A novel MILP formulation for short-term scheduling of multistage multi-product batch plants

This study presents a continuous-time mixed-integer linear programming mode l for short-term scheduling of multistage multi-product batch plants. The m odel determines the optimal sequencing and the allocation of customer order s to non-identical processing units by minimizing the earliness and tardine ss of order completion. This is a highly combinatorial problem, especially when sequence-dependent relations considered to be are such as the setup ti me between consecutive orders. A common approach to this scheduling problem relies on the application of tetra-index binary variables, i.e. (order, or der, stage, unit) to represent all the combinations of order sequences and assignments to units in the various stages. This generates a huge number of binary variables and, as a consequence, much time is required for solution s. This study proposes a novel formulation that replaces the tetra-index bi nary variables by one set of tri-index binary variables (order, order, stag e) without losing the model's generality. By the elimination of the unit in dex, the new formulation requires considerably fewer binary variables, thus significantly shortening the solution time. (C) 2000 Elsevier Science Ltd. All rights reserved.