Scheduling unrelated parallel machines with family setups and resource constraints to minimize total tardiness

This work considers the unrelated parallel machines scheduling problem with family setups and resource constraints. In this problem, jobs are grouped into families and setup times are required between jobs belonging to different families. The processing of a job requires a certain amount of resource from a machine, which is supplied by upstream processes. The total resource consumed by the jobs processed on a machine must not exceed the resource supply up. The objective is to schedule the jobs on the machines so that the total tardiness of the jobs is minimized. In attempting to obtain optimal solutions for small size instances, a mixed integer linear programming (MILP) model is proposed. Since the problem is a NP-hard combinatorial optimization problem, to obtain near optimal solutions we develop two meta-heuristic algorithms based on Simulated Annealing and Iterated Greedy. Computational experiments show that the presented algorithms can be successfully applied to the problem.