Heuristics for parallel machine scheduling with GoS eligibility constraints

Heuristics for parallel machine scheduling with GoS eligibility constraints

The parallel machine scheduling problem with the consideration of GoS (grade of service) constraints originates from the service provision of different membership levels in the service industry. This scheduling problem has been widely found in industrial manufacturing and sustainable manufacturing practices. For example, in a sustainable manufacturing production line, multiple machines are set up as parallel machines to support each other to achieve shared manufacturing. However, the machines still have processing constraints with different service level constraints and do not support all jobs. This study investigates this parallel machine scheduling problem and uses the total completion time as the objective criterion. This criterion has not been studied in the literature for this scheduling problem. Several heuristics are proposed to solve the two-machine and multi-machine scheduling problems. The structure of these heuristics is mainly divided into two stages: the SPT rule and the insertion method. In addition, a fast method for calculating the total completion time is developed from the insertion method. The experimental results prove that the proposed heuristics are effective in solving this scheduling problem. For both small- and large-size problems, the proposed heuristics can obtain good solutions quickly and are potentially suitable for practical use.