Please use this identifier to cite or link to this item: https://doi.org/10.1214/009053606000001569
Title: Optimal strategies for a class of sequential control problems with precedence relations
Authors: Chan, H.P. 
Fuh, C.-D.
Hu, I.
Keywords: Kullback-Leibler number
Likelihood ratio
Markov chains
Multi-armed bandits
Optimal stopping
Scheduling
Single-machine job sequencing
Wald's equation
Issue Date: Aug-2007
Source: Chan, H.P., Fuh, C.-D., Hu, I. (2007-08). Optimal strategies for a class of sequential control problems with precedence relations. Annals of Statistics 35 (4) : 1722-1748. ScholarBank@NUS Repository. https://doi.org/10.1214/009053606000001569
Abstract: Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each phase, one can pursue the projects in any order. When pursuing the project with one unit of resource, the project state changes according to a Markov chain. The probability distribution of the Markov chain is known up to an unknown parameter. When pursued, the project generates a random reward depending on the phase and the state of the project and the unknown parameter. The decision maker faces two problems: (a) how to allocate resources to projects within each phase, and (b) when to enter the next phase, so that the total expected reward is as large as possible. In this paper we formulate the preceding problem as a stochastic scheduling problem and propose asymptotic optimal strategies, which minimize the shortfall from perfect information payoff. Concrete examples are given to illustrate our method. © Institute of Mathematical Statistics, 2007.
Source Title: Annals of Statistics
URI: http://scholarbank.nus.edu.sg/handle/10635/105287
ISSN: 00905364
DOI: 10.1214/009053606000001569
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