An Optimization Model for Production Scheduling in Parallel Machine Systems

The efficiency and quality of the manufacturing industry are greatly influenced by production scheduling, which makes it a crucial aspect. A well-designed production scheduling scheme can significantly enhance manufacturing efficiency and reduce enterprise costs. This paper presents a tailored optimization model designed to address a more complex production scheduling problem that incorporates parallel machines and preventive maintenance. The proposed solutions aim to achieve a balance between job sequence and machine reliability, considering the minimum maintenance cost rate for determining maintenance cycles of deteriorating machines in real manufacturing scenarios. Furthermore, the objective of minimizing the maximum completion time guides machine assignment and job sequence based on maintenance constraints. The innovation lies in the introduction of a greedy algorithm that utilizes a water injection model to address this NP-hard integrated problem. A pre-distribution model is constructed using the water injection model, and its solution is utilized as input for constructing the production scheduling model, which aids in determining machine assignment and job sequence. This algorithm demonstrates remarkable effectiveness and efficiency, enabling the achievement of an optimal solution. A numerical example is presented to illustrate the computational process, accompanied by an extensive discussion of the results showcasing improved performance. Furthermore, the optimization model developed in this paper can be adapted to tackle the production scheduling problem with modifications tailored for parallel machines.