Solving the Unrelated Parallel Machine Scheduling Problem with Additional Resources Using Constraint Programming

This work studies the Unrelated Parallel Machine scheduling problem subject to additional Resources (UPMR). A set of jobs are to be processed by a set of unrelated parallel machines. The processing time and the number of needed resources for each job depend on the machine processing it. Resources are renewable and available in a limited amount. The objective to minimize is the maximum completion time. We formulate the problem using a constraint programming model and solve it using the state-of-the-art solver. We compare the results of this model against the existing approaches of the literature on two sets of small and medium instances. On the set of small instances, we show that the proposed model outperforms existing approaches and optimality is attained for all instances of the set. We further investigate its performance on the medium instances and show that it is able to reach more optimal solutions than any performing approach.