Scenario Tree Generation for Multi-stage Stochastic Programs

We broaden the theoretical basis for generating scenario trees in multi-stage stochastic programming based on stability analysis. Numerical experience for constructing trees of demand and price scenarios in electricity portfolio management of a municipal power utility is also provided.

[1]  J. Dupacová,et al.  Scenario reduction in stochastic programming: An approach using probability metrics , 2000 .

[2]  M. Dempster.  Sequential Importance Sampling Algorithms for Dynamic Stochastic Programming , 2006 .

[3]  Helga Fetter,et al.  On the continuity of conditional expectations , 1977 .

[4]  Louis Anthony Cox,et al.  Wiley encyclopedia of operations research and management science , 2011 .

[5]  Werner Römisch,et al.  A note on scenario reduction for two-stage stochastic programs , 2007, Oper. Res. Lett..

[6]  W. Romisch,et al.  Mean-risk optimization of electricity portfolios using multiperiod polyhedral risk measures , 2005, 2005 IEEE Russia Power Tech.

[7]  Georg Ch. Pflug,et al.  Scenario tree generation for multiperiod financial optimization by optimal discretization , 2001, Math. Program..

[8]  B. Rustem,et al.  Simulation and optimization approaches to scenario tree generation , 2004 .

[9]  Teemu Pennanen,et al.  Epi-Convergent Discretizations of Multistage Stochastic Programs , 2005, Math. Oper. Res..

[10]  John Quigley,et al.  Eliciting subjective probability distributions from groups , 2011 .

[11]  W. Römisch.  Stability of Stochastic Programming Problems , 2003 .

[12]  Georg Ch. Pflug,et al.  Tree Approximations of Dynamic Stochastic Programs , 2007, SIAM J. Optim..

[13]  Werner Römisch,et al.  Scenario Reduction Algorithms in Stochastic Programming , 2003, Comput. Optim. Appl..

[14]  Werner Römisch,et al.  Scenario tree reduction for multistage stochastic programs , 2009, Comput. Manag. Sci..

[15]  Karl Frauendorfer,et al.  Barycentric scenario trees in convex multistage stochastic programming , 1996, Math. Program..

[16]  D. Kuhn.  Generalized Bounds for Convex Multistage Stochastic Programs , 2004 .

[17]  Werner Römisch,et al.  Scenario tree modeling for multistage stochastic programs , 2009, Math. Program..

[18]  W. Römisch,et al.  Stability and Scenario Trees for Multistage Stochastic Programs , 2010 .

[19]  Jitka Dupacová,et al.  Scenario reduction in stochastic programming , 2003, Math. Program..

[20]  Jitka Dupacová,et al.  Scenarios for Multistage Stochastic Programs , 2000, Ann. Oper. Res..

[21]  C. Lemieux.  Monte Carlo and Quasi-Monte Carlo Sampling , 2009 .

[22]  Alexander Shapiro,et al.  Inference of statistical bounds for multistage stochastic programming problems , 2003, Math. Methods Oper. Res..

[23]  R. Tyrrell Rockafellar,et al.  Continuous versus measurable recourse in N-stage stochastic programming☆☆☆ , 1974 .

[24]  S. Graf,et al.  Foundations of Quantization for Probability Distributions , 2000 .

[25]  Roy Kouwenberg,et al.  Scenario generation and stochastic programming models for asset liability management , 2001, Eur. J. Oper. Res..

[26]  Roger J.-B. Wets,et al.  On decision rules in stochastic programming , 1974, Math. Program..

[27]  Werner R Omisch,et al.  Scenario Generation , 2010 .

[28]  Sanjay Mehrotra,et al.  Epi-convergent scenario generation method for stochastic problems via sparse grid , 2008 .

[29]  Peter Kall,et al.  Stochastic Programming , 1995 .

[30]  Ronald Hochreiter,et al.  Financial scenario generation for stochastic multi-stage decision processes as facility location problems , 2007, Ann. Oper. Res..

[31]  Stein W. Wallace,et al.  Generating Scenario Trees for Multistage Decision Problems , 2001, Manag. Sci..

[32]  René Henrion,et al.  Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming , 2008 .

[33]  Dudley,et al.  Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets , 2002 .

[34]  Werner Römisch,et al.  Stability of Multistage Stochastic Programs , 2006, SIAM J. Optim..

[35]  R. Tyrrell Rockafellar,et al.  Variational Analysis , 1998, Grundlehren der mathematischen Wissenschaften.

[36]  A. Shapiro.  Monte Carlo Sampling Methods , 2003 .

[37]  René Henrion,et al.  Scenario reduction in stochastic programming with respect to discrepancy distances , 2006, Comput. Optim. Appl..

[38]  Teemu Pennanen,et al.  Epi-convergent discretizations of multistage stochastic programs via integration quadratures , 2008, Math. Program..