Solving Multi-stage Flexible Flow Shop Scheduling Problem with Cooling Times in the Steel Industry

Lotfi HIDRI

Abstract

Steel manufacturing includes multiple production stages, such as steel-making, and rolling. Multi-stage flexible flow shops are used for modelling this process. Cooling is one of the operations encountered in the steel-making process, which is essential for controlling the microstructure of the steel, as it directly affects its mechanical properties. A proper cooling operation can enhance the strength, hardness, and durability of the final product. Moreover, it helps to prevent defects such as metal warping and cracking, thereby ensuring a better quality and usability of the end product. While preparing the production schedule, the cooling time is generally ignored or included in the processing time for a certain task. As the cooling time can be more significant in some cases, this study considers it separately from the processing time. This paper tackles the complex problem of multi-stage flexible flow shop scheduling with cooling times, which is known to be strongly NP-hard. In order to find near-optimal solutions for this problem, a two-phase heuristic optimisation algorithm is proposed, using the solution obtained for the parallel machine scheduling problems with specific constraints such as release dates, cooling times, and delivery times. This paper also presents a novel and efficient lower bound for the aforementioned scheduling problem, which is employed for assessing the performance of the heuristic algorithm by relaxing the capacity constraints in all stages, except for one of them. The comprehensive experiments which were carried out based on standard benchmark test problems validate the effectiveness of the proposed methods.

Keywords

Multi-stage flexible flow shop, Steel-making industry, Cooling time, Heuristic, Lower bound.

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