Scheduling Of Identical Parallel Machines Under Unavailability Constraints

This paper considers an offline scheduling problem of identical parallel machines where every machine is subject to at most one unavailability period. We assume that the jobs can be interrupted and resumed at any available machine. In other words, if a job is interrupted because of the unavailability of a machine it can be whether resumed at the same machine when it becomes available, or at any other available machine. The objective is to minimize the completion time of the last job C
_max.
The problem can be represented as P
_m
|r-a, pmtn|C
_max.
To solve this problem, we proposed a new method based on list scheduling techniques. In addition, we developed new theoretical lower and upper bounds. Then, we developed absolute performance bounds for the method. An absolute performance bound is a bound between the method's makespan and the optimal makespan for all possible instances of the problem. In addition, we formulated the studied problem as a mixed integer quadratic model that is sued to generate optimal solutions. Finally, we conducted an experimental study in which many instances of different sizes and parameters were generated and solved. The results proved that the new methods are performing very well for most of the tested instances.