Makespan minimization of multi-slot just-in-time scheduling on single and parallel machines

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.