An Efficient Heuristic to Minimise the Total Penalty Costs for a Single Machine Scheduling Problem with an Overtime Allowance

This paper proposes an efficient heuristic to minimise the total penalty costs for a single machine scheduling problem with an overtime allowance. The total penalty costs were defined as the sum of tardiness, earliness, and overtime costs. The mechanism of the proposed heuristic was backward and forward scheduling, with a trade-off process among the components of the total penalty costs. The efficiency of the proposed heuristic was evaluated by the average relative percentage deviation (ARPD) of the total penalty costs that were obtained from the proposed heuristic and mathematical model using a set of up-to-50-job hypothetical data. The results showed that the proposed heuristic performed impressively well, with an overall ARPD value of 0.65%, for the case studies. In addition, for a given sequence of jobs, the proposed heuristic obtained the solutions within a very short computational time when compared to the mathematical model.