Mixed Integer Linear Programming in Process Scheduling: Modeling, Algorithms, and Applications

Abstract

This paper reviews the advances of mixed-integer linear programming (MILP) based approaches for the scheduling of chemical processing systems. We focus on the short-term scheduling of general network represented processes. First, the various mathematical models that have been proposed in the literature are classified mainly based on the time representation. Discrete-time and continuous-time models are presented along with their strengths and limitations. Several classes of approaches for improving the computational efficiency in the solution of MILP problems are discussed. Furthermore, a summary of computational experiences and applications is provided. The paper concludes with perspectives on future research directions for MILP based process scheduling technologies.Process scheduling has attracted an increasing amount of attention from both the academia and the industry in the past decade. The reason for this is twofold. First, it reflects the pressure faced by the chemical processing and manufacturing related industries to improve productivity and reduce costs. Second, it is driven by the substantial advances of related modeling and solution techniques, as well as the rapidly growing computational power. The problem of interest is to determine the most efficient way to produce a set of products in a time horizon given a set of limited resources and processing recipes. The activities to be scheduled usually take place in multiproduct and multipurpose plants, in which a wide variety of different products can be manufactured via the same recipe or different recipes by sharing limited resources, such as equipment, material, time, and utilities. These types of plants have long been employed to manufacture chemicals in small quantities which have high added-values or frequently changing process parameters or demands. Their inherent operational flexibility provides the platform for great benefits that can be obtained through good production schedules.Mathematical programming, especially Mixed Integer Linear Programming (MILP), because of its rigorousness, flexibility and extensive modeling capability, has become one of the most widely explored methods for process scheduling problems. Applications of MILP based scheduling methods range from the simplest single-stage *

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