Iterated local search for single machine total weighted tardiness batch scheduling

This paper presents an iterated local search (ILS) algorithm for the single machine total weighted tardiness batch scheduling problem. To our knowledge, this is one of the first attempts to apply ILS to solve a batching scheduling problem. The proposed algorithm contains a local search procedure that explores five neighborhood structures, and we show how to efficiently implement them. Moreover, we compare the performance of our algorithm with dynamic programming-based implementations for the problem, including one from the literature and two other ones inspired in biased random-key genetic algorithms and ILS. We also demonstrate that finding the optimal batching for the problem given a fixed sequence of jobs is $$\mathcal {NP}$$ NP -hard, and provide an exact pseudo-polynomial time dynamic programming algorithm for solving such problem. Extensive computational experiments were conducted on newly proposed benchmark instances, and the results indicate that our algorithm yields highly competitive results when compared to other strategies. Finally, it was also observed that the methods that rely on dynamic programming tend to be time-consuming, even for small size instances.