Single machine scheduling with assignable due dates to minimize maximum and total late work - Justkowiak, Jan-Erik; Kovalev, Sergey; Kovalyov, Mikhail Y.; Pesch, Erwin (European journal of operational research, 2023)
•Two problems of minimizing maximum late work and total late work in single machine scheduling are considered where due dates are assignable.•The problems have multiple applications in production and logistics.•The first problem is solved efficiently.•Two pseudo-polynomial dynamic programming algorithms and an FPTAS are described for the latter.•Comprehensive computational results illustrate their excellent performance. A single machine scheduling problem with assignable job due dates to minimize total late work has recently been introduced by Mosheiov, Oron, and Shabtay (2021). The problem was proved NP-hard in the ordinary sense, and no solution algorithm was proposed. In this note, we present two pseudo-polynomial dynamic programming algorithms and an FPTAS for this problem. Besides, we introduce a new single machine scheduling problem to minimize maximum late work of jobs with assignable due dates. We develop an O(nlogn) time algorithm for it, where n is the number of jobs. An optimal solution value of this new problem is a lower bound for the optimal value of the total late work minimization problem, and it is used in the FPTAS.