Constructive heuristics for the unrelated parallel machines scheduling problem with machine eligibility and setup times

Abstract This work considers a scheduling problem identified in a factory producing customised Heating, Ventilation and Air Conditioning (HVAC) equipment. More specifically, the metal folding section is modelled as unrelated parallel machines with machine eligibility and sequence-dependent setup times. The objective under consideration is the minimisation of the total tardiness. The problem is known to be NP-hard so approximate methods are needed to solve real-size instances. In order to embed the scheduling procedure into a decision support system providing high-quality solutions in nearly real time, the goal of this paper is to develop fast, efficient constructive heuristics for the problem. Due to the lack of methods for this specific problem, some existing heuristics and one metaheuristic are selected from related problems and adapted. In addition, a set of heuristics with novel repair and improvement phases are proposed. The performance of the methods adapted and the proposals are compared with the optimal/approximate solutions obtained by a solver for an MILP in two sets of instances with small and medium sizes. Additionally, big-size instances (representing more realistic cases for our company) have been solved using the proposed constructive heuristics, providing efficient solutions in negligible computational times. Even if the adaptation of heuristics performs reasonably well, these are outperformed by the new heuristic proposed in this paper. In addition, when the new heuristic is embedded in the metaheuristic adapted from a related the problem, the results obtained are excellent in terms of the quality of the solution, even if the computational effort is somewhat higher.