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THE SEQUENTIAL STOCHASTIC ASSIGNMENT PROBLEM WITH POSTPONEMENT OPTIONS

Published online by Cambridge University Press:  10 December 2012

Tianke Feng  and
Joseph C. Hartman
Tianke Feng
Affiliation:
Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA E-mail: fengtk@ufl.edu; hartman@ise.ufl.edu
Joseph C. Hartman
Affiliation:
Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA E-mail: fengtk@ufl.edu; hartman@ise.ufl.edu
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Abstract

The sequential and stochastic assignment problem (SSAP) has wide applications in logistics, finance, and health care management, and has been well studied in the literature. It assumes that jobs with unknown values arrive according to a stochastic process. Upon arrival, a job's value is made known and the decision-maker must immediately decide whether to accept or reject the job and, if accepted, to assign it to a resource for a reward. The objective is to maximize the expected reward from the available resources. The optimal assignment policy has a threshold structure and can be computed in polynomial time. In reality, there exist situations in which the decision-maker may postpone the accept/reject decision. In this research, we study the value of postponing decisions by allowing a decision-maker to hold a number of jobs which may be accepted or rejected later. While maintaining this queue of arrivals significantly complicates the analysis, optimal threshold policies exist under mild assumptions when the resources are homogeneous. We illustrate the benefits of delaying decisions through higher profits and lower risk in both cases of homogeneous and heterogeneous resources.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 1 , January 2013 , pp. 25 - 51
Copyright
Copyright © Cambridge University Press 2013

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References

REFERENCES

1.Albright, C. & Derman, C. (1972). Asymptotic optimal policies for the stochastic sequential assignment problem. Management Science 19: 46–51.CrossRefGoogle Scholar
2.Albright, S.C. (1974). Optimal sequential assignments with random arrival times. Management Science 21(1): 60–67.CrossRefGoogle Scholar
3.Albright, S.C. (1976). A Markov chain version of the secretary problem. Naval Research Logistics Quarterly 1: 151–159.CrossRefGoogle Scholar
4.Albright, S.C. (1977). A Bayesian approach to a generalized house selling problem. Management Science 24(4): 432–440.CrossRefGoogle Scholar
5.Amram, M. & Kulatilaka, N. (1999). Real options: managing strategic investment in an uncertain world. Boston: Harvard Business School Press.Google Scholar
6.Derman, C., Lieberman, G.J., & Ross, S.M. (1972). A sequential stochastic assignment problem. Management Science 7: 349–355.CrossRefGoogle Scholar
7.Elfving, G. (1967). A persistency problem connected with a point process. Journal of Applied Probability 4: 77–89.CrossRefGoogle Scholar
8.Hardy, G.H., Littlewood, J.E., & Pólya, G. (1934). Inequalities. Cambridge: The University Press.Google Scholar
9.Hentenryck, P. & Bent, R. (2006). Online stochastic and combinatorial optimization. Cambridge, MA: The MIT Press.Google Scholar
10.Ilhan, T., Iravani, S.M.R., & Daskin, M.S. (2011). Technical note—the adaptive knapsack problem with stochastic rewards. Operations Research 1: 242–248.CrossRefGoogle Scholar
11.Karlin, S. (1962). Stochastic models and optimal policy for selling an asset. Studies in Applied Probability and Management Science, Arrow, K. J., Karlin, S., Scarf, H., (eds.), Stanford, CA: Stanford University Press.Google Scholar
12.Kennedy, D.P. (1986). Optimal sequential assignment. Mathematics of Operations Research 4: 619–626.CrossRefGoogle Scholar
13.Kleywegt, A.J. & Papastavrou, J.D. (1998). The dynamic and stochastic knapsack problem. Operations Research 46(1): 17–35.CrossRefGoogle Scholar
14.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
15.Nakai, T. (1986a). A sequential stochastic assignment problem in a stationary Markov chain. Mathematica Japonica 31: 741–757.Google Scholar
16.Nakai, T. (1986b). A sequential stochastic assignment problem in a partially observable Markov chain. Mathematics of Operations Research 11: 230–240.CrossRefGoogle Scholar
17.Nikolaev, A.G. & Jacobson, S.H. (2010). Technical note — stochastic sequential decision-making with a random number of jobs. Operations Research 58(4): 1023–1027.CrossRefGoogle Scholar
18.Puterman, M.L. (1994). Markov decision processes: discrete stochastic dynamic programming. New Jersey: John Wiley & Sons.CrossRefGoogle Scholar
19.Powell, W. (2007). Approximate dynamic programming: solving the curses of dimensionality. New Jersey: John Wiley & Sons.CrossRefGoogle Scholar
20.Righter, R.L. (1987). The stochastic sequential assignment problem with random deadlines. Probability in the Engineering and Informational Sciences 1: 189–202.CrossRefGoogle Scholar
21.Righter, R.L. (1989). A resource allocation problem in a random environment. Operations Research 37(2): 329–337.CrossRefGoogle Scholar
22.Ross, S.M. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.Google Scholar
23.Saario, V. (1985). Limiting properties of the discounted house-selling problem. European Journal of Operational Research 20(2): 206–210.CrossRefGoogle Scholar
24.Sakaguchi, M. (1984a). A sequential stochastic assignment problem associated with a non-homogeneous Markov process. Mathematica Japonica 29(1): 13–22.Google Scholar
25.Sakaguchi, M. (1984b). A sequential stochastic assignment problem associated with unknown number of jobs. Mathematica Japonica 29(2): 141–152.Google Scholar
26.Su, X. & Zenios, S. (2005). Patient choice in kidney allocation: a sequential stochastic assignment model. Operations Research 53(3): 443–455.CrossRefGoogle Scholar
27.Triantis, A.J. (2000). Real options and corporate risk management. Journal of Applied Corporate Finance 13(2): 64–73.CrossRefGoogle Scholar
28.Trigeorgis, L. (1996). Real options: managerial flexibility and strategy in resource allocation. Cambridge, MA: MIT Press.Google Scholar
29.Van Hoek, R.I. (2001). The rediscovery of postponement a literature review and directions for research. Journal of Operations Management 19(2): 161–184.CrossRefGoogle Scholar
30.Zenios, S.A., Chertow, G.M., & Wein, L.M. (2000). Dynamic allocation of kidneys to candidates on the transplant waiting list. Operations Research 48(4): 549–569.CrossRefGoogle Scholar