Makespan minimization for batching work and rework process on a single facility with an aging effect: a hybrid meta-heuristic algorithm for sustainable production management

This paper takes into account a single facility that produces good quality as well as defective units in batches. In addition, units produced on the facility are inspected for quality in batches. Herein, after the inspection is completed, the defective units of the inspected batch are reworked. Each reworked unit has the required good quality. When the facility is related to reworking defective units, there is an aging effect in which the processing time of a defective unit depends on its position in a sequence. Subsequently, when reworking of all defective units in each batch is completed, a maintenance activity is required, after which the facility will be restored to its initial condition. In addition, it is assumed that the percentage of the defective units is the same in each batch. The objective is to find the number of batches and their (integer) size such that the makespan is minimized. The major contributions of this paper can be summarized in two aspects. Firstly, we propose a new reasonable model for an imperfect production of a single product, and secondly, to solve the proposed model, a hybrid meta-heuristic algorithm comprising genetic algorithm, variable neighborhood search and simulated annealing algorithms is developed. The experimental results confirms that the hybrid algorithm can be proposed to sustainably solve this problem.