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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

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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.

Information

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 

References

1.Albright, S.C. (1974). A markov-decision-chain approach to a stochastic assignment problem. Operations Research 22(1): 61–64.CrossRefGoogle Scholar
2.Albright, S.C. (1974). Optimal sequential assignment with random arrival time. Management Science 21(1): 60–67.CrossRefGoogle Scholar
3.Boda, K., Filar, J.A., Lin, Y., & Spanjers, L. (2004). Stochastic target hitting time and the problem of early retirement. IEEE Transactions on Automatic Control 49(3): 409–419.CrossRefGoogle Scholar
4.Derman, C., Lieberman, G.J., & Ross, S.M. (1972). A sequential stochastic assignment problem. Management Science 18(7): 349–355.CrossRefGoogle Scholar
5.McLay, L.A., Jacobson, S.H., & Nikolaev, A.G. (2009). A sequential stochastic passenger screening problem for aviation security. IIE Transactions 41(6): 575–591.CrossRefGoogle Scholar
6.Nikolaev, A.G. & Jacobson, S.H. (2010). Stochastic sequential decision-making with a random number of jobs. Operations Research 58: 1023–1027.CrossRefGoogle Scholar
7.Nikolaev, A.G., Jacobson, S.H., & McLay, L.A. (2007). A sequential stochastic seceurity system design problem for aviation security. Transportation Science 41(2): 182–194.CrossRefGoogle Scholar
8.Ohtsubo, Y. (2003). Value iteration methods in risk minimizing stopping problems. Journal of Computational and Applied Mathematics 152: 427–439.CrossRefGoogle Scholar
9.Ohtsubo, Y. (2004). Optimal threshold probability in undiscounted markov decision processes with a target set. Applied Mathematics and Computation 149: 519–532CrossRefGoogle Scholar
10.Ohtsubo, Y. & Toyonaga K. (2002). Optimal policy for minimizing risk models in markov decision processes. Journal of Mathematical Analysis and Applications 271: 66–81.CrossRefGoogle Scholar
11.Ohtsubo, Y. & Toyonaga, K. (2004). Equivalence classes for optimizing risk models in markov decision processes. Mathematical Methods of Operations Research 60: 239–250.CrossRefGoogle Scholar
12.Righter, R.L. (1987). The stochastic sequential assignment problem with random deadlines. Probabability in the Engineering and Informational Sciences 1: 189–202.CrossRefGoogle Scholar
13.Sakaguchi, M. & Ohtsubo, Y. (2010). Optimal threshold probability and expectation in semi-markov decision processes. Applied Mathematics and Computation 216: 2947–2958.CrossRefGoogle Scholar
14.Smith, J.E. & McCardle, K.F. (2002). Structural properties of stochastic dynamic programs. Operations Research 50(5): 796–809.CrossRefGoogle Scholar
15.Su, X. & Zenios, S.A. (2005). Patient choice in kidney allocation: A sequential stochastic assignment model. Operations Research 53(3): 443–455.CrossRefGoogle Scholar
16.White, D.J. (1993). Minimizing a threshold probability in discounted markov decision processes. Journal of Mathematical Analysis and Applications 173: 634–646.CrossRefGoogle Scholar
17.Wu, C. & Lin, Y. (1999). Minimizing risk models in markov decision processes with policies depending on target values. Journal of Mathematical Analysis and Applications 231: 47–67.CrossRefGoogle Scholar