A hybrid approach based on the variable neighborhood search and particle swarm optimization for parallel machine scheduling problems—A case study for solar cell industry

This paper studies a solar cell industry scheduling problem which is similar to the traditional hybrid flow shop scheduling (HFS). In a typical HFS with parallel machines problem, the allocation of machine resources for each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage could be determined. However, the challenge in solar cell manufacturing is the number of machines can be dynamically adjusted to complete the job within the shortest possible time. Therefore, the paper addresses a multi-stage HFS scheduling problem with characteristics of parallel processing, dedicated machines, sequence-independent setup time, and sequence-dependent setup time. The objective is to schedule the job production sequence, number of sublots, and dynamically allocate sublots to parallel machines such that the makespan time is minimized. The problem is formulated as a mixed integer linear programming (MILP) model. A hybrid approach based on the variable neighborhood search and particle swarm optimization (VNPSO) is developed to obtain the near-optimal solution. Preliminary computational study indicates that the developed VNPSO not only provides good quality solutions within a reasonable amount of time but also outperforms the classic branch and bound method and the current industry heuristic practiced by the case company.