A novel genetic algorithm for the hybrid flow shop scheduling with parallel batching and eligibility constraints

The hybrid flow shop with parallel batching (HFSPB) is a kind of flow shop production system wherein some stages may be populated by parallel processors that simultaneously process groups of jobs. This paper addresses the makespan minimization problem for a HFSPB system whose machines are characterized by both capacity and eligibility restrictions. Firstly, a mixed integer linear programming model concerning the proposed problem is presented. Then, a specific genetic algorithm (GA) that makes use of a permutation encoding scheme as well as a crossover operator specifically designed for effectively managing the batch processing is discussed. The relevant parameters of the developed algorithm were calibrated by means of a full factorial design of experiments, and an extensive comparison campaign has been carried out with the aim to statistically assess the performance of the proposed GA with respect to five alternative procedures, four of which arisen from the relevant literature. The obtained results, also supported by a properly developed ANOVA analysis, demonstrate the effectiveness of the proposed GA-based metaheuristics in tackling the HFSPB problem investigated, under both quality of solutions and computational burden viewpoints.