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Volumn , Issue , 2011, Pages 97-143

Multistage stochastic programming: A scenario tree based approach to planning under uncertainty

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EID: 84881126042     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4018/978-1-60960-165-2.ch006     Document Type: Chapter
Times cited : (57)

References (102)
  • 3
    • 33847420465 scopus 로고    scopus 로고
    • Coherent multiperiod risk adjusted values and Bellman's principle
    • doi:10.1007/s10479-006-0132-6
    • Artzner, P., Delbaen, F., Eber, J.-M., Heath, D., & Ku, H. (2007). Coherent multiperiod risk adjusted values and Bellman's principle. Annals of Operations Research, 152(1), 5-22. doi:10.1007/s10479-006-0132-6
    • (2007) Annals of Operations Research , vol.152 , Issue.1 , pp. 5-22
    • Artzner, P.1    Delbaen, F.2    Eber, J.-M.3    Heath, D.4    Ku, H.5
  • 5
    • 3042702298 scopus 로고    scopus 로고
    • Approximation to multistage stochastic optimization in multiperiod batch plant scheduling under demand uncertainty
    • doi:10.1021/ie030308+
    • Balasubramanian, J., & Grossmann, I. E. (2003). Approximation to multistage stochastic optimization in multiperiod batch plant scheduling under demand uncertainty. Industrial & Engineering Chemistry Research, 43, 3695-3713. doi:10.1021/ie030308+
    • (2003) Industrial & Engineering Chemistry Research , vol.43 , pp. 3695-3713
    • Balasubramanian, J.1    Grossmann, I.E.2
  • 6
    • 84881579627 scopus 로고
    • Dynamic programming treatment of the travelling salesman problem
    • doi:10.1145/321105.321111
    • Bellman, R. (1962). Dynamic programming treatment of the travelling salesman problem. Journal of the ACM, 9, 61-63. doi:10.1145/321105.321111
    • (1962) Journal of the ACM , vol.9 , pp. 61-63
    • Bellman, R.1
  • 10
    • 0020301982 scopus 로고
    • The value of the stochastic solution in stochastic linear programs with fixed recourse
    • doi:10.1007/BF01585113
    • Birge, J. R. (1992). The value of the stochastic solution in stochastic linear programs with fixed recourse. Mathematical Programming, 24, 314-325. doi:10.1007/BF01585113
    • (1992) Mathematical Programming , vol.24 , pp. 314-325
    • Birge, J.R.1
  • 12
    • 32044445036 scopus 로고    scopus 로고
    • Time consistent dynamic risk measures
    • doi:10.1007/s00186-005-0045-1
    • Boda, K., & Filar, J. A. (2006). Time consistent dynamic risk measures. Mathematical Methods of Operations Research, 63, 169-186. doi:10.1007/s00186-005-0045-1
    • (2006) Mathematical Methods of Operations Research , vol.63 , pp. 169-186
    • Boda, K.1    Filar, J.A.2
  • 15
    • 0030143103 scopus 로고    scopus 로고
    • Stochastic optimization of unit commitment: A new decomposition framework
    • doi:10.1109/59.496196
    • Carpentier, P., Cohen, G., & Culioli, J. C. (1996). Stochastic optimization of unit commitment: A new decomposition framework. IEEE Transactions on Power Systems, 11, 1067-1073. doi:10.1109/59.496196
    • (1996) IEEE Transactions On Power Systems , vol.11 , pp. 1067-1073
    • Carpentier, P.1    Cohen, G.2    Culioli, J.C.3
  • 16
    • 33847390618 scopus 로고    scopus 로고
    • Monte Carlo methods for multi-stage stochastic programs
    • University of Texas at Austin, Austin, TX
    • Chiralaksanakul, A. (2003). Monte Carlo methods for multi-stage stochastic programs. Unpublished doctoral dissertation, University of Texas at Austin, Austin, TX.
    • (2003) Unpublished Doctoral Dissertation
    • Chiralaksanakul, A.1
  • 17
    • 0023104635 scopus 로고
    • Discounted MDP's: Distribution functions and exponential utility maximization
    • doi:10.1137/0325004
    • Chung, K.-J., & Sobel, M. (1987). Discounted MDP's: Distribution functions and exponential utility maximization. SIAM Journal on Control and Optimization, 25(1), 49-62. doi:10.1137/0325004
    • (1987) SIAM Journal On Control and Optimization , vol.25 , Issue.1 , pp. 49-62
    • Chung, K.-J.1    Sobel, M.2
  • 19
    • 50949118676 scopus 로고    scopus 로고
    • Value function based reinforcement learning in changing Markovian environments
    • Csáji, B., & Monostori, L. (2008). Value function based reinforcement learning in changing Markovian environments. Journal of Machine Learning Research, 9, 1679-1709.
    • (2008) Journal of Machine Learning Research , vol.9 , pp. 1679-1709
    • Csáji, B.1    Monostori, L.2
  • 20
    • 0000813562 scopus 로고
    • Linear programming under uncertainty
    • doi:10.1287/mnsc.1.3-4.197
    • Dantzig, G. B. (1955). Linear programming under uncertainty. Management Science, 1, 197-206. doi:10.1287/mnsc.1.3-4.197
    • (1955) Management Science , vol.1 , pp. 197-206
    • Dantzig, G.B.1
  • 21
    • 84898095461 scopus 로고    scopus 로고
    • December, Paper presented at the NIPS-08 Workshop on Model Uncertainty and Risk in Reinforcement Learning, Whistler, BC
    • Defourny, B., Ernst, D., & Wehenkel, L. (2008, December). Risk-aware decision making and dynamic programming. Paper presented at the NIPS-08 Workshop on Model Uncertainty and Risk in Reinforcement Learning, Whistler, BC.
    • (2008) Risk-aware Decision Making and Dynamic Programming
    • Defourny, B.1    Ernst, D.2    Wehenkel, L.3
  • 23
    • 77953562445 scopus 로고    scopus 로고
    • Distributionally robust optimization under moment uncertainty with application to data-driven problems
    • doi:10.1287/opre.1090.0741
    • Delage, E., & Ye, Y. (2010). Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research, 58(3), 596-612. doi:10.1287/opre.1090.0741
    • (2010) Operations Research , vol.58 , Issue.3 , pp. 596-612
    • Delage, E.1    Ye, Y.2
  • 26
    • 10044238568 scopus 로고    scopus 로고
    • Duality gaps in nonconvex stochastic optimization
    • doi:10.1007/s10107-003-0496-1
    • Dentcheva, D., & Römisch, W. (2004). Duality gaps in nonconvex stochastic optimization. Mathematical Programming, 101(3), 515-535. doi:10.1007/s10107-003-0496-1
    • (2004) Mathematical Programming , vol.101 , Issue.3 , pp. 515-535
    • Dentcheva, D.1    Römisch, W.2
  • 28
    • 0005093698 scopus 로고
    • The minimax approach to stochastic programming and an illustrative application
    • doi:10.1080/17442508708833436
    • Dupacova, J. (1987). The minimax approach to stochastic programming and an illustrative application. Stochastics, 20, 73-88. doi:10.1080/17442508708833436
    • (1987) Stochastics , vol.20 , pp. 73-88
    • Dupacova, J.1
  • 29
    • 0141719144 scopus 로고    scopus 로고
    • Recursive multiple-priors
    • doi:10.1016/S0022-0531(03)00097-8
    • Epstein, L., & Schneider, M. (2003). Recursive multiple-priors. Journal of Economic Theory, 113, 1-13. doi:10.1016/S0022-0531(03)00097-8
    • (2003) Journal of Economic Theory , vol.113 , pp. 1-13
    • Epstein, L.1    Schneider, M.2
  • 32
    • 67349139106 scopus 로고    scopus 로고
    • On a mixture of the fix-and-relax coordination and Lagrangian substitution schemes for multistage stochastic mixed integer programming
    • doi:10.1007/s11750-009-0090-7
    • Escudero, L. F. (2009). On a mixture of the fix-and-relax coordination and Lagrangian substitution schemes for multistage stochastic mixed integer programming. Top (Madrid), 17, 5-29. doi:10.1007/s11750-009-0090-7
    • (2009) Top (Madrid) , vol.17 , pp. 5-29
    • Escudero, L.F.1
  • 33
    • 33646430006 scopus 로고    scopus 로고
    • Extremely randomized trees
    • doi:10.1007/s10994-006-6226-1
    • Geurts, P., Ernst, D., & Wehenkel, L. (2006). Extremely randomized trees. Machine Learning, 63, 3-42. doi:10.1007/s10994-006-6226-1
    • (2006) Machine Learning , vol.63 , pp. 3-42
    • Geurts, P.1    Ernst, D.2    Wehenkel, L.3
  • 35
    • 33745684030 scopus 로고    scopus 로고
    • A class of stochastic programs with decision dependent uncertainty
    • doi:10.1007/s10107-006-0715-7
    • Goel, V., & Grossmann, I. E. (2006). A class of stochastic programs with decision dependent uncertainty. Mathematical Programming, 108, 355-394. doi:10.1007/s10107-006-0715-7
    • (2006) Mathematical Programming , vol.108 , pp. 355-394
    • Goel, V.1    Grossmann, I.E.2
  • 36
    • 36849072045 scopus 로고    scopus 로고
    • Graph implementations for nonsmooth convex programs
    • In Blondel, V., Boyd, S., & Kimura, H. (Eds.), London, UK: Springer-Verlag
    • Grant, M., & Boyd, S. (2008). Graph implementations for nonsmooth convex programs. In Blondel, V., Boyd, S., & Kimura, H. (Eds.), Recent advances in learning and control. Lecture Notes in Control and Information Sciences (Vol. 371, pp. 95-110). London, UK: Springer-Verlag.
    • (2008) Recent Advances In Learning and Control. Lecture Notes In Control and Information Sciences , vol.371 , pp. 95-110
    • Grant, M.1    Boyd, S.2
  • 38
    • 84959844370 scopus 로고
    • Changing tastes and coherent dynamic choice
    • doi:10.2307/2296609
    • Hammond, P. J. (1976). Changing tastes and coherent dynamic choice. The Review of Economic Studies, 43, 159-173. doi:10.2307/2296609
    • (1976) The Review of Economic Studies , vol.43 , pp. 159-173
    • Hammond, P.J.1
  • 40
    • 0037321577 scopus 로고    scopus 로고
    • Scenario reduction algorithms in stochastic programming
    • doi:10.1023/A:1021805924152
    • Heitsch, H., & Römisch, W. (2003). Scenario reduction algorithms in stochastic programming. Computational Optimization and Applications, 24, 187-206. doi:10.1023/A:1021805924152
    • (2003) Computational Optimization and Applications , vol.24 , pp. 187-206
    • Heitsch, H.1    Römisch, W.2
  • 41
    • 58249116102 scopus 로고    scopus 로고
    • Scenario tree modeling for multistage stochastic programs
    • doi:10.1007/s10107-007-0197-2
    • Heitsch, H., & Römisch, W. (2009). Scenario tree modeling for multistage stochastic programs. Mathematical Programming, 118(2), 371-406. doi:10.1007/s10107-007-0197-2
    • (2009) Mathematical Programming , vol.118 , Issue.2 , pp. 371-406
    • Heitsch, H.1    Römisch, W.2
  • 42
    • 47549102808 scopus 로고    scopus 로고
    • Numerical study of discretizations of multistage stochastic programs
    • Hilli, P., & Pennanen, T. (2008). Numerical study of discretizations of multistage stochastic programs. Kybernetika, 44, 185-204.
    • (2008) Kybernetika , vol.44 , pp. 185-204
    • Hilli, P.1    Pennanen, T.2
  • 43
    • 33745805403 scopus 로고    scopus 로고
    • A fast learning algorithm for deep belief nets
    • doi:10.1162/neco.2006.18.7.1527
    • Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006). A fast learning algorithm for deep belief nets. Neural Computation, 18, 1527-1554. doi:10.1162/neco.2006.18.7.1527
    • (2006) Neural Computation , vol.18 , pp. 1527-1554
    • Hinton, G.E.1    Osindero, S.2    Teh, Y.-W.3
  • 44
    • 33847404432 scopus 로고    scopus 로고
    • Financial scenario generation for stochastic multi-stage decision processes as facility location problems
    • doi:10.1007/s10479-006-0140-6
    • Hochreiter, R., & Pflug, G. C. (2007). Financial scenario generation for stochastic multi-stage decision processes as facility location problems. Annals of Operations Research, 152, 257-272. doi:10.1007/s10479-006-0140-6
    • (2007) Annals of Operations Research , vol.152 , pp. 257-272
    • Hochreiter, R.1    Pflug, G.C.2
  • 46
    • 0000154793 scopus 로고
    • Risk-sensitive Markov decision processes
    • doi:10.1287/mnsc.18.7.356
    • Howard, R. A., & Matheson, J. (1972). Risk-sensitive Markov decision processes. Management Science, 18(7), 356-369. doi:10.1287/mnsc.18.7.356
    • (1972) Management Science , vol.18 , Issue.7 , pp. 356-369
    • Howard, R.A.1    Matheson, J.2
  • 47
    • 0037321138 scopus 로고    scopus 로고
    • A heuristic for moment matching scenario generation
    • doi:10.1023/A:1021853807313
    • Høyland, K., Kaut, M., & Wallace, S. W. (2003). A heuristic for moment matching scenario generation. Computational Optimization and Applications, 24, 169-185. doi:10.1023/A:1021853807313
    • (2003) Computational Optimization and Applications , vol.24 , pp. 169-185
    • Høyland, K.1    Kaut, M.2    Wallace, S.W.3
  • 48
    • 69949103828 scopus 로고    scopus 로고
    • The value of multistage stochastic programming in capacity planning under uncertainty
    • doi:10.1287/opre.1080.0623
    • Huang, K., & Ahmed, S. (2009). The value of multistage stochastic programming in capacity planning under uncertainty. Operations Research, 57, 893-904. doi:10.1287/opre.1080.0623
    • (2009) Operations Research , vol.57 , pp. 893-904
    • Huang, K.1    Ahmed, S.2
  • 49
    • 34249830842 scopus 로고
    • Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs
    • doi:10.1007/BF02060936
    • Infanger, G. (1992). Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs. Annals of Operations Research, 39, 69-95. doi:10.1007/BF02060936
    • (1992) Annals of Operations Research , vol.39 , pp. 69-95
    • Infanger, G.1
  • 51
    • 0036832951 scopus 로고    scopus 로고
    • A sparse sampling algorithm for near-optimal planning in large Markov Decision Processes
    • doi:10.1023/A:1017932429737
    • Kearns, M. J., Mansour, Y., & Ng, A. Y. (2002). A sparse sampling algorithm for near-optimal planning in large Markov Decision Processes. Machine Learning, 49(2-3), 193-208. doi:10.1023/A:1017932429737
    • (2002) Machine Learning , vol.49 , Issue.2-3 , pp. 193-208
    • Kearns, M.J.1    Mansour, Y.2    Ng, A.Y.3
  • 52
    • 77952511490 scopus 로고    scopus 로고
    • Galerkin methods in dynamic stochastic programming
    • doi:10.1080/02331931003696368
    • Koivu, M., & Pennanen, T. (2010). Galerkin methods in dynamic stochastic programming. Optimization, 59, 339-354. doi:10.1080/02331931003696368
    • (2010) Optimization , vol.59 , pp. 339-354
    • Koivu, M.1    Pennanen, T.2
  • 53
    • 0035900037 scopus 로고    scopus 로고
    • Scenario generation and stochastic programming models for asset liability management
    • doi:10.1016/S0377-2217(00)00261-7
    • Kouwenberg, R. (2001). Scenario generation and stochastic programming models for asset liability management. European Journal of Operational Research, 134, 279-292. doi:10.1016/S0377-2217(00)00261-7
    • (2001) European Journal of Operational Research , vol.134 , pp. 279-292
    • Kouwenberg, R.1
  • 54
    • 77952493106 scopus 로고    scopus 로고
    • Numerical evaluation of approximation methods in stochastic programming
    • doi:10.1080/02331931003700756
    • Küchler, C., & Vigerske, S. (2010). Numerical evaluation of approximation methods in stochastic programming. Optimization, 59, 401-415. doi:10.1080/02331931003700756
    • (2010) Optimization , vol.59 , pp. 401-415
    • Küchler, C.1    Vigerske, S.2
  • 56
    • 0000643498 scopus 로고
    • Rules rather than discretion: The inconsistency of optimal plans
    • doi:10.1086/260580
    • Kydland, F. E., & Prescott, E. C. (1977). Rules rather than discretion: The inconsistency of optimal plans. The Journal of Political Economy, 85, 473-492. doi:10.1086/260580
    • (1977) The Journal of Political Economy , vol.85 , pp. 473-492
    • Kydland, F.E.1    Prescott, E.C.2
  • 61
    • 0032632474 scopus 로고    scopus 로고
    • Monte Carlo bounding techniques for determining solution quality in stochastic programs
    • doi:10.1016/S0167-6377(98)00054-6
    • Mak, W.-K., Morton, D. P., & Wood, R. K. (1999). Monte Carlo bounding techniques for determining solution quality in stochastic programs. Operations Research Letters, 24(1-2), 47-56. doi:10.1016/S0167-6377(98)00054-6
    • (1999) Operations Research Letters , vol.24 , Issue.1-2 , pp. 47-56
    • Mak, W.-K.1    Morton, D.P.2    Wood, R.K.3
  • 64
    • 70450197241 scopus 로고    scopus 로고
    • Stochastic approximation approach to stochastic programming
    • doi:10.1137/070704277
    • Nemirovski, A., Juditsky, A., Lan, G., & Shapiro, A. (2009). Stochastic approximation approach to stochastic programming. SIAM Journal on Optimization, 19, 1574-1609. doi:10.1137/070704277
    • (2009) SIAM Journal On Optimization , vol.19 , pp. 1574-1609
    • Nemirovski, A.1    Juditsky, A.2    Lan, G.3    Shapiro, A.4
  • 67
    • 0001565276 scopus 로고    scopus 로고
    • On optimal allocation of indivisibles under uncertainty
    • doi:10.1287/opre.46.3.381
    • Norkin, V. I., Ermoliev, Y. M., & Ruszczyński, A. (1998). On optimal allocation of indivisibles under uncertainty. Operations Research, 46, 381-395. doi:10.1287/opre.46.3.381
    • (1998) Operations Research , vol.46 , pp. 381-395
    • Norkin, V.I.1    Ermoliev, Y.M.2    Ruszczyński, A.3
  • 68
    • 2342563487 scopus 로고    scopus 로고
    • Optimal quadratic quantization for numerics: The Gaussian case
    • doi:10.1515/156939603322663321
    • Pages, G., & Printems, J. (2003). Optimal quadratic quantization for numerics: The Gaussian case. Monte Carlo Methods and Applications, 9, 135-166. doi:10.1515/156939603322663321
    • (2003) Monte Carlo Methods and Applications , vol.9 , pp. 135-166
    • Pages, G.1    Printems, J.2
  • 69
    • 45749127048 scopus 로고    scopus 로고
    • Epi-convergent discretizations of multistage stochastic programs via integration quadratures
    • doi:10.1007/s10107-007-0113-9
    • Pennanen, T. (2009). Epi-convergent discretizations of multistage stochastic programs via integration quadratures. Mathematical Programming, 116, 461-479. doi:10.1007/s10107-007-0113-9
    • (2009) Mathematical Programming , vol.116 , pp. 461-479
    • Pennanen, T.1
  • 70
    • 84967647219 scopus 로고    scopus 로고
    • Hackensack, NJ: World Scientific Publishing Company. doi:10.1142/9789812708724
    • Pflug, G. C., & Römisch, W. (2007). Modeling, measuring and managing risk. Hackensack, NJ: World Scientific Publishing Company. doi:10.1142/9789812708724
    • (2007) Modeling, Measuring and Managing Risk
    • Pflug, G.C.1    Römisch, W.2
  • 72
    • 77950462140 scopus 로고    scopus 로고
    • Stochastic programming in transportation and logistics
    • In Ruszczyński, A., & Shapiro, A. (Eds.), Amsterdam, The Netherlands: Elsevier
    • Powell, W. B., & Topaloglu, H. (2003). Stochastic programming in transportation and logistics. In Ruszczyński, A., & Shapiro, A. (Eds.), Stochastic programming. Handbooks in operations research and management science (Vol. 10, pp. 555-635). Amsterdam, The Netherlands: Elsevier.
    • (2003) Stochastic Programming. Handbooks In Operations Research and Management Science , vol.10 , pp. 555-635
    • Powell, W.B.1    Topaloglu, H.2
  • 73
    • 0003410675 scopus 로고
    • Dordrecht, The Netherlands: Kluwer Academic Publishers
    • Prékopa, A. (1995). Stochastic programming. Dordrecht, The Netherlands: Kluwer Academic Publishers.
    • (1995) Stochastic Programming
    • Prékopa, A.1
  • 75
    • 0036873891 scopus 로고    scopus 로고
    • Quantitative stability in stochastic programming: The method of probability metrics
    • Rachev, S. T., & Römisch, W. (2002). Quantitative stability in stochastic programming: The method of probability metrics. Mathematical Programming, 27(4), 792-818.
    • (2002) Mathematical Programming , vol.27 , Issue.4 , pp. 792-818
    • Rachev, S.T.1    Römisch, W.2
  • 78
    • 0004267646 scopus 로고
    • Princeton, NJ: Princeton University Press
    • Rockafellar, R. T. (1970). Convex analysis. Princeton, NJ: Princeton University Press.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 79
    • 0002062038 scopus 로고    scopus 로고
    • Optimization of conditional value-at-risk
    • Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2(3), 21-41.
    • (2000) Journal of Risk , vol.2 , Issue.3 , pp. 21-41
    • Rockafellar, R.T.1    Uryasev, S.2
  • 80
    • 0000514655 scopus 로고
    • Scenarios and policy aggregation in optimization under uncertainty
    • doi:10.1287/moor.16.1.119
    • Rockafellar, R. T., & Wets, R. J.-B. (1991). Scenarios and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16, 119-147. doi:10.1287/moor.16.1.119
    • (1991) Mathematics of Operations Research , vol.16 , pp. 119-147
    • Rockafellar, R.T.1    Wets, R.J.-B.2
  • 81
    • 84963107372 scopus 로고
    • A note on measurement of utility
    • doi:10.2307/2967612
    • Samuelson, P. A. (1937). A note on measurement of utility. The Review of Economic Studies, 4(2), 155-161. doi:10.2307/2967612
    • (1937) The Review of Economic Studies , vol.4 , Issue.2 , pp. 155-161
    • Samuelson, P.A.1
  • 82
    • 0000151690 scopus 로고    scopus 로고
    • Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis reduction
    • doi:10.1007/BF02680560
    • Schultz, R., Stougie, L., & Van der Vlerk, M. H. (1998). Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis reduction. Mathematical Programming, 83, 229-252. doi:10.1007/BF02680560
    • (1998) Mathematical Programming , vol.83 , pp. 229-252
    • Schultz, R.1    Stougie, L.2    Van der Vlerk, M.H.3
  • 83
    • 0013300221 scopus 로고
    • Network planning with random demand
    • doi:10.1007/BF02110042
    • Sen, S., Doverspike, R. D., & Cosares, S. (1994). Network planning with random demand. Telecommunication Systems, 3, 11-30. doi:10.1007/BF02110042
    • (1994) Telecommunication Systems , vol.3 , pp. 11-30
    • Sen, S.1    Doverspike, R.D.2    Cosares, S.3
  • 84
    • 31744441041 scopus 로고    scopus 로고
    • Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming
    • doi:10.1007/s10107-005-0592-5
    • Sen, S., & Sherali, H. (2006). Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming. Mathematical Programming, 106, 203-223. doi:10.1007/s10107-005-0592-5
    • (2006) Mathematical Programming , vol.106 , pp. 203-223
    • Sen, S.1    Sherali, H.2
  • 85
    • 33644553800 scopus 로고    scopus 로고
    • A stochastic programming approach to power portfolio optimization
    • doi:10.1287/opre.1050.0264
    • Sen, S., Yu, L., & Genc, T. (2006). A stochastic programming approach to power portfolio optimization. Operations Research, 54, 55-72. doi:10.1287/opre.1050.0264
    • (2006) Operations Research , vol.54 , pp. 55-72
    • Sen, S.1    Yu, L.2    Genc, T.3
  • 86
    • 21044447935 scopus 로고    scopus 로고
    • Inference of statistical bounds for multistage stochastic programming problems
    • doi:10.1007/s001860300280
    • Shapiro, A. (2003a). Inference of statistical bounds for multistage stochastic programming problems. Mathematical Methods of Operations Research, 58(1), 57-68. doi:10.1007/s001860300280
    • (2003) Mathematical Methods of Operations Research , vol.58 , Issue.1 , pp. 57-68
    • Shapiro, A.1
  • 87
    • 77950512601 scopus 로고    scopus 로고
    • Monte Carlo sampling methods
    • In Ruszczyński, A., & Shapiro, A. (Eds.), Amsterdam, The Netherlands: Elsevier
    • Shapiro, A. (2003b). Monte Carlo sampling methods. In Ruszczyński, A., & Shapiro, A. (Eds.), Stochastic programming. Handbooks in operations research and management science (Vol. 10, pp. 353-425). Amsterdam, The Netherlands: Elsevier.
    • (2003) Stochastic Programming. Handbooks In Operations Research and Management Science , vol.10 , pp. 353-425
    • Shapiro, A.1
  • 88
    • 28044447588 scopus 로고    scopus 로고
    • On complexity of multistage stochastic programs
    • doi:10.1016/j.orl.2005.02.003
    • Shapiro, A. (2006). On complexity of multistage stochastic programs. Operations Research Letters, 34(1), 1-8. doi:10.1016/j.orl.2005.02.003
    • (2006) Operations Research Letters , vol.34 , Issue.1 , pp. 1-8
    • Shapiro, A.1
  • 89
    • 64949118607 scopus 로고    scopus 로고
    • On a time-consistency concept in risk averse multistage stochastic programming
    • doi:10.1016/j.orl.2009.02.005
    • Shapiro, A. (2009). On a time-consistency concept in risk averse multistage stochastic programming. Operations Research Letters, 37, 143-147. doi:10.1016/j.orl.2009.02.005
    • (2009) Operations Research Letters , vol.37 , pp. 143-147
    • Shapiro, A.1
  • 91
    • 58149433367 scopus 로고
    • Rational choice and the structure of the environment
    • doi:10.1037/h0042769
    • Simon, H. A. (1956). Rational choice and the structure of the environment. Psychological Review, 63, 129-138. doi:10.1037/h0042769
    • (1956) Psychological Review , vol.63 , pp. 129-138
    • Simon, H.A.1
  • 92
    • 33947731462 scopus 로고    scopus 로고
    • Simulation-based optimal sensor scheduling with application to observer trajectory planning
    • doi:10.1016/j.automatica.2006.11.019
    • Singh, S. S., Kantas, N., Vo, B.-N., Doucet, A., & Evans, R. J. (2007). Simulation-based optimal sensor scheduling with application to observer trajectory planning. Automatica, 43, 817-830. doi:10.1016/j.automatica.2006.11.019
    • (2007) Automatica , vol.43 , pp. 817-830
    • Singh, S.S.1    Kantas, N.2    Vo, B.-N.3    Doucet, A.4    Evans, R.J.5
  • 94
    • 84963071606 scopus 로고
    • Myopia and inconsistency in dynamic utility maximization
    • doi:10.2307/2295722
    • Strotz, R. H. (1955). Myopia and inconsistency in dynamic utility maximization. The Review of Economic Studies, 23, 165-180. doi:10.2307/2295722
    • (1955) The Review of Economic Studies , vol.23 , pp. 165-180
    • Strotz, R.H.1
  • 96
    • 84875379930 scopus 로고    scopus 로고
    • The MathWorks, Inc, Retrieved from
    • The MathWorks, Inc. (2004). Matlab. Retrieved from http://www.mathworks.com
    • (2004) Matlab
  • 97
    • 77952545266 scopus 로고    scopus 로고
    • Convex approximations for a class of mixed-integer recourse models
    • doi:10.1007/s10479-009-0591-7
    • Van der Vlerk, M. H. (2010). Convex approximations for a class of mixed-integer recourse models. Annals of Operations Research, 177, 139-151. doi:10.1007/s10479-009-0591-7
    • (2010) Annals of Operations Research , vol.177 , pp. 139-151
    • Van der Vlerk, M.H.1
  • 100
    • 0037322974 scopus 로고    scopus 로고
    • The sample average approximation method applied to stochastic routing problems: A computational study
    • doi:10.1023/A:1021814225969
    • Verweij, B., Ahmed, S., Kleywegt, A., Nemhauser, G., & Shapiro, A. (2003). The sample average approximation method applied to stochastic routing problems: A computational study. Computational Optimization and Applications, 24(2-3), 289-333. doi:10.1023/A:1021814225969
    • (2003) Computational Optimization and Applications , vol.24 , Issue.2-3 , pp. 289-333
    • Verweij, B.1    Ahmed, S.2    Kleywegt, A.3    Nemhauser, G.4    Shapiro, A.5
  • 102
    • 0016084468 scopus 로고
    • Stochastic programs with fixed recourse: The equivalent deterministic program
    • doi:10.1137/1016053
    • Wets, R. J.-B. (1974). Stochastic programs with fixed recourse: The equivalent deterministic program. SIAM Review, 16, 309-339. doi:10.1137/1016053
    • (1974) SIAM Review , vol.16 , pp. 309-339
    • Wets, R.J.-B.1


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