A matheuristic approach for an integrated lot-sizing and scheduling problem with a period-based learning effect

TL;DR

This paper introduces a matheuristic approach for a complex multi-product lot-sizing and scheduling problem with a novel period-based learning effect, demonstrating effective solutions and insights into the impact of learning on manufacturing costs.

Contribution

It develops a new MILP model with a period-based learning effect and proposes matheuristic methods to solve large-scale instances efficiently.

Findings

The simplified model performs well in solution quality and computational time.

Proposed matheuristics achieve satisfactory results for large instances.

Incorporating post-processing with lot-streaming significantly improves objectives.

Abstract

This research investigates a multi-product capacitated lot-sizing and scheduling problem incorporating a novel learning effect, namely the period-based learning effect. This is inspired by a real case in a core analysis laboratory under a job shop setting. Accordingly, a Mixed-Integer Linear Programming (MILP) model is extended based on the big-bucket formulation, optimizing the total tardiness and overtime costs. Given the complexity of the problem, a cutting plane method is employed to simplify the model. Afterward, three matheuristic methods based on the rolling horizon approach are devised, incorporating two lower bounds and a local search heuristic. Furthermore, a post-processing approach is implemented to incorporate lot-streaming possibility. Computational experiments demonstrate: 1) the simplified model performs effectively in terms of both solution quality and computational time; and 2) although the model encounters challenges with large-scale instances, the proposed matheuristic methods achieve satisfactory outcomes; and 3) it can be inferred that the complexity of the models and solution methods are independent of the learning effect; however, the value of learning effect may impact the performance of the lower bounds; 4) in manufacturing settings, where the lot-streaming is possible, incorporating post-processing can drastically improve the objective function; 5) the impact of the period-based learning effect in the results is significant, and the model's sensitivity to time-based parameters (e.g., learning rate) is more than cost-based ones (e.g., tardiness cost).