Strategic delay in job shop scheduling: non-zero start time optimisation under multi-constraint environments

Traditional job shop scheduling models typically assume non-delay schedules, where all jobs start as early as possible, often at time zero, to minimise makespan or related costs. However, in real-world environments with multiple constraints, such as the manufacturing, aviation, and medical industries, this assumption may not yield optimal results. This study presents a strategic delay scheduling model, where the start time of each job is flexible, rather than being restricted to zero or its earliest possible moment. Unlike passive delays imposed by predecessor constraints, these non-zero start times represent a proactive strategic choice to synchronise with resource availability. By allowing optimised non-zero start times and discontinuous job execution within time windows, the model effectively aligns critical resources with specific availability windows to minimise unnecessary expenditures by reducing idle costs. To implement this model, a space-efficient encoding scheme guided by structural symmetry is proposed. Computational experiments show that the proposed encoding scheme achieves an average 56.46% reduction in idle costs compared to traditional non-delay ones. These results suggest that strategic delay is an effective approach for enhancing resource utilisation in cost-sensitive industries where idle time carries a significant financial penalty.