A heuristic approach to minimizing weighted tardiness and overtime costs in single resource scheduling

Many firms face practical scheduling challenges in balancing the costs of overtime against the costs of tardiness, where tardiness costs vary by job or project. This paper addresses this challenge by considering scheduling jobs for processing during a finite number of discrete periods on a single resource. The resource can process jobs in two modes, regular time and overtime, at different costs per unit time, and jobs cannot be preempted. Each job has associated release and due dates, and tardy jobs incur a job-specific cost per period tardy. The schedule planner wishes to minimize the sum of weighted job tardiness and resource overtime costs. We provide a pseudopolynomial time algorithm for determining the optimal usage of regular time and overtime for any fixed sequence of jobs. We use this algorithm as a subroutine for heuristically solving the general scheduling problem using a priority sequencing rule. A local search algorithm then improves upon the initial solution generated by the priority rules. We use a strengthened linear programming formulation to provide good lower bounds for assessing the performance of the heuristics. Computational tests show that the algorithm generates close to optimal solutions for problems with high tardiness costs in reasonable computing time.