Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T03:47:31.070Z Has data issue: false hasContentIssue false
  • English
  • Français

Limiting Behavior of the Target-Dependent Stochastic Sequential Assignment Problem

Part of: Markov processes Special processes

Published online by Cambridge University Press:  30 January 2018

Golshid Baharian  and
Sheldon H. Jacobson
Golshid Baharian*
Affiliation:
University of Illinois at Urbana-Champaign
Sheldon H. Jacobson*
Affiliation:
University of Illinois at Urbana-Champaign
*
∗ Postal address: Research Center of CHU Sainte-Justine, 3175 Cote Sainte-Catherine, local A-714, Montreal, Québec H3T 1C5, Canada. Email address: gbahari2@illinois.edu
∗∗ Postal address: Department of Computer Science, 201 N. Goodwin Ave., Urbana, IL 61801, USA. Email address: shj@illinois.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The stochastic sequential assignment problem assigns distinct workers to sequentially arriving tasks with stochastic parameters. In this paper the assignments are performed so as to minimize the threshold probability, which is the probability of the long-run reward per task failing to achieve a target value (threshold). As the number of tasks approaches infinity, the problem is studied for independent and identically distributed (i.i.d.) tasks with a known distribution function and also for tasks that are derived from r distinct unobservable distributions (governed by a Markov chain). Stationary optimal policies are presented, which simultaneously minimize the threshold probability and achieve the optimal long-run expected reward per task.

Keywords

Sequential assignmentthreshold probabilitystationary policyhidden Markov chain

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 943 - 953
Copyright
© Applied Probability Trust 

References

Albright, S. C. (1974). A Markov-decision-chain approach to a stochastic assignment problem. Operat. Res. 22, 61–64.CrossRefGoogle Scholar
Albright, S. C. (1976). A Markov chain version of the secretary problem. Naval Res. Logistics Quart. 23, 151–159.CrossRefGoogle Scholar
Albright, S. C. (1977). A Bayesian approach to a generalized house selling problem. Manag. Sci. 24, 432–440.CrossRefGoogle Scholar
Albright, S. C. and Derman, C. (1972). Asymptotic optimal policies for the stochastic sequential assignment problem. Manag. Sci. 19, 46–51.CrossRefGoogle Scholar
Baharian, G. and Jacobson, S. H. (2013). Limiting behavior of the stochastic sequential assignment problem. Naval Res. Logistics 60, 321–330.CrossRefGoogle Scholar
Derman, C., Lieberman, G. J. and Ross, S. M. (1972). A sequential stochastic assignment problem. Manag. Sci. 18, 349–355.CrossRefGoogle Scholar
Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. Springer, London.CrossRefGoogle Scholar
Nakai, T. (1986). A sequential stochastic assignment problem in a partially observable Markov chain. Math. Operat. Res. 11, 230–240.CrossRefGoogle Scholar
Nikolaev, A. G. and Jacobson, S. H. (2010). Stochastic sequential decision-making with a random number of Jobs. Operat. Res. 58, 1023–1027.CrossRefGoogle Scholar
Nikolaev, A. G., Jacobson, S. H. and McLay, L. A. (2007). A sequential stochastic security system design problem for aviation security. Transportation Sci. 41, 182–194.CrossRefGoogle Scholar
Su, X. and Zenios, S. A. (2005). Patient choice in kidney allocation: a sequential stochastic assignment model. Operat. Res. 53, 443–455.CrossRefGoogle Scholar