Makespan minimization for parallel machine scheduling of semi-resumable and non-resumable jobs with multiple availability constraints

ABSTRACT The problem of makespan minimization for parallel machine scheduling with multiple non-availability periods for non-resumable, semi-resumable and resumable jobs is considered in this paper. The discussion of this problem is very limited in the current state of the literature, with most cases only considering a small subset of the problem such as a single machine with multiple non-availability periods or several machines with only one non-availability period. The problem is formulated as a mixed-integer linear programming model and solved optimally using CPLEX for small problems with multiple availability constraints on all machines. Several heuristic approaches are then applied to the problem to provide near-optimal solutions while significantly reducing the computation time. Numerical results are obtained for several experiments and the performance of the heuristic methods is analysed.