Cost Constrained Fixed Job Scheduling
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 proc- essor, and the cost of that processing is the product of the processing time and the processor’s unit time process- ing 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.
KeywordsFinish Time Feasible Schedule Total Processing Time Minimum Cost Flow Partition Property
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