MIP formulations for identical parallel machine scheduling problem with single server

Abstract

This paper considers the problem of scheduling a set of independent jobs on an arbitrary number of identical parallel machines with setup consideration and a makespan objective. The setup operations are performed by one available server. We propose two mixed integer programming (MIP) formulations to solve optimally this problem. The performance of each model is compared with another MIP proposed in the literature. It turns out that our formulation based on time-indexed variables outperforms the other models.