Integrating preventive maintenance to two-stage assembly flow shop scheduling: MILP model, constructive heuristics and meta-heuristics

In this paper, flexible preventive maintenance (PM) activities are incorporated into two-stage assembly flow shop scheduling where m dedicated machines in the fabrication stage and one machine in the assembly stage. The operational status of each machine is described by a continuous variable, maintenance level. The maintenance level value is inversely proportional to the processing time. Once a PM activity is performed, this value will return to the initial value. Different from the PM at fixed predefined time intervals, flexible PM can be carried out at any time point, but the maintenance levels are not less than 0. Hence, a MILP model with maintenance level constraints is formulated to minimize the total completion time and maintenance time. Regarding the methods, a latest PM decision strategy is proposed to determine the execution time of PM activities. This new strategy is embedded into 15 constructive heuristics and 7 meta-heuristics (three variants of iterated local search, three variants of Q-learning-based ant colony system with local search and a Q-learning-based hyper-heuristics) to address this new problem. The final experimental analysis demonstrates the significance of the integrated model and the effectiveness of the proposed constructive heuristics and meta-heuristics.