet product quality specifications. They did not provide an integrated solution that considers resources allocation and temporal decisions as well . Several efforts [1,4,6,9-10] have been made to address the problem of scheduling of gasoline blending operations. Most of them have considered only select aspects of the full gasoline-blending problem. An integrated treatment of recipe, blending, scheduling, and distribution is missing. Recently, Li et al.  and Li and Karimi  developed single-grid and multi-grid slot-based continuous-time formulations for the simultaneous treatment of recipe, blending, and scheduling. They incorporated many problem features such as non-identical parallel blenders, minimum run length and amount in a blend run, constant blending rates, changeover, one blender charging at most one tank at a time, multi-purpose product tanks, piecewise constant profiles for blend component qualities and feed rates, etc. They developed a schedule adjustment procedure to solve successive MILPs instead of the non-convex MINLP. Castillo and Mahalec [12-13] addressed the same problem as that of Li et al.  and Li and Karimi  and developed a discrete-time formulation. They also imposed additional operational features including minimum blend run thresholds. To solve the large-scale optimization model, they proposed the inventory pinch based solution algorithm which decomposed the entire problem into three levels. As a result, no global optimization approach has been presented to solve this overall problem.
In the presentation, we first develop a new unit-specific event-based continuous-time formulation for the integrated treatment of recipe, blending, and scheduling of gasoline blending and delivery operations. We include all operational features of Li et al. , Li and Karimi , and Castillo and Mahalec [12-13] such as non-identical parallel blenders, minimum blend length and amount in a blend run, constant blending rate in a blend run, product independent, production dependent, and product sequence dependent transition times, one blender charging at most one tank at a time, multi-purpose product tanks, piecewise constant profiles for blend component qualities and feed rates, etc. We use linear blending indices to develop appropriate linear blending correlations for properties. The non-convexities mainly arise from forcing constant blending rates during blend runs. To solve this model to e- (e.g., 1%) global optimality, we propose a hybrid global optimization approach in which we first allow blending rates to vary during blending runs, then we follow the adjustment procedure from Li et al.  and Li and Karimi  to obtain feasible solutions where constant blending rates are enforced. These feasible solutions are used as starting points to initialize commercial solvers (e.g., CONOPT ) to generate local optimal solutions. After that, we fix the constant blending rates to construct MILP problems and develop an iterative MILP and NLP procedure to improve solution quality until some termination criteria are met. Finally, we use the global optimization solver ANTIGONE to further improve the solution quality if the e- global optimality is not obtained after the iterative MILP and NLP procedure. We solve 14 industrial-scale examples from Li and Karimi  to illustrate the effectiveness of our proposed formulation and hybrid global optimization approach. The computational results demonstrate that our proposed formulation does improve the MILP relaxation of Li and Karimi . Furthermore, all 14 examples are solved to be 1% global optimality within reasonable computational effort.
Keywords: gasoline; blending; scheduling; non-convex; mixed integer nonlinear programming (MINLP); global optimization
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