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STOCHASTIC SEQUENTIAL ASSIGNMENT PROBLEM WITH THRESHOLD CRITERIA

Published online by Cambridge University Press:  28 March 2013

Golshid Baharian  and
Sheldon H. Jacobson
Golshid Baharian
Affiliation:
Industrial and Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL E-mail: gbahari2@illinois.edu
Sheldon H. Jacobson
Affiliation:
Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL E-mail: shj@illinois.edu
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Abstract

The stochastic sequential assignment problem (SSAP) allocates distinct workers to sequentially arriving tasks with stochastic parameters to maximize the expected total reward. In this paper, the assignment of tasks is performed under the threshold criterion, which seeks a policy that minimizes the probability of the total reward failing to achieve a target value. A Markov-decision-process approach is employed to model the problem, and sufficient conditions for the existence of a deterministic Markov optimal policy are derived, along with fundamental properties of the optimal value function. An algorithm to approximate the optimal value function is presented, and convergence results are established.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 3 , July 2013 , pp. 277 - 296
Copyright
Copyright © Cambridge University Press 2013 

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