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

Abstract

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. Scope and purpose This paper addresses a practical job or project scheduling problem in which the schedule planner is concerned with both overtime and tardy delivery costs. In many scheduling contexts, when multiple jobs compete for a resource with limited capacity, operations managers must determine the sequence in which to process jobs. One lever management can use to avoid tardy project or job delivery is through the use of overtime, which typically comes at an increased cost to the firm. When different jobs have different priorities and, therefore, different tardiness costs, the problem of determining the best plan for sequencing jobs and for using overtime to complete jobs is highly complex and has not been adequately addressed in the literature. This paper provides a heuristic scheduling algorithm for solving these problems. The problem considered generalizes several well-known problems in the single-machine scheduling literature (M. Pinedo, Scheduling: Theory, Algorithms and Systems, Upper Saddle River, Prentice-Hall, NJ, 2002), while the heuristic algorithm is based on highly effective local search methods (Ghosh and Chakravarti, Comput. Oper. Res. 26(3) (1999) 271) developed for providing good solutions for difficult combinatorial optimization problems.