Order scheduling with tardiness objective: Improved approximate solutions

The problem addressed in this paper belongs to the topic of order scheduling, in which customer orders - composed of different individual jobs - are scheduled so the objective sought refers to the completion times of the complete orders. Despite the practical and theoretical relevance of this problem, the literature on order scheduling is not very abundant as compared to job scheduling. However, there are several contributions with the objectives of minimising the weighted sum of completion times of the orders, the number of late orders, or the total tardiness of the orders. In this paper, we focus in the last objective, which is known to be NP-hard and for which some constructive heuristics have been proposed. We intend to improve this state-of-the-art regarding approximate solutions by proposing two different methods: Whenever extremely fast (negligible time) solutions are required, we propose a new constructive heuristic that incorporates a look-ahead mechanism to estimate the objective function at the time that the solution is being built. For the scenarios where longer decision intervals are allowed, we propose a novel matheuristic strategy to provide extremely good solutions. The extensive computational experience carried out shows that the two proposals are the most efficient for the indicated scenarios.