Mathematical Models and Optimal Algorithms for Lot Scheduling Considering Job Splitting and Due Dates in Green Logistics

Lot scheduling is a promising manufacturing mode in green logistics that can efficiently save energy and reduce production costs. It has been widely applied to integrate circuit tests in semiconductor factories, textile processing in garment workshops, etc. Each processing lot is of a fixed capacity and identical processing time, and completes more than one job simultaneously. Jobs with sizes and due dates are allowed to be arbitrarily split and processed in consecutive lots. They are delivered immediately upon completion. To the best of our knowledge, in the domain of lot scheduling, there exist no mathematical programming models that describe the above features simultaneously. In this work, we focus on the single machine environment and mainly consider two lot scheduling problems with the objectives of minimizing the maximum lateness and the total tardiness, respectively. For the problems, we first propose new mixed integer linear programming models (solved by commercial solvers), which enable a systematic understanding of the studied problems and serve as a mathematical programming basis for more complicated problems. We then prove that the Earliest Due-Date (EDD) first rule and the Shortest Processing Time (SPT) first rule can optimally solve the two problems, respectively, provided that the due dates and job sizes are agreeable, i.e., a later due date indicates a larger size of job. Experimental results show the efficiency of our methods and managerial insights are drawn.