Data-driven Single Machine Scheduling Minimizing Weighted Number of Tardy Jobs

Abstract

We tackle a single-machine scheduling problem where each job is characterized by weight, duration, due date, and deadline, while the objective is to minimize the weighted number of tardy jobs. The problem is strongly NP-hard and has practical applications in various domains, such as customer service and production planning. The best known exact approach uses a branch-and-bound structure, but its efficiency varies depending on the distribution of job parameters. To address this, we propose a new data-driven heuristic algorithm that considers the parameter distribution and uses machine learning and integer linear programming to improve the optimality gap. The algorithm also guarantees to obtain a feasible solution if it exists. Experimental results show that the proposed approach outperforms the current state-of-the-art heuristic.

This work was supported by the Czech MEYS under the ERC CZ project POSTMAN no. LL1902, by the Grant Agency of the Czech Technical University in Prague, grant No. SGS22/167/OHK3/3T/13 and by the Grant Agency of the Czech Republic under the Project GACR 22-31670S. This article is part of the RICAIP project that has received funding from the EU’s Horizon 2020 research and innovation programme under grant agreement No 857306.