Bag-of-Tasks Scheduling with Rejection in Large Computing Systems

We are given a set of m identical parallel machines and a set of n jobs in large computing systems, where each job J(j) consists of a bag of bj identical tasks with a processing time p(j), and has a rejection penalty wj. Job J(j )is either accepted in which case all the b(j) tasks must be processed by one of the machines, or rejected which incurs a rejection penalty w(j). The problem of bag-of-tasks scheduling with rejection is to find a feasible schedule, so as to minimize the makespan plus the total rejection penalty of all rejected jobs. In this paper, we present a polynomial time approximation scheme.