• single machine;
  • batch scheduling;
  • step-deterioration;
  • flowtime


Both topics of batch scheduling and of scheduling deteriorating jobs have been very popular among researchers in the last two decades. In this article, we study a model combining these two topics. We consider a classical batch scheduling model with unit-jobs and batch-independent setup times, and a model of step-deterioration of processing times. The objective function is minimum flowtime. The optimal solution of the relaxed version (allowing non-integer batch sizes) is shown to have a unique structure consisting of two consecutive decreasing arithmetic sequences of batch sizes. We also introduce a simple and efficient rounding procedure that guarantees integer batch sizes. The entire solution procedure requires an effort of O(n) (where nis the number of jobs.) © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012