Robust Single-machine Scheduling based on Bad-scenario Set

This paper discusses a single-machine scheduling problem with uncertain processing times, which are described by scenario approach. A new robust optimization model is built based on the concept of bad-scenario set. The optimization objective aims to minimize the performance deviation compared to the corresponding optimal solution. To obtain the optimal solution of the robust model problem, a branch and bound algorithm is developed, and a pruning rule and a method of getting the upper bound and lower bound values are designed. A large number of instances were tested, and the computational results are reported to demonstrate the advantages of the proposed robust optimization model and the effectiveness of the developed algorithm.