Maximizing service level in a β-robust job shop scheduling model

In the realm of scheduling problems, different sources of uncertainty such as probabilistic durations of jobs or stochastic breakdowns of machines can arise. Given this, one highly desirable characteristic of an intelligent schedule is to bring better punctuality with less efficiency-loss because a dominant factor in customer appreciation is punctuality. It is also one of the most intangible topics for managers when a due date is predetermined to deliver jobs. In this paper, we address the β-robust job shop scheduling problem when the processing time of each operation is a normal random variable. We intend to minimize the deviation of makespan from a common due date for all jobs which corresponds to maximizing the service level, defined as probability of the makespan not exceeding the given due date. We develop a branch-and-bound algorithm to solve the problem. Using a set of generated benchmark instances, the performance of the developed algorithm has been evaluated.