Deterioration-Aware Collaborative Energy-Efficient Batch Scheduling and Maintenance for Unrelated Parallel Machines Based on Improved MOEA/D

The deterioration phenomenon is common and lasting as machines' service time increases within energy-intensive manufacturing processes such as heat treatment, which may bring about processes time extension or even the breakdown of a machine. It is crucial to collaboratively optimize batch scheduling and maintenance to ensure stable, efficient production, and achieve energy efficiency. This study takes into account preventive maintenance, where a maintenance activity is carried out after a certain number of batches are processed. A novel multi-objective mixed-integer programming model for unrelated parallel batching machines is proposed to minimize the makespan, total completion time and total energy consumption. The entire problem is broken down into four sub-issues: job division, job dispatching, batch formation and batch sequencing. Given the NP-hard nature of the problem, three heuristic algorithms based on several structural properties are designed according to the features of the latter three parts. Meanwhile, an integrated methodology, a Multi-Objective Evolutionary Algorithm based on Decomposition combined with Variable Neighborhood Search (MOEA/D-VNS), is put forward to handle job division and the multi-dimensional collaborative optimization problem. The performance of the proposed algorithms is compared with that of other typical dominance-based evolutionary algorithms. Extensive numerical experiments are conducted to validate the effectiveness of the proposed model and algorithms.