Single-Machine Batch Delivery Scheduling and Common due Date Assignment with Identical Processing Times

Abstract

This paper considers the problem of single-machine batch delivery scheduling with an assignable common due date where all jobs have identical processing times. Finished jobs are delivered in batches and the cost per batch delivery is fixed and independent of the number of jobs in the batch. For our problem, the penalties of earliness-tardiness are assumed to be arbitrarily weighted but the holding costs are equally weighted. The objective is to determine the common due date and find an optimal schedule to minimize the sum of total weighted earliness, tardiness, holding, due date, and delivery costs. We present some basic properties of the structure of the optimal schedule for the problem, and provide a polynomial dynamic programming algorithm.