Minimizing earliness and tardiness penalties in a single-machine problem with a common due date

Scheduling problems involving both earliness and tardiness costs have received significant attention in recent years. This type of problem became important with the advent of the just-in-time (JIT) concept, where early or tardy deliveries are highly discouraged. In this paper we examine the single-machine scheduling problem with a common due date. Performance is measured by the minimization of the sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, we propose a tabu search-based heuristic and a genetic algorithm which exploit specific properties of the optimal solution. Hybrid strategies are also analyzed to improve the performance of these methods. The proposed approaches are examined through a computational comparative study with 280 benchmark problems with up to 1000 jobs.