A Continuous Time Mixed Integer Linear Programming Model for Short Term Scheduling of Multistage Batch Plants

Abstract

The problem of short term scheduling of batch plants consists of determining the optimal production policy for satisfying the production demands for different products at due dates and/or at the end of a given time horizon. The objective of the work is to propose an optimization model and solution method to the short term scheduling of batch plants with multiple stages which may contain equipment in parallel. A large scale mixed integer linear programming (MILP) model with continuous time domain representation is proposed that relies on the use of parallel time axes for units and tasks. Although in principle an LP-based branch and bound method can be used to solve the problem, there is a limitation when the instances become large. The first solution strategy that is proposed consists of the use of preordering constraints. Furthermore, a second strategy relies on a decomposition scheme for large systems which is based on the solution of an MILP model that minimizes total in process time in which assignments are determined and the subsequent solution of an LP to minimize earliness and to eliminate unnecessary setups. Several examples are presented, including a large real world problem, to illustrate the performance of the model and solution method