Preprocessing and tightening methods for time-indexed MIP chemical production scheduling models

Abstract

We propose a series of preprocessing algorithms for the generation of strong valid inequalities for time-indexed, discrete and continuous, mixed-integer programming scheduling models for problems in network production environments. Specifically, starting from time-and inventory-related instance data, the proposed algorithms use constraint propagation techniques to calculate parameters that are used to bound the number of times subsets of tasks can be executed in a feasible solution. We also extend some of the propagation ideas to generate three classes of new tightening constraints. The proposed methods result in tightening constraints expressed in terms of assignment binary variables (if task is assigned to start on unit at time point) which are present in all time-indexed MIP models, therefore they are applicable to all time-indexed models accounting for a wide range of processing features. Finally, the methods are shown to lead to up to two orders of magnitude reduction in computational time when optimal solutions are found and significantly improve optimality gap when a time limit is enforced.

Discrete-time mixed-integer programming models and solution methods for production scheduling in multistage facilities

“…Merchan and Maravelias extended these methods to generate tightening constraints for maximization problems in network environments (Merchan and Maravelias, 2016). In this case, the external restrictions come from initial inventory and available time.…”

“…Thus, only the methods developed for maximization problems in network environments based on time-based data are applicable to sequential environments. Merchan and Maravelias consider the calculation of explicit time windows for each unit and task-unit combination (Merchan and Maravelias, 2016) using the following parameters: Earliest start time of task in unit Earliest start time of unit , Shortest tail of task in unit , i.e. minimum time to the end of the horizon from the end of execution of in so that it leads to final products.…”

“…Merchan and Maravelias also proposed tightening constraints based on variable earliest start time and shortest tail (Merchan and Maravelias, 2016). Let , respectively denote the actual start time and tail of task in unit .…”

“…Tightening methods based on variable time windows were recently introduced for network environments (Merchan and Maravelias, 2016). Earliest start time and shortest tail parameters were treated as variables used to formulate constraints that are tighter than ones employing fixed counterparts.…”

“…It is necessary to develop constraints that describe the dependency between start times -and between tails-of different batches. There are two cases that can be extended to MBPSP: (1) subsequent tasks, and (2) tasks that share a common unit (Merchan and Maravelias, 2016). Case (1) is already covered through equations (67) and (68), since in sequential environments the intermediate material produced by batch on stage can only be consumed by the same batch on its next stage, .…”