A Novel Arc-Flow-Graph-Based Modeling and Optimization Method for Parallel-Machine Parallel-Batch Scheduling Problems with Non-Identical Release Time and Product Specifications

Batch processing machine scheduling problems (BPMSP) are an important branch of production scheduling problems and are widely used in many industries including semiconductor manufacturing and metal processing, etc. In this paper, we propose a novel pattern transfer graph and an arc flow graph for a parallel-batch processing problem of jobs with non-identical release time and specifications on parallel machine scenarios with capacity limits. They are used to describe the process of job transfer between batches and the arrangement within batches. Based on them, a novel mixed linear integer programming model is formulated. Unlike the general models, the scale of the formulation is independent of the number of jobs but only related to the number of different kinds of processing time, release time, and specifications of jobs. We compare our model with the state-of-the-art model and demonstrate its significant advantage in solving large-scale instances. In addition, its performance is also tested on a practical problem of nonferrous metal processing to show its great industrial application potential.