Modified ATCR rule for fixed and variable costs of tardiness

Delay in fulfilling customer orders leads to tardiness penalties, which can be reduced through effective scheduling. This paper focuses on minimizing two key tardiness-related objectives for the single machine problem: the weighted number of tardy jobs and total weighted tardiness. These objectives represent the fixed and variable costs of tardiness penalties, respectively. We establish a precedence relation between any two adjacent jobs in a sequence and extend it to develop the modified Apparent Tardiness Cost with Ready times (ATCR) priority index. Based on this priority index, we propose a dispatching rule-based heuristic and enhance its performance by incorporating adjacent pairwise interchange of jobs. Numerical study demonstrated that the heuristic has a high level of accuracy and superior time performance compared to the benchmark solutions obtained by a branch & bound algorithm for smaller instances and a genetic algorithm for larger instances. Our heuristic works for both the single and identical parallel machine environments.