The Largest-Z-ratio-First algorithm is 0.8531-approximate for scheduling unreliable jobs on m parallel machines

In this paper we analyze the worst-case performance of a greedy algorithm called Largest-Z-ratio-First for the problem of scheduling unreliable jobs on m parallel machines. Each job is characterized by a success probability and a reward earned in the case of success. In the case of failure, the jobs subsequently sequenced on that machine cannot be performed. The objective is to maximize the expected reward. We show the algorithm provides an approximation ratio of ≃0.853196, and that the bound is tight.