Mathematical models for multi-stage hybrid assembly flow-shop scheduling with preventive maintenance and release times

Abstract

Effective job scheduling is crucial in production to reduce costs, improve customer satisfaction, enhance efficiency, and boost competitiveness, leading to transformative impacts in production environments. This article presents a pioneering approach that addresses assembly and processing at multiple stages in the scheduling process. Specifically, we introduce the first formulation of mixed integer linear programs (MILP) for a Multi-stage Hybrid Assembly Flow-shop with identical parallel machines. The models incorporate considerations for job release times and service tasks to implement preventive maintenance and effectively captures the intricacies of a Multistage Assembly flow-shop. Existing literature in Assembly flow-shop scheduling primarily focuses on the two-stage assembly flow-shop scheduling problem (TSAFSP) and its extensions, such as the three-stage assembly flow-shop scheduling problem, the Distributed two-stage assembly flow-shop scheduling problem (DTSAFSP), the Distributed assembly permutation flow-shop Scheduling Problem (DAPFSP), and the multi-stage assembly flow shop (MSAF). Our work deals with a challenging NP-hard problem. Inspired by a real-life production site dedicated to manufacturing heavy machinery, we validate our proposed mathematical models by solving various instances of the problem using exact methods. The experimental results confirm the effectiveness and robustness of our approach in tackling multi-stage hybrid assembly flow shop scheduling challenges.