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

Stochastic programming approaches to stochastic scheduling

Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces diffculties in analysis that may be addressed in a variety of ways. In this paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44935/1/10898_2004_Article_BF00121682.pd

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

Cost Rate Heuristics for Semi-Markov Decision Processes

In response to the computational complexity of the dynamic programming/backwards induction approach to the development of optimal policies for semi-Markov decision processes, we propose a class of heuristics which result from an inductive process which proceeds forwards in time. These heuristics always choose actions in such a way as to maximize some measure of the current cost rate. We describe a procedure for calculating such cost-rate heuristics. The quality of the performance of such policies is related to the speed of evolution (in a cost sense) of the process. These ideas find natural expression in a dass of Bayesian sequential decision problems. One such ( a simple model of preventive maintenance) is described in detail . Cost-rate heuristics for this problem are calculated and assessed computationally.National Research CouncilNaval Weapons Support Center, Crane, IN.Naval Postgraduate School Research FoundationApproved for public release; distribution is unlimited

Cost Rate Heuristics for Semi-Markov Decision Processes

The article of record as published may be found at https://www.jstor.org/stable/3214900In response to the computational complexity of the dynamic programming/backwards induction approach to the development of optimal policies for semi-Markov decision processes, we propose a class of heuristics resulting from an inductive process which proceeds forwards in time. These heuristics always choose actions in such a way as to minimize some measure of the current cost rate. We describe a procedure for calculating such cost rate heuristics. The quality of the performance of such policies is related to the speed of evolution (in a cost sense) of the process. A simple model of preventive maintenance is described in detail. Cost rate heuristics for this problem are calculated and assessed computationally.Dr Bailey was supported by the Naval Weapons Support Centre, Crane, IN, and Dr Whitaker by the Naval Postgraduate School Research FoundatioResearch supported by the National Research Council by means of a Senior Research Associateship at the Department of Operations Research, Naval Postgraduate School, Monterey, Californi

A static allocation model for the outsourcing of warranty repairs

There has been a strong recent trend among original equipment manufacturers toward the outsourcing of work relating to the repair of items under warranty. In the typical cases where a large manufacturer uses several vendors to perform such work, we develop and analyse models to support decisions concerning how the work should be distributed among them. We depart from previous work in arguing the importance of an approach to the modelling of goodwill costs which takes explicit account of the delays experienced by customers. Theoretical considerations and numerical work both lend strong support to the contention that simple greedy approaches to workload allocation work well

Dynamic resource allocation in a multi-product make-to-stock production system

We consider optimal policies for a production facility in which several (K) products are made to stock in order to satisfy exogenous demand for each. The single machine version of this problem in which the facility manufactures at most one product at a time to minimise inventory costs has been much studied. We achieve a major generalisation by formulating the production problem as one involving dynamic allocation of a key resource which drives the manufacture of all products under an assumption that each additional unit of resource allocated to a product achieves a diminishing return of increased production rate. A Lagrangian relaxation of the production problem induces a decomposition into K single product problems in which the production rate may be varied but is subject to charge. These reduced problems are of interest in their own right. Under mild conditions of full indexability the Lagrangian relaxation is solved by a production policy with simple index-like structure. This in turn suggests a natural index heuristic for the original production problem which performs strongly in a numerical study. The paper discusses the importance of full indexability and makes proposals for the construction of production policies involving resource idling when it fails