A Metaheuristic Approach for Minimizing Total Weighted Tardiness in Single Machine Scheduling Problem

Single machine scheduling plays a critical role in production and operations management. This process involves planning the order in which jobs are to be processed on a machine to achieve maximum efficiency with limited resources. One of the most important single-machine scheduling problems is minimizing the total weighted tardiness. In this problem, jobs have importance levels (weights), deadlines (due dates), and processing times. The tardiness time of each job is multiplied by the weight value and contributes to the objective function. The objective function value in this problem is aimed to be minimized. No mathematical formulation obtains the optimal solution since the problem is in the Np-hard class. This study addresses the minimization of weighted tardiness with the grey wolf and artificial bee colony optimization algorithms. These methods, developed for solving continuous problems, are adapted to the discrete problem of minimizing the weighted tardiness. The results of the two methods are compared, and gap values are given. Datasets from Or-Library are used for the computational evaluation. As a result, it is observed that the artificial bee colony gives smaller gap values than the grey wolf optimization algorithm.