Algorithms for Minimizing Maximum Lateness with Unit Length Tasks and Resource Constraints

Blazewicz, J., W. Kubiak and S. Martello, Algorithms for minimizing maximum lateness with unit length tasks and resource constraints, Discrete Applied Mathematics 42 (1993) 1233138. The problem we consider is that of scheduling n unit length tasks on identical processors in the presence of additional scarce resources. The objective is to minimize maximum lateness. It has been known for some time that the problem is NP-hard even for two processors and one resource type. In the present paper we show that the problem can be solved in O(n log n) time, even for an arbitrary number of resources if the instance of the problem has the saturation property (i.e., no resource unit is idle in an optimal schedule). For the more general problem without saturation, two heuristic algorithms and a branch and bound approach are proposed. The results of computational tests of the above methods are also reported.