A beam search heuristic for scheduling a single machine with release dates and sequence dependent setup times to minimize the makespan

• A novel mixed integer linear program is proposed for the scheduling problem.
• Experiments showed that a commercial solver can only solve small instances.
• A beam search (BS) heuristic is proposed to solve larger instances.
• Experiments showed that the BS heuristic finds high quality solutions at low cost.

This paper considers the problem of scheduling a set of jobs subject to arbitrary release dates and sequence-dependent setup times on a single machine with the objective of minimizing the maximum completion of all the jobs, or makespan. This problem is often found in manufacturing processes such as painting and metalworking. A new mixed integer linear program (MILP) is firstly proposed. Because the problem is known to be NP-hard, a beam search heuristic is developed. Computational experiments are carried out using a well-known set of instances from the literature. Our results show that the proposed heuristic is effective in finding high quality solutions at low computational cost.