Robustness of single machine scheduling problems to earliness and tardiness penalty errors

The Early/Tardy Machine Scheduling Problem is often proposed as a model of the situation faced by just-in-time manufacturers, whereby the objective is to minimize the weighted sum of early and tardy penalties for each job, and each penalty is proportional to the amount of time the job is early or tardy. Relatively little attention has been given in the literature to either the determination of these penalties or the effect that errors in estimating these penalties have on the final schedule. In this paper, we examine the sensitivity of the final schedule to errors in estimating these penalties. Results indicate that for some classes of problems, very large estimation errors can be sustained without compromising solution quality, whereas other problem classes require more careful evaluation of these penalties. Fortunately, the different classes of problem situations are relatively easy to identify.