Mixed-Integer Linear Programming Model for Refinery Short-Term Scheduling of Crude Oil Unloading with Inventory Management

Abstract

This paper addresses the problem of inventory management of a refinery that imports several types of crude oil which are delivered by different vessels. This problem involves optimal operation of crude oil unloading, its transfer from storage tanks to charging tanks, and the charging schedule for each crude oil distillation unit. A mixed-integer optimization model is developed which relies on time discretization. The problem involves bilinear equations due to mixing operations. However, the linearity in the form of a mixed-integer linear program (MILP) is maintained by replacing bilinear terms with individual component flows. The LP-based branch and bound method is applied to solve the model, and several techniques, such as priority branching and bounding, and special ordered sets are implemented to reduce the computation time. This formulation and solution method was applied to an industrial-size problem involving 3 vessels, 6 storage tanks, 4 charging tanks, and 3 crude oil distillation units over 15 time intervals. The MILP model contained 105 binary variables, 991 continuous variables, and 2154 constraints and was effectively solved with the proposed solution approach.

A Novel Priority-Slot Based Continuous-Time Formulation for Crude-Oil Scheduling Problems

“…In the case of the refinery problems introduced by Lee et al 1 , it can be shown that the number of relevant operations is bounded as long as the number of distillations is bounded. For example, if problem 1 is constrained to be solved with a maximum of 3 distillation operations, the maximum number of operations is 13 as in the sequence 7461483525746.…”

“…This paper presents a new continuous-time formulation, called single-operation sequencing (SOS) model, which can be used to solve the crude-oil operations problem introduced by Lee et al 1 . It is different from previous formulations as it requires to postulate the number of priority-slots in which operations take place instead of specifying the number of time intervals or event points to be used in the schedule.…”

“…Lee et al 1 defined a precise crude-oil scheduling problem involving crude unloading at berths, developped a discrete-time MINLP model, and solved a linear relaxation of the model. Later, Wenkay and Hui 12 improved the model and proposed an iterative approach to solve the MINLP model, taking into account nonlinear blending constraints.…”

“…The scheduling horizon is divided into fixed length sub-intervals, which are then divided in several variable length time-slots. In parallel, Jia et al 16 developed an operation specific event model and applied it to the problems introduced by Lee et al 1 , using a linear approximation of storage costs. A comparison of computational performances between both continuous-time and discrete-time models is given, showing tremendous decrease in CPU time.…”

Scheduling of a multiproduct pipeline system

“…Mixed integer models handle several subsections of the refinery, such as the Liquefied Petroleum Gas (LPG) production unit. Lee, Pinto, Grossmann, and Park (1996) develop a MILP model for the management and scheduling of crude oil that considers blending specification for the types of crude oil. Shah (1996) presents an MILP for crude oil scheduling of a system consisting of one port that connects one refinery through a pipeline.…”