Scheduling Model for a Multi‐Product Batch Plant Using a Pre‐Ordering Approach

Abstract

A scheduling model for a multi-product, multistage batch plant with parallel units is presented. The objective is to maximize the weighted completion times of orders in every processing stage while imposing a penalty on the slower orders. The proposed model uses the continuous-time representation mode and describes the allocations of tasks, units and stages by a set of binary variables. In order to reduce the model size and provide a more effective solution to the model, a pre-ordering approach that sorts the processing sequence of orders is developed. The pre-ordering approach identifies the infeasible assignments through which the number of binary variables is significantly reduced. Illustrative examples are provided to show that the size of the proposed model is small, and therefore, needs much less computational effort in comparison with the existing models in the literature.

A supervised self-organizing approach for large-scale multistage batch scheduling problems

“…Eq. (6) indicates that the TSOU with smaller time allowance is more likely to be selected, which will help the TSOUs finished on time. The selected TSOU will apply to RMSOUs for resources before being processed if need be.…”

“…The probability with which the TSOU t i,s in the IS j is selected by the ESOU u j in the second selection can be calculated by Eq. (6) with IS j instead of IW j . If there is no TSOU selected in the second selection, the ESOU will wait for the TSOU previously selected.…”

“…Various MILP-based approaches using different time representations have been proposed for scheduling of multistage batch facilities [2][3][4]. Moreover, some heuristic rules are used to reduce the size of MILP models [5][6]. However, the preordering constraints usually affect the optimality of the scheduling model, especially when the makespan is minimized.…”