Makespan minimization of multi-slot just-in-time scheduling on single and parallel machines - Dereniowski, Dariusz; Kubiak, Wiesław (Journal of scheduling, 2010)
The paper addresses the problem of multi-slot just-in-time scheduling. Unlike the existing literature on this subject, it studies a more general criterion—the minimization of the schedule makespan rather than the minimization of the number of slots used by schedule. It gives an O ( n log 2 n )-time optimization algorithm for the single machine problem. For arbitrary number of m >1 identical parallel machines it presents an O ( n log n )-time optimization algorithm for the case when the processing time of each job does not exceed its due date. For the general case on m >1 machines, it proposes a polynomial time constant factor approximation algorithm.