Scheduling preemptable tasks on parallel processors with limited availability

It is well known that in the majority of cases the problem of preemptive task scheduling on m parallel identical processors with the objective of minimizing makespan can be solved in polynomial time. For example, for tree-like precedence constraints the algorithm of Muntz and Co€man can be applied. In this paper, this problem is generalized to cover the case of parallel processors which are available in certain time intervals only. It will be shown that this problem becomes NP-hard in the strong sense in case of trees and identical processors. If tasks form chains and are processed by identical processors with a staircase pattern of availability, the problem can be solved in low-order polynomial time for Cmax criterion, and a linear programming approach is required for Lmax criterion. Network ̄ow and linear programming approaches will be proposed for independent tasks scheduled on, respectively, uniform and unrelated processors with arbitrary patterns of availability for schedule length and maximum lateness criteria. Ó 2000 Published by Elsevier Science B.V. All rights reserved.