Switched max-plus linear-dual inequalities for makespan minimization: the case study of an industrial bakery shop

TL;DR

This paper models an industrial bakery's scheduling problem using switched max-plus linear-dual inequalities, demonstrating a faster solution approach for minimizing makespan in flow shops with time constraints.

Contribution

It introduces a novel modeling approach with switched max-plus linear-dual inequalities for flow shop scheduling with time windows.

Findings

The max-plus algebra approach yields faster solutions than standard methods.

The modeling approach is applicable to any permutation flow shop with time-window constraints.

The method improves scheduling efficiency in industrial settings.

Abstract

In this paper, an industrial bakery shop is modeled by switched max-plus linear-dual inequalities (SLDIs). SLDIs are timed discrete event systems suitable for describing flow shops with time-window constraints and switching operating modes, where each mode corresponds to a job type. We consider the scheduling problem of minimizing the makespan of the shop, and we show that the application of methods based on the max-plus algebra leads to a faster solution compared to standard techniques. The results of the paper are general, in the sense that they can be applied to any permutation flow shop with time-window constraints.