Scheduling in parallel machines with two servers: The restrictive case

Abstract

In this paper we study the Parallel machine scheduling problem with Two Servers in the Restrictive case (PTSR). Before its processing, the job must be loaded on a common loading server. After a machine completes processing one job, an unloading server is needed to remove the job from the machine. During the loading, respectively the unloading, operation, both the machine and the loading, respectively the unloading, server are occupied. The objective function involves the minimization of the makespan. A Mixed Integer Linear Programming (MILP) model is proposed for the solution of this difficult problem. Due to the NP-hardness of the problem, a Variable Neighborhood Search (VNS) algorithm is proposed. The proposed VNS algorithm is compared against a state-of-the-art solver using a randomly generated data set. The results indicate that, the obtained solutions computed in a short amount of CPU time are of high quality. Specifically, the VNS solution approach outperformed IBM CPLEX Optimizer for instances with 15 and 20 jobs.