Complexity and Approximation Results for Setup-Minimal Batch Scheduling with Deadlines on a Single Processor

Abstract

We address the problem of sequencing n jobs that are partitioned into F families on a single processor. A setup operation is needed at the beginning of the schedule and whenever a job of one family is succeeded by a job of another family. These setup operations are assumed to not require time but are associated with a fixed setup cost which is identical for all setup operations. Jobs must be completed no later than by a given deadline. The objective is to schedule all jobs such that the total setup cost is minimized. This objective is identical to minimizing the number of setup operations. We provide a sketch of the proof of the problem’s strong NP-hardness as well as some properties of optimal solutions and an $O(n \log n + nF)$ algorithm that approximates the cost of an optimal schedule by a factor of F. For details, we refer to our full paper.