Customer order scheduling to minimize the number of late jobs

• DOI: 10.1016/j.ejor.2006.10.021
• Publication Date: 2006-12-14T12:10:57Z
• Authors: B.M.T. Lin; A.V. Kononov
• Keywords: Due date

In the order scheduling problem, every job (order) consists of several tasks (product items), each of which will be processed on a dedicated machine. The completion time of a job is defined as the time at which all its tasks are finished. Minimizing the number of late jobs was known to be strongly NP-hard. In this note, we show that no FPTAS exists for the two-machine, common due date case, unless P = NP. We design a heuristic algorithm and analyze its performance ratio for the unweighted case. An LP-based approximation algorithm is presented for the general multicover problem. The algorithm can be applied to the weighted version of the order scheduling problem with a common due date.