Abstract
In this paper, we study primal and dual formulations of multistage stochastic programs (SP). Using a dual formulation, we discuss a decomposition/cutting plane algorithm that can be used to solve such problems. The algorithm, which is based on a scenario decomposition derived from the dual statement of the problem, is best viewed as a conceptual algorithm. Nevertheless, it lends itself to the use of sampled data, and enhancements necessary to produce a computationally viable method are discussed.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35514-6_15
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Keywords
- Stochastic Program
- Master Problem
- Stochastic Linear Program
- Stochastic Decomposition
- Multistage Stochastic Program
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References
J.R. Birge (1985), Decomposition and partitioning methods for multistage stochastic linear programs, Operations Research, 22, pp. 989–1007.
D. Carifio, T. Kent, D. Myers, C. Stacy, M. Sylrams, A. Turner, K. Watanabe and W. Ziemba (1994), The Russell-Yasuda Kasai Model: An asset/liablity model of a Japanese insurance company using multi-stage stochastic programming, Interfaces, 24, pp. 29–49.
M.A.H. Dempster (1981), The expected value of perfect information in the optimal evolution of stochastic systems, in M. Arato, E. Ver-mes, and A.V. Balakrishnan (eds.), Stochastic Differential Systems, Lecture Notes in Information and Control, 36, Springer, Berlin, pp. 25–40.
M.A.H. Dempster (1988), On stochastic programming II: Dynamic problems under risk, Stochastics, 25, pp. 15–42.
H.G. Gassmann (1990), MSLiP: A computer code for the multistage stochastic linear programming problem, Mathematical Programming, 47, pp. 407–423.
J.L. Higle and S. Sen (1991), Stochastic Decomposition: An Algorithm for Two Stage Linear Programs with Recourse, Mathematics of Operations Research, 16, no. 3, pp. 650–669.
J.L. Higle and S. Sen (1996a), Stochastic Decomposition: A Statistical Method for Large Scale Stochastic Linear Programming, Kluwer Academic Publishers, Dordrecht.
J.L. Higle and S. Sen (1996b), Duality and statistical tests of optimality for two stage stochastic programs, Mathematical Programming, (Series B), v75, pp. 257–275.
J.L. Higle and S. Sen (1997), Multi—stage Stochastic Programs: Duality and its Implications, submitted to Mathematical Programming.
R.T. Rockafellar and R.J-B. Wets (1991), Scenarios and policy aggregation in opimization under uncertainty, Mathematics of Operations Research, 16, pp. 119–147.
S. Sen, R.D. Doverspike and S. Cosares (1994), Network planning with random demand, Telecommunications Systems, 3, pp. 11–30.
S. Sen, J.L. Higle and B. Rayco (1999), A Scenario Stochastic Decomposition Algorithm for Multistage Stochastic Programming, SIE Department, University of Arizona, Tucson, AZ 85721.
R.J-B. Wets (1975), On the relation between stochastic and deterministic optimization, in A. Bensoussan and J.L. Lions (eds.), Control Theory, Numerical Methods, and Computer Systems Modeling, Lecture Notes in Economics and Mathematical Systems, 107, pp. 350–361.
R.J-B. Wets (1989), Stochastic Programming, in: G.L. Nemhauser, A.H.G. Rinooy Kan, and M.J. Todd (eds.) Handbook of Operations Research: Optimization, North-Holland, Amsterdam, pp. 573–629.
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© 2000 IFIP International Federation for Information Processing
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Higle, J.L., Sen, S. (2000). Algorithmic Implications of Duality in Stochastic Programs. In: Powell, M.J.D., Scholtes, S. (eds) System Modelling and Optimization. CSMO 1999. IFIP — The International Federation for Information Processing, vol 46. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35514-6_8
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DOI: https://doi.org/10.1007/978-0-387-35514-6_8
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