A heuristic method for multi-objective hybrid flow shop scheduling problem with parent-child relationships and space constraints

In modern ship manufacturing, a ship is divided into hundreds of blocks in the design stage, and the productivity of the block manufacturing process is vital to ship delivery. This paper investigates the production scheduling problem of ship blocks with the parent-child relationship; this relationship is characterised by the fact that sibling jobs at the same BOM layer must be processed on adjacent machines at their assembly stages. We formulate this problem as a multi-objective hybrid flow shop scheduling problem: the first objective is to minimise the total deviation from the target time of the jobs and the second one is to minimise the total processing time. To solve this problem, we propose a heuristic method based on the multi-objective genetic algorithm, in which an adjacent machine priority method is first proposed to generate feasible solutions that satisfy the space constraints. Then, we improve the individual quality in crossover and mutation of the algorithm via tabu search. We verify the performance of our algorithm by test instances generated from real manufacturing data of a shipbuilding company. Results show that the proposed method outperforms the existing algorithms when identifying the Pareto optimal solutions, especially for large-sized problems.