A New Mathematical Model to Minimize Penalty Costs for a Single Machine with an Overtime Constraint

The problem studied in this paper was to schedule jobs in a single machine production system with an overtime constraint. A new mathematical model is now proposed to minimize the total penalty cost, which is described as tardiness, overtime, earliness, and the idle time costs. The proposed math model is capable of improving some impractical overtime concepts, as reported in the literature. The proposed model was evaluated by using a set of hypothetical data that was generated from a new instance generator for scheduling problems named IGSP. Since the proposed math model is classified as NP-hard, the optimal solutions can be determined only for the problem of `up-to-20-jobs' within 120 minutes. Hence, for a large-scale problem, a satisfactory metaheuristic is required, in order to determine a near-optimal solution, within a short computational time.