Integrated production, inventory, and batch delivery scheduling with due date assignment and two competing agents

This paper considers several integrated production, inventory, and batch delivery scheduling problems on a single machine with due date assignment and two competing agents, each of which seeks to optimize its own performance. All the jobs of the first agent have a common due date, which is a decision variable to be determined by the decision maker, whereas the due dates of the jobs of the second agent are exogenously given. The jobs of the same agent are processed sequentially in batches and the batch processing time is equal to the total processing time of the jobs in the batch, where the batch size can be either bounded or unbounded. A batch is available only when all the jobs in it are completed. An available batch is delivered to its agent immediately, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. Finished jobs are kept in inventory, if necessary, incurring an additional holding cost. The first agent wishes to find a job sequence, a common due date, and a dispatch date for each of its jobs that jointly minimize the total cost comprising the earliness, weighted number of tardy jobs, job holding, due date assignment, and batch delivery costs, while the second agent seeks to minimize one of the following criteria plus the batch delivery cost: the maximum value of a regular scheduling criterion, total completion time, and weighted number of tardy jobs. The overall objective is to minimize the objective value of the first agent, subject to the objective value of the second agent not exceeding a given threshold. For each of the problems considered, we study its computational complexity and develop exact and/or approximation solution algorithms.