Abstract. In this paper, we study the problem of cost constrained fixed job scheduling (CCFJS). In this problem, there are a number of processors, each of which belongs to one of several classes. The unit time processing cost for a processor varies with the class to which the processor belongs. There are N jobs, each of which must be processed from a given start time to a given finish time without preemption. A job can be processed by any processor, and the cost of that processing is the product of the processing time and the processor’s unit time processing cost. The problem is to find a feasible scheduling of the jobs such that the total processing cost is within a given cost bound. This problem (CCFJS) arises in several applications, including off-line multimedia gateway call routing. We show that CCFJS can be solved by a network flow based algorithm when there are only two classes of processors. For more than two classes of processors, we prove that CCFJS is not only NP-Complete, but also that there is no constant ratio approximation algorithm. Finally, we present an approximation algorithm, derive its worst-case performance ratio (non constant), and show that it has a constant approximation ratio in several special cases.
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