MINIMIZING THE MAKESPAN IN A SINGLE MACHINE SCHEDULING PROBLEM WITH A FLEXIBLE MAINTENANCE

ABSTRACT This paper considers a single machine scheduling problem with a flexible maintenance, we consider the machine should be stopped to maintain or to reset for a constant time r during the scheduling period. Meanwhile we assume that the maintenance period [s, t] is arranged previously; and the time r would not be longer than the maintenance period [s, t] (i.e. r ≤ t-s). The time s (t) is the earliest (latest) time at which the machine starts (stops) its maintenance. The objective is to minimize the makespan (maximum completion time). This scheduling problem is often occurred in computer center, NC-machine and IC-testing machine for the jobs scheduling and repairmen arrangement. In this paper, the proposed problem is shown to be NP-hard. A heuristic algorithm with computational experiments is provided. An extension with more than one maintenance intervals is also considered.