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

Index policies for shooting problems

We consider a scenario in which a single Red wishes to shoot at a collection of Blue targets, one at a time, to maximise some measure of return obtained from Blues killed before Red's own (possible) demise. Such a situation arises in various military contexts such as the conduct of air defence by Red in the face of Blue SEAD (suppression of enemy air defences). A class of decision processes called multi-armed bandits has been previously deployed to develop optimal policies for Red in which she attaches a calibrating (Gittins) index to each Blue target and optimally shoots next at the Blue with largest index value. The current paper seeks to elucidate how a range of developments of index theory are able to accommodate features of such problems which are of practical military import. Such features include levels of risk to Red which are policy dependent, Red having imperfect information about the Blues she faces, an evolving population of Blue targets and the possibility of Red disengagement. The paper concludes with a numerical study which both compares the performance of (optimal) index policies to a range of competitors and also demonstrates the value to Red of (optimal) disengagement