Allocation of tasks to specialized processors: A planning approach

This paper addresses the problem of scheduling randomly arriving tasks of different types at a diversified service system. Servers at such a system differ in that each may specialize in one task type, but can also perform others perhaps less rapidly and adequately than does a specialist. We consider the issue of how much redirection of tasks from specialists to non-specialists may be desirable in such a system and propose a static model in which tasks are randomly assigned to servers. Two scheduling strategies for individual servers are also considered: one in which each server performs the tasks assigned to him or her in order of their arrival and the second in which each server schedules his or her workload optimally. The problems for finding the best random assignment probabilities are formulated as mathematical programs. Results from a numerical example provide information that is both informative and useful in decision-making.