Just-in-time single-batch-processing machine scheduling

In this paper, we study a single-batch-processing machine (SBPM) scheduling problem by considering a just-in-time criterion. Our objective is to minimize the total weighted earliness and tardiness (WET) penalties of jobs, where the penalty rates of jobs are job-independent but the earliness and tardiness penalty rates are different, and different jobs may have different due dates. An SBPM can process several jobs simultaneously as a batch. We first model this scheduling problem using a mixed-integer linear model. We design two priority rules, i.e., earliest due date (EDD) and earliest starting time (EST), to sort jobs. Based on our analysis on the mathematical properties of this scheduling problem, we propose two heuristic algorithms AABF and ITSLS to construct and improve the near-optimal schedules. We also devise a lower bound method on a new approximate time-indexed formulation. Extensive numerical experiments demonstrate the effectiveness and efficiency of our algorithms.