New Fitness Evaluation for a Single Machine Scheduling Problem with an Overtime Option

Abstract

This research studies a single machine scheduling problem with overtime option. The objective is to minimise the total penalty cost (TPC), which is the sum of tardiness, earliness, and overtime costs. A new fitness evaluation heuristic (FEH) capable of minimising TPC is developed. Since FEH works well only when the sequence of jobs is known, it is then integrated into the fitness evaluation step of a variable neighbourhood search (VNS-FEH) to determine the optimal sequence of jobs that obtains the minimum TPC. Effectiveness of the proposed VNS-FEH is evaluated by using real data from three industrial case studies consisting of five job sizes (5, 10, 20, 50, 100) for each, resulting in 270 experiments. The best common parameter setting (BCS) of VNS-FEH applicable for all of the case studies is determined. The results show that TPC obtained from VNS-FEH with its BCS is deviated on average from the best TPC of 0.02%. Moreover, it is better than the bound obtained from the mathematical model with the relative percentage improvement (RPI) of 37.22%.