Minimizing the total weighted completion time on unrelated parallel machines with stochastic times

This paper addresses the problem of batch scheduling in an unrelated parallel machine environment with sequence dependent setup times and an objective of minimizing the weighted mean completion time. Identical jobs are batched together and are available at time zero. Processing time of each job of a batch is determined according to both the machine it will be assigned to and the batch group to which the job belongs. The jobs' processing times and setup times are stochastic for better depiction of the real world. This is a NP-hard problem and in this paper, a solution heuristic is developed and compared to existing ones using simulation. The results and analysis obtained from the computational experiments proved the superiority of the proposed algorithm PMWP over the other algorithms presented.