On scheduling to minimize earliness-tardiness and batch delivery costs with a common due date

Abstract

In this paper, we consider a single-machine scheduling problem where all jobs have a common due date. The problem is to minimize the sum of earliness and tardiness penalties and the delivery costs of the tardy jobs, where the tardy jobs are delivered in batches with a fixed cost per batch. Our approach is to use a pseudo-polynomial dynamic programming algorithm to solve the problem. We also discuss some special cases that are solvable in polynomial time and show that for a given schedule of tardy jobs, the problem of scheduling the batch deliveries is equivalent to the dynamic lot sizing problem. We describe how the general problem is much more difficult. Finally, we present the results of empirical testing of the dynamic program and a number of heuristics developed.