메뉴 건너뛰기




Volumn , Issue , 2011, Pages 1-469

Introduction to Stochastic Programming

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84926477808     PISSN: 14318598     EISSN: 21971773     Source Type: Book Series    
DOI: None     Document Type: Chapter
Times cited : (139)

References (442)
  • 2
    • 38549096152 scopus 로고    scopus 로고
    • Dynamic bid prices in revenue management
    • ) pp
    • D. Adelman, “Dynamic bid prices in revenue management,” Operations Research 55 (2007) pp. 647–661.
    • (2007) Operations Research , vol.55 , pp. 647-661
    • Adelman, D.1
  • 3
    • 33644511396 scopus 로고    scopus 로고
    • Convexity and decomposition of mean-risk stochastic programs
    • ) pp
    • S. Ahmed, “Convexity and decomposition of mean-risk stochastic programs,” Mathematical Programming Series A 106 (2006) pp. 433–446.
    • (2006) Mathematical Programming Series A , vol.106 , pp. 433-446
    • Ahmed, S.1
  • 4
    • 21144438339 scopus 로고    scopus 로고
    • A finite branch and bound algorithm for two-stage stochastic integer programs
    • ) pp
    • S. Ahmed, M. Tawarmalani, and N. V. Sahinidis, “A finite branch and bound algorithm for two-stage stochastic integer programs,” Mathematical Programming 100 (2004) pp.355-377.
    • (2004) Mathematical Programming , vol.100 , pp. 355-377
    • Ahmed, S.1    Tawarmalani, M.2    Sahinidis, N.V.3
  • 5
    • 85098108255 scopus 로고    scopus 로고
    • E.D. Andersen, “ The homogeneous and self-dual model and algorithm for linear optimization,” MOSEK Technical report: TR-1-2009, Copenhagen, DK, 2009
    • E.D. Andersen, “ The homogeneous and self-dual model and algorithm for linear optimization,” MOSEK Technical report: TR-1-2009, Copenhagen, DK, 2009.
  • 7
    • 34249972221 scopus 로고
    • A combined Phase I–Phase II projective algorithm for linear programming
    • ) pp
    • K.M. Anstreicher, “A combined Phase I–Phase II projective algorithm for linear programming,” Mathematical Programming 43 (1989) pp. 209–223.
    • (1989) Mathematical Programming , vol.43 , pp. 209-223
    • Anstreicher, K.M.1
  • 8
    • 84990704714 scopus 로고
    • Performance of a benchmark parallel implementation of the Van Slyke and Wets algorithm for two-stage stochastic programs on the Sequent/Balance
    • ) pp
    • K.A. Ariyawansa and D.D. Hudson, “Performance of a benchmark parallel implementation of the Van Slyke and Wets algorithm for two-stage stochastic programs on the Sequent/Balance,” Concurrency Practice and Experience 3 (1991) pp. 109–128.
    • (1991) Concurrency Practice and Experience , vol.3 , pp. 109-128
    • Ariyawansa, K.A.1    Hudson, D.D.2
  • 12
    • 0000542426 scopus 로고
    • Approximation and convergence in nonlinear optimization
    • in: O.L. Mangasarian, R.R. Meyer and S.M. Robinson, Eds., Academic Press, New York–London, ) pp
    • H. Attouch and R.J-B Wets, “Approximation and convergence in nonlinear optimization” in: O.L. Mangasarian, R.R. Meyer and S.M. Robinson, Eds., Nonlinear programming, 4 (Academic Press, New York–London, 1981) pp. 367–394.
    • (1981) Nonlinear Programming , vol.4 , pp. 367-394
    • Attouch, H.1    Wets, R.J.-B.2
  • 13
    • 0042270345 scopus 로고
    • The value of information and stochastic programming
    • ) pp
    • M. Avriel and A.C. Williams, “The value of information and stochastic programming,” Operations Research 18 (1970) pp. 947–954.
    • (1970) Operations Research , vol.18 , pp. 947-954
    • Avriel, M.1    Williams, A.C.2
  • 14
    • 0040501585 scopus 로고
    • A cutting plane method from analytic centers for stochastic programming
    • ) pp
    • O. Bahn, J.-L. Goffin, O. du Merle, and J.-Ph. Vial, “A cutting plane method from analytic centers for stochastic programming,” Mathematical Programming, 69 (1995) pp. 45–73.
    • (1995) Mathematical Programming , vol.69 , pp. 45-73
    • Bahn, O.1    Goffin, J.-L.2    Merle, O.D.3    Vial, J.-P.4
  • 18
    • 0001454852 scopus 로고
    • On minimizing a convex function subject to linear inequalities
    • ) pp
    • E.M.L. Beale, “On minimizing a convex function subject to linear inequalities,” J. Royal Statistical Society, Series B 17 (1955) pp. 173–184.
    • (1955) J. Royal Statistical Society, Series B , vol.17 , pp. 173-184
    • Beale, E.M.L.1
  • 19
    • 84974144054 scopus 로고
    • “The use of quadratic programming in stochastic linear programming,” Rand Report P-2404-1
    • E.M.L. Beale, “The use of quadratic programming in stochastic linear programming,” Rand Report P-2404-1, The Rand Corporation (1961).
    • (1961) The Rand Corporation
    • Beale, E.M.L.1
  • 20
    • 0006139810 scopus 로고
    • Multi-time-period stochastic programming
    • M.A.H. Dempster, Ed., Academic Press, New York, NY, ) pp
    • E.M.L. Beale, J.J.H. Forrest, and C.J. Taylor, “Multi-time-period stochastic programming” in: M.A.H. Dempster, Ed., Stochastic Programming (Academic Press, New York, NY, 1980) pp. 387–402.
    • (1980) Stochastic Programming , pp. 387-402
    • Beale, E.M.L.1    Forrest, J.J.H.2    Taylor, C.J.3
  • 21
    • 0022699239 scopus 로고
    • A first order approach to a class of multi-time-period stochastic programming problems
    • ) pp
    • E.M.L. Beale, G.B. Dantzig, and R.D. Watson, “A first order approach to a class of multi-time-period stochastic programming problems,” Mathematical Programming Study 27 (1986) pp. 103–117.
    • (1986) Mathematical Programming Study , vol.27 , pp. 103-117
    • Beale, E.M.L.1    Dantzig, G.B.2    Watson, R.D.3
  • 22
    • 0003787146 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R. Bellman, Dynamic Programming (Princeton University Press, Princeton, NJ, 1957).
    • (1957) Dynamic Programming
    • Bellman, R.1
  • 23
    • 33644695242 scopus 로고    scopus 로고
    • Extending the Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems
    • Ben-Tal, A., Boyd, S., Nemirovski, A., Extending the Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems, Mathematical Programming 107:1-2 (2006), 63–89.
    • (2006) Mathematical Programming , vol.107 , Issue.1-2 , pp. 63-89
    • Ben-Tal, A.1    Boyd, S.2    Nemirovski, A.3
  • 25
    • 0022806911 scopus 로고
    • Expected utility, penalty functions, and duality in stochastic nonlinear programming
    • ) pp
    • A. Ben-Tal and M. Teboulle, “Expected utility, penalty functions, and duality in stochastic nonlinear programming,” Management Science 32 (1986) pp. 1445–1466.
    • (1986) Management Science , vol.32 , pp. 1445-1466
    • Ben-Tal, A.1    Teboulle, M.2
  • 26
    • 9644308639 scopus 로고
    • Partitioning procedures for solving mixed-variables programming problems
    • ) pp
    • J. F. Benders, “Partitioning procedures for solving mixed-variables programming problems,” Numerische Mathematik 4 (1962) pp. 238–252.
    • (1962) Numerische Mathematik , vol.4 , pp. 238-252
    • Benders, J.F.1
  • 27
    • 26444522237 scopus 로고
    • Some numerical methods in stochastic linear programming under risk and uncertainty
    • M.A.H. Dempster, Ed., Academic Press, New York, NY, ) pp
    • B. Bereanu, “Some numerical methods in stochastic linear programming under risk and uncertainty” in: M.A.H. Dempster, Ed., Stochastic Programming (Academic Press, New York, NY, 1980) pp. 169–205.
    • (1980) Stochastic Programming , pp. 169-205
    • Bereanu, B.1
  • 29
    • 0022099769 scopus 로고
    • Optimal server location on a network operating as a M/G/1 queue
    • ) pp
    • O. Berman, R.C. Larson, and S.S. Chiu, “Optimal server location on a network operating as a M/G/1 queue,” Operations Research 33 (1985) pp. 746–770.
    • (1985) Operations Research , vol.33 , pp. 746-770
    • Berman, O.1    Larson, R.C.2    Chiu, S.S.3
  • 32
    • 77953089426 scopus 로고    scopus 로고
    • Optimality of affine policies in multistage robust optimization
    • ) pp
    • D. Bertsimas, D.A. Iancu, and P.A. Parrilo, “Optimality of affine policies in multistage robust optimization,” Mathematics of Operations Research 35 (2010) pp. 363–394.
    • (2010) Mathematics of Operations Research , vol.35 , pp. 363-394
    • Bertsimas, D.1    Iancu, D.A.2    Parrilo, P.A.3
  • 34
    • 14944365520 scopus 로고    scopus 로고
    • Probabilistic combinatorial optimization: Moments, semidefinite programming and asymptotic bounds
    • ) pp
    • D. Bertsimas, K. Natarajan, and C-P. Teo, “Probabilistic combinatorial optimization: Moments, semidefinite programming and asymptotic bounds,” SIAM J. of Optimization 15 (2004) pp. 185-209.
    • (2004) SIAM J. of Optimization , vol.15 , pp. 185-209
    • Bertsimas, D.1    Natarajan, K.2    Teo, C.-P.3
  • 35
    • 23844499733 scopus 로고    scopus 로고
    • Optimal inequalities in probability: A convex programming approach
    • ) pp
    • D. Bertsimas and I. Popescu, “ Optimal inequalities in probability: A convex programming approach,” SIAM Journal of Optimization, 15 (2004) pp. 780–804.
    • (2004) SIAM Journal of Optimization , vol.15 , pp. 780-804
    • Bertsimas, D.1    Popescu, I.2
  • 36
    • 33644689113 scopus 로고    scopus 로고
    • Tractable approximations to robust conic optimization problems
    • ) pp
    • D. Bertsimas and M. Sim, “Tractable approximations to robust conic optimization problems,” Mathematical Programming 107 (2006) pp. 5–36.
    • (2006) Mathematical Programming , vol.107 , pp. 5-36
    • Bertsimas, D.1    Sim, M.2
  • 37
    • 0002313454 scopus 로고
    • Optimizing resource acquisition decisions by stochastic programming
    • ) pp
    • D. Bienstock and J.F. Shapiro, “Optimizing resource acquisition decisions by stochastic programming,” Management Science 34 (1988) pp. 215–229.
    • (1988) Management Science , vol.34 , pp. 215-229
    • Bienstock, D.1    Shapiro, J.F.2
  • 39
    • 84936543084 scopus 로고    scopus 로고
    • Ph.D. Dissertation and Technical Report SOL 80-29, Systems Optimization Laboratory, Stanford University (Stanford, CA, 1980)
    • J.R. Birge, “Solution Methods for Stochastic Dynamic Linear Programs,” Ph.D. Dissertation and Technical Report SOL 80-29, Systems Optimization Laboratory, Stanford University (Stanford, CA, 1980).
    • Solution Methods for Stochastic Dynamic Linear Programs
    • Birge, J.R.1
  • 40
    • 0020301982 scopus 로고
    • The value of the stochastic solution in stochastic linear programs with fixed recourse
    • ) pp
    • J.R. Birge, “The value of the stochastic solution in stochastic linear programs with fixed recourse,” Mathematical Programming 24 (1982) pp. 314–325.
    • (1982) Mathematical Programming , vol.24 , pp. 314-325
    • Birge, J.R.1
  • 41
    • 85098179719 scopus 로고    scopus 로고
    • J.R. Birge, “Using sequential approximations in the L-shaped and generalized programming algorithms for stochastic linear programs,” Technical Report 83-12, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1983); available at http://hdl.handle.net/2027.42/3642
    • J.R. Birge, “Using sequential approximations in the L-shaped and generalized programming algorithms for stochastic linear programs,” Technical Report 83-12, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1983); available at http://hdl.handle.net/2027.42/3642.
  • 43
    • 0021855437 scopus 로고
    • Aggregation in stochastic linear programming
    • ) pp
    • J.R. Birge, “Aggregation in stochastic linear programming,” Mathematical Programming 31 (1985a) pp. 25–41.
    • (1985) Mathematical Programming , vol.31 , pp. 25-41
    • Birge, J.R.1
  • 44
    • 0022129190 scopus 로고
    • Decomposition and partitioning methods for multi–stage stochastic linear programs
    • ) pp
    • J.R. Birge, “Decomposition and partitioning methods for multi–stage stochastic linear programs,” Operations Research 33 (1985b) pp. 989–1007.
    • (1985) Operations Research , vol.33 , pp. 989-1007
    • Birge, J.R.1
  • 45
    • 0040946879 scopus 로고
    • Exhaustible recourse models with uncertain returns from exploration investment
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • J.R. Birge, “Exhaustible recourse models with uncertain returns from exploration investment” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988a) pp. 481–488.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 481-488
    • Birge, J.R.1
  • 46
    • 0041468812 scopus 로고
    • The relationship between the L-shaped method and dual basis factorization for stochastic linear programming
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • J.R. Birge, “The relationship between the L-shaped method and dual basis factorization for stochastic linear programming” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988b) pp. 267–272.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 267-272
    • Birge, J.R.1
  • 47
    • 85098155242 scopus 로고    scopus 로고
    • Multistage stochastic planning models using piecewise linear response functions
    • Eds., Resource Planning under Uncertainty for Electric Power Systems (NSF
    • J.R. Birge, “Multistage stochastic planning models using piecewise linear response functions” in: G. Dantzig and P. Glynn, Eds., Resource Planning under Uncertainty for Electric Power Systems (NSF, 1989).
    • G. Dantzig and P. Glynn , pp. 1989
    • Birge, J.R.1
  • 48
    • 85098124113 scopus 로고    scopus 로고
    • J.R. Birge, “Quasi-Monte Carlo methods for option evaluation,” Technical Report, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1994); available at http://hdl.handle.net/2027.42/3632
    • J.R. Birge, “Quasi-Monte Carlo methods for option evaluation,” Technical Report, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1994); available at http://hdl.handle.net/2027.42/3632.
  • 49
    • 0346829723 scopus 로고    scopus 로고
    • Option methods for incorporating risk into linear capacity planning models
    • ), pp
    • J.R. Birge, “Option methods for incorporating risk into linear capacity planning models,” Manufacturing and Service Operations Management 2 (2000), pp. 189–194.
    • (2000) Manufacturing and Service Operations Management , vol.2 , pp. 189-194
    • Birge, J.R.1
  • 50
    • 85098166589 scopus 로고    scopus 로고
    • J.R. Birge and M.A.H. Dempster, “Optimality conditions for match-up strategies in stochastic scheduling and related dynamic stochastic optimization problems,” Technical Report 92-58, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1992); available at http://hdl.handle.net/2027.42/3645
    • J.R. Birge and M.A.H. Dempster, “Optimality conditions for match-up strategies in stochastic scheduling and related dynamic stochastic optimization problems,” Technical Report 92-58, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1992); available at http://hdl.handle.net/2027.42/3645.
  • 51
    • 0003130576 scopus 로고    scopus 로고
    • A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs
    • ) pp
    • J.R. Birge, C.J. Donohue, D.F. Holmes, and O.G. Svintsiski, “A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs,” Mathematical Programming 75 (1996) pp. 327–352.
    • (1996) Mathematical Programming , vol.75 , pp. 327-352
    • Birge, J.R.1    Donohue, C.J.2    Holmes, D.F.3    Svintsiski, O.G.4
  • 52
    • 0342458735 scopus 로고
    • Bounding separable recourse functions with limited distribution information
    • ) pp
    • J.R. Birge and J. Dulá, “Bounding separable recourse functions with limited distribution information,” Annals of Operations Research 30 (1991) pp. 277–298.
    • (1991) Annals of Operations Research , vol.30 , pp. 277-298
    • Birge, J.R.1    Dulá, J.2
  • 53
    • 38249011080 scopus 로고
    • Prior reduced fill-in in the solution of equations in interior point algorithms
    • ) pp
    • J.R. Birge, R.M. Freund, and R.J. Vanderbei, “Prior reduced fill-in in the solution of equations in interior point algorithms,” Operations Research Letters 11 (1992) pp. 195–198.
    • (1992) Operations Research Letters , vol.11 , pp. 195-198
    • Birge, J.R.1    Freund, R.M.2    Vanderbei, R.J.3
  • 54
    • 0027002128 scopus 로고
    • Efficient solution of two-stage stochastic linear programs using interior point methods
    • ) pp
    • J.R. Birge and D.F. Holmes, “Efficient solution of two-stage stochastic linear programs using interior point methods,” Computational Optimization and Applications 1 (1992) pp. 245– 276.
    • (1992) Computational Optimization and Applications , vol.1 , pp. 245-276
    • Birge, J.R.1    Holmes, D.F.2
  • 55
    • 0023981220 scopus 로고
    • A multicut algorithm for two-stage stochastic linear programs
    • ) pp
    • J.R. Birge and F.V. Louveaux, “A multicut algorithm for two-stage stochastic linear programs,” European Journal of Operations Research 34 (1988) pp. 384–392.
    • (1988) European Journal of Operations Research , vol.34 , pp. 384-392
    • Birge, J.R.1    Louveaux, F.V.2
  • 56
    • 35148839193 scopus 로고
    • Bounds on expected project tardiness
    • ) pp
    • J.R. Birge and M.J. Maddox, “Bounds on expected project tardiness,” Operations Research 43 (1995) pp. 838–850.
    • (1995) Operations Research , vol.43 , pp. 838-850
    • Birge, J.R.1    Maddox, M.J.2
  • 57
    • 0002851630 scopus 로고    scopus 로고
    • Using second moment information in stochastic scheduling
    • G. Yin and Q. Zhang, Eds., Springer-Verlag, New York, NY, ) pp
    • J.R. Birge and M.J. Maddox, “Using second moment information in stochastic scheduling” in: G. Yin and Q. Zhang, Eds., Recent Advances in Control and Manufacturing Systems (Springer-Verlag, New York, NY, 1996) pp. 99–120.
    • (1996) Recent Advances in Control and Manufacturing Systems , pp. 99-120
    • Birge, J.R.1    Maddox, M.J.2
  • 58
    • 0001238788 scopus 로고
    • Computing block-angular Karmarkar projections with applications to stochastic programming
    • ) pp
    • J.R. Birge and L. Qi, “Computing block-angular Karmarkar projections with applications to stochastic programming,” Management Science 34 (1988) pp. 1472–1479.
    • (1988) Management Science , vol.34 , pp. 1472-1479
    • Birge, J.R.1    Qi, L.2
  • 59
    • 0012629012 scopus 로고
    • Semiregularity and generalized subdifferentials with applications to optimization
    • ) pp
    • J.R. Birge and L. Qi, “Semiregularity and generalized subdifferentials with applications to optimization,” Mathematics of Operations Research 18 (1993) pp. 982–1006.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 982-1006
    • Birge, J.R.1    Qi, L.2
  • 60
    • 0011830307 scopus 로고
    • Subdifferential convergence in stochastic programs
    • ) pp
    • J.R. Birge and L. Qi, “Subdifferential convergence in stochastic programs,” SIAM J. Optimization 5 (1995) pp. 436–453.
    • (1995) SIAM J. Optimization , vol.5 , pp. 436-453
    • Birge, J.R.1    Qi, L.2
  • 61
    • 21344469634 scopus 로고    scopus 로고
    • Parallel decomposition of large-scale stochastic nonlinear programs
    • ), pp
    • J.R. Birge and C.H. Rosa, “Parallel decomposition of large-scale stochastic nonlinear programs,” Annals of Operations Research 64 (1996), pp. 39–65.
    • (1996) Annals of Operations Research , vol.64 , pp. 39-65
    • Birge, J.R.1    Rosa, C.H.2
  • 62
    • 0002106859 scopus 로고
    • Upper bounds on the expected value of a convex function using subgradient and conjugate function information
    • ) pp
    • J.R. Birge and M. Teboulle, “Upper bounds on the expected value of a convex function using subgradient and conjugate function information,” Mathematics of Operations Research 14 (1989) pp. 745–759.
    • (1989) Mathematics of Operations Research , vol.14 , pp. 745-759
    • Birge, J.R.1    Teboulle, M.2
  • 63
    • 0042585527 scopus 로고
    • Refining bounds for stochastic linear programs with linearly transformed independent random variables
    • ) pp
    • J.R. Birge and S.W. Wallace, “Refining bounds for stochastic linear programs with linearly transformed independent random variables,” Operations Research Letters 5 (1986) pp. 73– 77.
    • (1986) Operations Research Letters , vol.5 , pp. 73-77
    • Birge, J.R.1    Wallace, S.W.2
  • 64
    • 0024001667 scopus 로고
    • A separable piecewise linear upper bound for stochastic linear programs
    • ) pp
    • J.R. Birge and S.W. Wallace, “A separable piecewise linear upper bound for stochastic linear programs,” SIAM Journal on Control and Optimization 26 (1988) pp. 725–739.
    • (1988) SIAM Journal on Control and Optimization , vol.26 , pp. 725-739
    • Birge, J.R.1    Wallace, S.W.2
  • 66
    • 0022698417 scopus 로고
    • Designing approximation schemes for stochastic optimization problems, in particular, for stochastic programs with recourse
    • ) pp
    • J.R. Birge and R.J-B Wets, “Designing approximation schemes for stochastic optimization problems, in particular, for stochastic programs with recourse,” Mathematical Programming Study 27 (1986) pp. 54–102.
    • (1986) Mathematical Programming Study , vol.27 , pp. 54-102
    • Birge, J.R.1    Wets, R.J.-B.2
  • 67
    • 0023295926 scopus 로고
    • Computing bounds for stochastic programming problems by means of a generalized moment problem
    • ) pp
    • J.R. Birge and R.J-B Wets, “Computing bounds for stochastic programming problems by means of a generalized moment problem,” Mathematics of Operations Research 12 (1987) pp. 49–162.
    • (1987) Mathematics of Operations Research , vol.12 , pp. 49-162
    • Birge, J.R.1    Wets, R.J.-B.2
  • 68
    • 4043083200 scopus 로고
    • Sublinear upper bounds for stochastic programs with recourse
    • ) pp
    • J.R. Birge and R.J-B Wets, “Sublinear upper bounds for stochastic programs with recourse,” Mathematical Programming 43 (1989) pp. 131–149.
    • (1989) Mathematical Programming , vol.43 , pp. 131-149
    • Birge, J.R.1    Wets, R.J.-B.2
  • 69
    • 56749153647 scopus 로고    scopus 로고
    • Successive linear approximation solution of infinite horizon dynamic stochastic programs
    • ) pp
    • J.R. Birge and G. Zhao, “Successive linear approximation solution of infinite horizon dynamic stochastic programs,”SIAM Journal on Optimization 18 (2007) pp. 1165–1186.
    • (2007) ”SIAM Journal on Optimization , vol.18 , pp. 1165-1186
    • Birge, J.R.1    Zhao, G.2
  • 70
    • 0023983758 scopus 로고
    • On upper bounds of sequential stochastic production planning problems
    • ) pp
    • G.R. Bitran and D. Sarkar, “On upper bounds of sequential stochastic production planning problems,” European Journal of Operational Research 34 (1988) pp. 191–207.
    • (1988) European Journal of Operational Research , vol.34 , pp. 191-207
    • Bitran, G.R.1    Sarkar, D.2
  • 71
    • 0021484235 scopus 로고
    • Deterministic approximations to stochastic production problems
    • ) pp
    • G.R. Bitran and H. Yanasse, “Deterministic approximations to stochastic production problems,” Operations Research 32 (1984) pp. 999–1018.
    • (1984) Operations Research , vol.32 , pp. 999-1018
    • Bitran, G.R.1    Yanasse, H.2
  • 72
    • 0020167733 scopus 로고
    • The value function of an integer program
    • ) pp
    • C.E. Blair and R.G. Jeroslow, “The value function of an integer program,” Mathematical Programming 23 (1982) pp. 237–273.
    • (1982) Mathematical Programming , vol.23 , pp. 237-273
    • Blair, C.E.1    Jeroslow, R.G.2
  • 73
    • 85015692260 scopus 로고
    • The pricing of options and corporate liabilities
    • ) pp
    • F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy 81 (1973) pp. 737–654.
    • (1973) Journal of Political Economy , vol.81 , pp. 737-654
    • Black, F.1    Scholes, M.2
  • 74
  • 75
    • 0000130180 scopus 로고
    • Convex set functions in d-spaces
    • ) pp
    • C. Borell, “Convex set functions in d-spaces,” Periodica Mathematica Jungarica 6 (1975) pp. 111–136.
    • (1975) Periodica Mathematica Jungarica , vol.6 , pp. 111-136
    • Borell, C.1
  • 76
    • 0001457345 scopus 로고
    • Airline seat allocation with multiple nested fare classes
    • ) pp
    • S.L. Brumelle and J.I. McGill, “Airline seat allocation with multiple nested fare classes,” Operations Research 41 (1993) pp. 127–137.
    • (1993) Operations Research , vol.41 , pp. 127-137
    • Brumelle, S.L.1    McGill, J.I.2
  • 77
    • 12344268988 scopus 로고    scopus 로고
    • Uncertain convex programs: Randomized solutions and confidence levels
    • ) pp
    • G. Calafiore and M.C. Campi, “Uncertain convex programs: randomized solutions and confidence levels,” Mathematical Programming 102(2005) pp. 25-46.
    • (2005) Mathematical Programming , vol.102 , pp. 25-46
    • Calafiore, G.1    Campi, M.C.2
  • 78
    • 0002341731 scopus 로고
    • The Russel-Yasuda Kasai model: An asset/liability model for a Japanese insurance company using multistage stochastic programming
    • ) pp
    • D.R. Cariño, T. Kent, D.H. Myers, S. Stacy, M. Sylvanus, A.L. Turner, K. Watanabe, and W.T. Ziemba, “The Russel-Yasuda Kasai model: An asset/liability model for a Japanese insurance company using multistage stochastic programming,” Interfaces 24 (1994) pp. 29-49.
    • (1994) Interfaces , vol.24 , pp. 29-49
    • Cariño, D.R.1    Kent, T.2    Myers, D.H.3    Stacy, S.4    Sylvanus, M.5    Turner, A.L.6    Watanabe, K.7    Ziemba, W.T.8
  • 79
    • 0008230792 scopus 로고    scopus 로고
    • L-shaped decomposition of two-stage stochastic programs with integer recourse
    • ) pp
    • C.C. Carøe and J. Tind, “L-shaped decomposition of two-stage stochastic programs with integer recourse,” Mathematical Programming 83 (1998) pp. 451-464.
    • (1998) Mathematical Programming , vol.83 , pp. 451-464
    • Carøe, C.C.1    Tind, J.2
  • 80
    • 0001380612 scopus 로고
    • Formulating stochastic programs for interior point methods
    • ) pp
    • T. Carpenter, I. Lustig, and J. Mulvey, “Formulating stochastic programs for interior point methods,” Operations Research 39 (1991) pp. 757–770.
    • (1991) Operations Research , vol.39 , pp. 757-770
    • Carpenter, T.1    Lustig, I.2    Mulvey, J.3
  • 81
    • 0043263090 scopus 로고
    • Exhaustible resource models: The value of information
    • ) pp
    • H.P. Chao, “Exhaustible resource models: the value of information,” Operations Research 29 (1981) pp. 903–923.
    • (1981) Operations Research , vol.29 , pp. 903-923
    • Chao, H.P.1
  • 82
    • 0002395681 scopus 로고
    • Chance-constrained programming
    • ) pp
    • A. Charnes and W.W. Cooper, “Chance-constrained programming,” Management Science 5 (1959) pp. 73–79.
    • (1959) Management Science , vol.5 , pp. 73-79
    • Charnes, A.1    Cooper, W.W.2
  • 83
    • 0002431201 scopus 로고
    • Deterministic equivalents for optimizing and satisficing under chance constraints
    • ) pp
    • A. Charnes and W.W. Cooper, “Deterministic equivalents for optimizing and satisficing under chance constraints,” Operations Research 11 (1963) pp. 18–39.
    • (1963) Operations Research , vol.11 , pp. 18-39
    • Charnes, A.1    Cooper, W.W.2
  • 84
    • 0038136570 scopus 로고
    • Response to ‘Decision problems under risk and chance constrained programming: Dilemmas in the transition
    • ) pp
    • A. Charnes and W.W. Cooper, “Response to ‘Decision problems under risk and chance constrained programming: dilemmas in the transition’,” Management Science 29 (1983) pp. 750– 753.
    • (1983) Management Science , vol.29 , pp. 750-753
    • Charnes, A.1    Cooper, W.W.2
  • 85
    • 0000512134 scopus 로고
    • Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil
    • ) pp
    • A. Charnes, W.W. Cooper, and G.H. Symonds, “Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil,” Management Science 6 (1958) pp. 235–263.
    • (1958) Management Science , vol.6 , pp. 235-263
    • Charnes, A.1    Cooper, W.W.2    Symonds, G.H.3
  • 86
    • 85098201359 scopus 로고    scopus 로고
    • M. Chen and S. Mehrotra, “Epi-convergent scenario generation method for stochastic problems via sparse grid,” Technical Report 8, Northwestern University, December 2007 (Stochastic Programming E-print Series,http://edoc.hu-berlin.de/docviews/abstract. php?lang=ger&id=28882)
    • M. Chen and S. Mehrotra, “Epi-convergent scenario generation method for stochastic problems via sparse grid,” Technical Report 8, Northwestern University, December 2007 (Stochastic Programming E-print Series,http://edoc.hu-berlin.de/docviews/abstract. php?lang=ger&id=28882).
  • 87
    • 0041603476 scopus 로고
    • Further development of a primal-dual interior point method
    • ) pp
    • I.C. Choi, C.L. Monma, and D.F. Shanno, “Further development of a primal-dual interior point method,” ORSA Journal on Computing 2 (1990) pp. 304–311.
    • (1990) ORSA Journal on Computing , vol.2 , pp. 304-311
    • Choi, I.C.1    Monma, C.L.2    Shanno, D.F.3
  • 89
    • 0004139889 scopus 로고
    • Freeman, New York/San Francisco, CA
    • V. Chvátal, Linear Programming (Freeman, New York/San Francisco, CA, 1980).
    • (1980) Linear Programming
    • Chvátal, V.1
  • 90
    • 84936375302 scopus 로고
    • Moment problem with given covariance structure in stochastic programming
    • ) pp
    • T. Cipra, “Moment problem with given covariance structure in stochastic programming,” Ekonom.-Mat. Obzor 21 (1985) pp. 66–77.
    • (1985) Ekonom.-Mat. Obzor , vol.21 , pp. 66-77
    • Cipra, T.1
  • 91
    • 34249924053 scopus 로고
    • Stochastic programming with random processes
    • ) pp
    • T. Cipra, “Stochastic programming with random processes,” Annals of Operations Research 30 (1991) pp. 95–105.
    • (1991) Annals of Operations Research , vol.30 , pp. 95-105
    • Cipra, T.1
  • 94
    • 33847554918 scopus 로고
    • The valuation of options for alternative stochastic processing
    • ) pp
    • J. Cox and S. Ross, “The valuation of options for alternative stochastic processing,” Journal of Financial Economics 3 (1976) pp. 145–166.
    • (1976) Journal of Financial Economics , vol.3 , pp. 145-166
    • Cox, J.1    Ross, S.2
  • 96
    • 0000813562 scopus 로고
    • Linear programming under uncertainty
    • ) pp
    • G.B. Dantzig, “Linear programming under uncertainty,” Management Science 1 (1955) pp. 197–206.
    • (1955) Management Science , vol.1 , pp. 197-206
    • Dantzig, G.B.1
  • 98
    • 0001803205 scopus 로고
    • Parallel processors for planning under uncertainty
    • ) pp
    • G.B. Dantzig and P. Glynn, “Parallel processors for planning under uncertainty,” Annals of Operations Research 22 (1990) pp. 1–21.
    • (1990) Annals of Operations Research , vol.22 , pp. 1-21
    • Dantzig, G.B.1    Glynn, P.2
  • 99
    • 0042240291 scopus 로고
    • Large-scale stochastic linear programs—Importance sampling and Benders decomposition
    • in: C. Brezinski and U. Kulisch, Eds., North-Holland, Amsterdam, ) pp
    • G.B. Dantzig and G. Infanger, “Large-scale stochastic linear programs—Importance sampling and Benders decomposition” in: C. Brezinski and U. Kulisch, Eds., Computational and applied mathematics, I (Dublin, 1991) (North-Holland, Amsterdam, 1991) pp. 111–120.
    • (1991) Computational and Applied Mathematics, I (Dublin, 1991) , pp. 111-120
    • Dantzig, G.B.1    Infanger, G.2
  • 101
  • 102
    • 0001391104 scopus 로고
    • The decomposition principle for linear programs
    • ) pp
    • G.B. Dantzig and P. Wolfe, “The decomposition principle for linear programs,” Operations Research 8 (1960) pp. 101–111.
    • (1960) Operations Research , vol.8 , pp. 101-111
    • Dantzig, G.B.1    Wolfe, P.2
  • 104
    • 0000861179 scopus 로고
    • Three-digit accurate multiple normal probabilities
    • ) pp
    • I. Deák, “Three-digit accurate multiple normal probabilities,” Numerische Mathematik 35 (1980) pp. 369–380.
    • (1980) Numerische Mathematik , vol.35 , pp. 369-380
    • Deák, I.1
  • 105
    • 0003116965 scopus 로고
    • Multidimensional integration and stochastic programming
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • I. Deák, “Multidimensional integration and stochastic programming,” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988) pp. 187–200.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 187-200
    • Deák, I.1
  • 107
    • 5544258192 scopus 로고    scopus 로고
    • On constraint sampling in the linear programming approach to approximate dynamic programming
    • ) pp
    • D.P. de Farias and B. Van Roy, “ On constraint sampling in the linear programming approach to approximate dynamic programming,”Mathematics of Operations Research 29 (2004) pp. 462-478.
    • (2004) Mathematics of Operations Research , vol.29 , pp. 462-478
    • de Farias, D.P.1    van Roy, B.2
  • 109
    • 0003769747 scopus 로고
    • Introduction to Stochastic Programming
    • M.A.H. Dempster, Ed., Academic Press, New York, NY, ) pp
    • M.A.H. Dempster, “Introduction to Stochastic Programming” in: M.A.H. Dempster, Ed., Stochastic Programming (Academic Press, New York, NY, 1980) pp. 3–59.
    • (1980) Stochastic Programming , pp. 3-59
    • Dempster, M.A.H.1
  • 110
    • 0042243737 scopus 로고
    • The expected value of perfect information in the optimal evolution of stochastic problems
    • in: M. Arato, D. Vermes, and A.V. Balakrishnan, Eds., ) pp
    • M.A.H. Dempster, “The expected value of perfect information in the optimal evolution of stochastic problems” in: M. Arato, D. Vermes, and A.V. Balakrishnan, Eds., Stochastic Differential Systems (Lecture Notes in Information and Control, Vol. 36, 1981) pp. 25–40.
    • (1981) Stochastic Differential Systems (Lecture Notes in Information and Control, Vol. 36 , pp. 25-40
    • Dempster, M.A.H.1
  • 111
    • 0003013577 scopus 로고
    • On stochastic programming II: Dynamic problems under risk
    • ) pp
    • M.A.H. Dempster, “On stochastic programming II: dynamic problems under risk,” Stochastics 25 (1988) pp. 15–42.
    • (1988) Stochastics , vol.25 , pp. 15-42
    • Dempster, M.A.H.1
  • 112
    • 31344452943 scopus 로고    scopus 로고
    • Sequential importance sampling algorithms for dynamic stochastic programming
    • ), pp
    • M.A.H. Dempster, “Sequential importance sampling algorithms for dynamic stochastic programming,” Jounral of Mathematical Sciences 133 (2006), pp. 1422–1444.
    • (2006) Jounral of Mathematical Sciences , vol.133 , pp. 1422-1444
    • Dempster, M.A.H.1
  • 113
    • 33845938236 scopus 로고
    • Computational experience with an approximate method for the distribution problem
    • M.A.H. Dempster, Ed., Academic Press, New York, NY, ) pp
    • M.A.H. Dempster and A. Papagaki-Papoulias, “Computational experience with an approximate method for the distribution problem” in: M.A.H. Dempster, Ed., Stochastic Programming (Academic Press, New York, NY, 1980) pp. 223–243.
    • (1980) Stochastic Programming , pp. 223-243
    • Dempster, M.A.H.1    Papagaki-Papoulias, A.2
  • 115
    • 73549107865 scopus 로고    scopus 로고
    • Robust stochastic dominance and its application to riskaverse optimization
    • ) pp
    • D. Dentcheva and A. Ruszczyński, “Robust stochastic dominance and its application to riskaverse optimization,”Mathematical Programming, Series B 123 (2010) pp. 85–100.
    • (2010) ”Mathematical Programming, Series B , vol.123 , pp. 85-100
    • Dentcheva, D.1    Ruszczyński, A.2
  • 117
    • 46449136488 scopus 로고    scopus 로고
    • The Abridged Nested Decomposition Method for Multistage Stochastic Programs
    • ) pp
    • Christopher J. Donohue and John R. Birge, “The Abridged Nested Decomposition Method for Multistage Stochastic Programs,” Algorithmic Operations Research 1 (2006) pp. 20–30.
    • (2006) Algorithmic Operations Research , vol.1 , pp. 20-30
    • Donohue, C.J.1    Birge, J.R.2
  • 118
    • 0027113519 scopus 로고
    • An upper bound on the expectation of simplicial functions of multivariate random variables
    • ) pp
    • J.H. Dulá, “An upper bound on the expectation of simplicial functions of multivariate random variables,” Mathematical Programming 55 (1991) pp. 69–80.
    • (1991) Mathematical Programming , vol.55 , pp. 69-80
    • Dulá, J.H.1
  • 119
    • 0038937889 scopus 로고
    • A dynamic stochastic approximation method
    • ) pp
    • V. Dupač, “A dynamic stochastic approximation method,” Annals of Mathematical Statistics 6 (1965) pp. 1695–1702.
    • (1965) Annals of Mathematical Statistics , Issue.6 , pp. 1695-1702
    • Dupač, V.1
  • 120
    • 0043272827 scopus 로고
    • Minimax stochastic programs with nonconvex nonseparable penalty functions
    • A. Prékopa, Ed., ) pp
    • J. Dupačová, “Minimax stochastic programs with nonconvex nonseparable penalty functions” in: A. Prékopa, Ed., Progress in Operations Research (Janos Bolyai Math. Soc., 1976) pp. 303–316.
    • (1976) Progress in Operations Research (Janos Bolyai Math. Soc , pp. 303-316
    • Dupačová, J.1
  • 121
    • 77950502788 scopus 로고
    • The minimax approach to stochastic linear programming and the moment problem
    • ) pp
    • J. Dupačová, “The minimax approach to stochastic linear programming and the moment problem,” Ekonom.-Mat. Obzor 13 (1977) pp. 297–307.
    • (1977) Ekonom.-Mat. Obzor , vol.13 , pp. 297-307
    • Dupačová, J.1
  • 122
    • 0021201714 scopus 로고
    • Stability in stochastic programming with recourse-contaminated distributions
    • ) pp
    • J. Dupačová, “Stability in stochastic programming with recourse-contaminated distributions,” Mathematical Programming Study 28 (1984) pp. 72–83.
    • (1984) Mathematical Programming Study , vol.28 , pp. 72-83
    • Dupačová, J.1
  • 123
    • 33751100070 scopus 로고
    • Stability and sensitivity analysis for stochastic programming
    • ) pp
    • J. Dupačová, “Stability and sensitivity analysis for stochastic programming,” Annals of Operations Research 27 (1990) pp. 115–142.
    • (1990) Annals of Operations Research , vol.27 , pp. 115-142
    • Dupačová, J.1
  • 124
    • 33751071102 scopus 로고    scopus 로고
    • Scenario reduction in stochastic programming: An approach using probability metrics
    • ) pp
    • J. Dupačová, N. Gröwe-Kuska and W. Römisch, “Scenario reduction in stochastic programming: An approach using probability metrics,” Mathematical Programming, Ser. A 95 (2003) pp. 493–511.
    • (2003) Mathematical Programming, Ser. A , vol.95 , pp. 493-511
    • Dupačová, J.1    Gröwe-Kuska, N.2    Römisch, W.3
  • 125
    • 0001421130 scopus 로고
    • Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems
    • ) pp
    • J. Dupačová and R.J-B Wets, “Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems,” Annals of Statistics 16 (1988) pp. 1517–1549.
    • (1988) Annals of Statistics , vol.16 , pp. 1517-1549
    • Dupačová, J.1    Wets, R.J.-B.2
  • 126
    • 0242720687 scopus 로고    scopus 로고
    • The stochastic single resource service-provision problem
    • S. Dye, L. Stougie, and A. Tomasgard, “The stochastic single resource service-provision problem,”Naval Research Logistics 50 (2003) pp. 869887.
    • (2003) Naval Research Logistics , vol.50
    • Dye, S.1    Stougie, L.2    Tomasgard, A.3
  • 127
    • 17744390930 scopus 로고    scopus 로고
    • A simple randomised algorithm for convex optimisation
    • Dept. of Mathematics and Computer Science, Eindhoven Technical University, Eindhoven
    • M. Dyer, R. Kannan, and L. Stougie, “A simple randomised algorithm for convex optimisation,” SPORReport 2002-05, Dept. of Mathematics and Computer Science, Eindhoven Technical University, Eindhoven, 2002.
    • (2002) Sporreport , vol.2002-5
    • Dyer, M.1    Kannan, R.2    Stougie, L.3
  • 128
    • 33644529428 scopus 로고    scopus 로고
    • Computational complexity of stochastic programming problems
    • ) pp
    • M. Dyer and L. Stougie, “Computational complexity of stochastic programming problems,” Mathematical Programming, Ser. A 106 (2006) pp. 423–432.
    • (2006) Mathematical Programming, Ser. A , vol.106 , pp. 423-432
    • Dyer, M.1    Stougie, L.2
  • 129
    • 0015160689 scopus 로고
    • Generalized cutting plane algorithms
    • ) pp
    • B.C. Eaves and W.I. Zangwill, “Generalized cutting plane algorithms,” SIAM J. Control 9 (1971) pp. 529–542.
    • (1971) SIAM J. Control , vol.9 , pp. 529-542
    • Eaves, B.C.1    Zangwill, W.I.2
  • 131
    • 0030282576 scopus 로고    scopus 로고
    • New second-order bounds on the expectation of saddle functions with applications to stochastic linear programming
    • ) pp
    • N.C.P. Edirisinghe, “New second-order bounds on the expectation of saddle functions with applications to stochastic linear programming,” Operations Research 44 (1996) pp. 909–922.
    • (1996) Operations Research , vol.44 , pp. 909-922
    • Edirisinghe, N.C.P.1
  • 132
    • 0012335588 scopus 로고
    • Bounds on the expectation of a convex function of a random variable
    • Santa Monica, CA
    • H.P. Edmundson, “Bounds on the expectation of a convex function of a random variable,” RAND Corporation Paper 982, Santa Monica, CA (1956).
    • (1956) RAND Corporation Paper , vol.982
    • Edmundson, H.P.1
  • 134
    • 0024700442 scopus 로고
    • A scenario approach to capacity planning
    • ) pp
    • G.D. Eppen, R.K. Martin, and L. Schrage, “A scenario approach to capacity planning,” Operations Research 37 (1989) pp. 517–527.
    • (1989) Operations Research , vol.37 , pp. 517-527
    • Eppen, G.D.1    Martin, R.K.2    Schrage, L.3
  • 135
    • 0000842941 scopus 로고
    • Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework
    • ), pp
    • Epstein, L. and S. Zin, “Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework,” Econometrica 57 (1989), pp. 937-969.
    • (1989) Econometrica , vol.57 , pp. 937-969
    • Epstein, L.1    Zin, S.2
  • 136
    • 85098130099 scopus 로고    scopus 로고
    • Y. Ermoliev, “On the stochastic quasigradient method and quasi-Feyer sequences,” Kibernetika 5 (2) (1969) pp. 73–83 (in Russian; also published in English as Cybernetics 5 (1969) pp. 208–220)
    • Y. Ermoliev, “On the stochastic quasigradient method and quasi-Feyer sequences,” Kibernetika 5 (2) (1969) pp. 73–83 (in Russian; also published in English as Cybernetics 5 (1969) pp. 208–220).
  • 138
    • 0020498889 scopus 로고
    • Stochastic quasigradient methods and their applications to systems optimization
    • ) pp
    • Y. Ermoliev, “Stochastic quasigradient methods and their applications to systems optimization,” Stochastics 9 (1983) pp. 1–36.
    • (1983) Stochastics , vol.9 , pp. 1-36
    • Ermoliev, Y.1
  • 139
    • 0002783313 scopus 로고
    • Stochastic quasigradient methods
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • Y. Ermoliev, “Stochastic quasigradient methods” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988) pp. 141–186.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 141-186
    • Ermoliev, Y.1
  • 140
    • 85098202247 scopus 로고
    • Stochastic optimization problems with partially known distribution functions
    • ) pp
    • Y. Ermoliev, A. Gaivoronski, and C. Nedeva, “Stochastic optimization problems with partially known distribution functions,” SIAM Journal on Control and Optimization 23 (1985) pp. 377–394.
    • (1985) SIAM Journal on Control and Optimization , vol.23 , pp. 377-394
    • Ermoliev, Y.1    Gaivoronski, A.2    Nedeva, C.3
  • 144
    • 0002879508 scopus 로고
    • The allocation of aircraft to routes: An example of linear programming under uncertain demands
    • ) pp
    • A. Ferguson and G.B. Dantzig, “The allocation of aircraft to routes: an example of linear programming under uncertain demands,” Management Science 3 (1956) pp. 45–73.
    • (1956) Management Science , vol.3 , pp. 45-73
    • Ferguson, A.1    Dantzig, G.B.2
  • 146
    • 85098231377 scopus 로고
    • Asymptotically stable solutions to stochastic problems of Bolza
    • in: F. Archetti, G. Di Pillo, and M Lucertini, Eds., ) pp
    • S.D. Flåm, “Asymptotically stable solutions to stochastic problems of Bolza” in: F. Archetti, G. Di Pillo, and M Lucertini, Eds., Stochastic Programming (Lecture Notes in Information and Control 76, 1986) pp. 184–193.
    • (1986) Stochastic Programming (Lecture Notes in Information and Control 76 , pp. 184-193
    • Flåm, S.D.1
  • 150
    • 0022162277 scopus 로고
    • A simplex algorithm for piecewise-linear programming. I: Derivation and proof
    • ) pp
    • R. Fourer, “A simplex algorithm for piecewise-linear programming. I: derivation and proof,” Mathematical Programming 33 (1985) pp. 204–233.
    • (1985) Mathematical Programming , vol.33 , pp. 204-233
    • Fourer, R.1
  • 151
    • 0042584129 scopus 로고
    • A simplex algorithm for piecewise-linear programming. II: Finiteness, feasibility, and degeneracy
    • ) pp
    • R. Fourer, “A simplex algorithm for piecewise-linear programming. II: finiteness, feasibility, and degeneracy,” Mathematical Programming 41 (1988) pp. 281–315.
    • (1988) Mathematical Programming , vol.41 , pp. 281-315
    • Fourer, R.1
  • 153
    • 0022954116 scopus 로고
    • Implementation and relative efficiency of quasirandom sequence generators
    • ) pp
    • B. Fox, “Implementation and relative efficiency of quasirandom sequence generators,” ACM Transactions on Mathematical Software 12 (1986) pp. 362–376.
    • (1986) ACM Transactions on Mathematical Software , vol.12 , pp. 362-376
    • Fox, B.1
  • 154
    • 0025388562 scopus 로고
    • A successive linear approximation procedure for stochastic, dynamic vehicle allocation problems
    • ) pp
    • L. Frantzeskakis and W. Powell, “A successive linear approximation procedure for stochastic, dynamic vehicle allocation problems,” Transportation Science 24 (1990) pp. 40–57.
    • (1990) Transportation Science , vol.24 , pp. 40-57
    • Frantzeskakis, L.1    Powell, W.2
  • 155
    • 77950487015 scopus 로고
    • Bounding procedures for multistage stochastic dynamic networks
    • ) pp
    • L.F. Frantzeskakis and W.B. Powell, “Bounding procedures for multistage stochastic dynamic networks,” Networks 23 (1993) pp. 575–595.
    • (1993) Networks , vol.23 , pp. 575-595
    • Frantzeskakis, L.F.1    Powell, W.B.2
  • 156
  • 157
    • 0041540267 scopus 로고
    • Solving S.L.P. recourse problems with arbitrary multivariate distributions – the dependent case
    • ) pp
    • K. Frauendorfer, “Solving S.L.P. recourse problems with arbitrary multivariate distributions – the dependent case,” Mathematics of Operations Research 13 (1988b) pp. 377–394.
    • (1988) Mathematics of Operations Research , vol.13 , pp. 377-394
    • Frauendorfer, K.1
  • 160
    • 0023844906 scopus 로고
    • A solution method for SLP recourse problems with arbitrary multivariate distributions—the independent case
    • ) pp
    • K. Frauendorfer and P. Kall, “A solution method for SLP recourse problems with arbitrary multivariate distributions—the independent case,” Problems in Control and Information Theory 17 (1988) pp. 177–205.
    • (1988) Problems in Control and Information Theory , vol.17 , pp. 177-205
    • Frauendorfer, K.1    Kall, P.2
  • 161
    • 0004979275 scopus 로고
    • Implementation of stochastic quasigradient methods
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • A.A. Gaivoronski, “Implementation of stochastic quasigradient methods” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988) pp. 313–352.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 313-352
    • Gaivoronski, A.A.1
  • 163
    • 34250253863 scopus 로고
    • An economic interpretation of stochastic programs
    • ) pp
    • S.J. Gartska, “An economic interpretation of stochastic programs,” Mathematical Programming 18 (1980) pp. 62–67.
    • (1980) Mathematical Programming , vol.18 , pp. 62-67
    • Gartska, S.J.1
  • 164
    • 0013302557 scopus 로고
    • Computation in discrete stochastic programs with recourse
    • ) pp
    • S.J. Gartska and D. Rutenberg, “Computation in discrete stochastic programs with recourse,” Operations Research 21 (1973) pp. 112–122.
    • (1973) Operations Research , vol.21 , pp. 112-122
    • Gartska, S.J.1    Rutenberg, D.2
  • 165
    • 34250423189 scopus 로고
    • On decision rules in stochastic programming
    • ) pp
    • S.J. Gartska and R.J-B Wets, “On decision rules in stochastic programming,” Mathematical Programming 7 (1974) pp. 117–143.
    • (1974) Mathematical Programming , vol.7 , pp. 117-143
    • Gartska, S.J.1    Wets, R.J.-B.2
  • 166
    • 0012236480 scopus 로고
    • Conditional probability and conditional expectation of a random vector
    • in: Y. Ermoliev and R. Wets, Eds., SpringerVerlag, Berlin, ) pp
    • H.I. Gassmann, “Conditional probability and conditional expectation of a random vector” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (SpringerVerlag, Berlin, 1988) pp. 237–254.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 237-254
    • Gassmann, H.I.1
  • 167
    • 0024816102 scopus 로고
    • Optimal harvest of a forest in the presence of uncertainty
    • ) pp
    • H.I. Gassmann, “Optimal harvest of a forest in the presence of uncertainty,” Canadian Journal of Forest Research 19 (1989) pp. 1267–1274.
    • (1989) Canadian Journal of Forest Research , vol.19 , pp. 1267-1274
    • Gassmann, H.I.1
  • 168
    • 34249957971 scopus 로고
    • MSLiP: A computer code for the multistage stochastic linear programming problem
    • ) pp
    • H.I. Gassmann, “MSLiP: a computer code for the multistage stochastic linear programming problem,” Mathematical Programming 47 (1990) pp. 407–423.
    • (1990) Mathematical Programming , vol.47 , pp. 407-423
    • Gassmann, H.I.1
  • 169
    • 0022698014 scopus 로고
    • A tight upper bound for the expectation of a convex function of a multivariate random variable
    • ) pp
    • H.I. Gassmann and W.T. Ziemba, “A tight upper bound for the expectation of a convex function of a multivariate random variable,” Mathematical Programming Study 27 (1986) pp. 39–53.
    • (1986) Mathematical Programming Study , vol.27 , pp. 39-53
    • Gassmann, H.I.1    Ziemba, W.T.2
  • 170
    • 0023293619 scopus 로고
    • A variant of Karmarkar’s linear programming algorithm for problems in standard form
    • ) pp
    • D.M. Gay, “A variant of Karmarkar’s linear programming algorithm for problems in standard form,” Mathematical Programming 37 (1987) pp. 81–90.
    • (1987) Mathematical Programming , vol.37 , pp. 81-90
    • Gay, D.M.1
  • 172
    • 0000461093 scopus 로고
    • An exact algorithm for the vehicle routing problem with stochastic demands and customers
    • ) pp
    • M. Gendreau, G. Laporte, and R. Séguin, “An exact algorithm for the vehicle routing problem with stochastic demands and customers,” Transportation Science 29 (1995) pp. 143–155.
    • (1995) Transportation Science , vol.29 , pp. 143-155
    • Gendreau, M.1    Laporte, G.2    Séguin, R.3
  • 173
    • 0000462003 scopus 로고
    • Elements of large-scale mathematical programming
    • ) pp
    • A.M. Geoffrion, “Elements of large-scale mathematical programming,” Management Science 16 (1970) pp. 652–675.
    • (1970) Management Science , vol.16 , pp. 652-675
    • Geoffrion, A.M.1
  • 174
    • 0014974581 scopus 로고
    • Duality in nonlinear programming: A simplified applications-oriented development
    • ) pp
    • A.M. Geoffrion, “Duality in nonlinear programming: a simplified applications-oriented development,” SIAM Rev. 13 (1971) pp. 1–37.
    • (1971) SIAM Rev , vol.13 , pp. 1-37
    • Geoffrion, A.M.1
  • 175
  • 176
    • 0040143071 scopus 로고
    • Nested decomposition and multistage linear programs
    • ) pp
    • C.R. Glassey, “Nested decomposition and multistage linear programs,” Management Science 20 (1973) pp. 282–292.
    • (1973) Management Science , vol.20 , pp. 282-292
    • Glassey, C.R.1
  • 177
    • 63949085263 scopus 로고    scopus 로고
    • Exploiting structure in parallel implementation of interior point methods for optimization
    • ) pp
    • J. Gondzio and A. Grothey, “Exploiting structure in parallel implementation of interior point methods for optimization,” Computational Management Science 6 (2009) pp. 135-160.
    • (2009) Computational Management Science , vol.6 , pp. 135-160
    • Gondzio, J.1    Grothey, A.2
  • 178
    • 85098129660 scopus 로고
    • A new approach to multistage stochastic linear programs
    • ) pp
    • R.C. Grinold, “A new approach to multistage stochastic linear programs,” Mathematical Programming Study 6 (1976) pp. 19–29.
    • (1976) Mathematical Programming Study , vol.6 , pp. 19-29
    • Grinold, R.C.1
  • 179
    • 0020748382 scopus 로고
    • Model building techniques for the correction of end effects in multistage convex programs
    • ) pp
    • R.C. Grinold, “Model building techniques for the correction of end effects in multistage convex programs,” Operations Research 31 (1983) pp. 407–431.
    • (1983) Operations Research , vol.31 , pp. 407-431
    • Grinold, R.C.1
  • 181
    • 4544311041 scopus 로고    scopus 로고
    • Boosted sampling: Approximation algorithms for stochastic optimization problems
    • in: L. Babai, Ed., ACM Press, New York, ) pp
    • A. Gupta, M. Pál, R. Ravi, and A. Sinha, “Boosted sampling: Approximation algorithms for stochastic optimization problems,” in: L. Babai, Ed., Proc. 36th Annual ACM Sympos. Theory Comput., Chicago, IL,USA, June 13-16, 2004 (ACM Press, New York, 2004) pp. 417-425.
    • (2004) Proc. 36Th Annual ACM Sympos. Theory Comput., Chicago, IL,USA, June 13-16 , vol.2004 , pp. 417-425
    • Gupta, A.1    Pál, M.2    Ravi, R.3    Sinha, A.4
  • 183
    • 38549176849 scopus 로고    scopus 로고
    • LP rounding approximation algorithms for stochastic network design
    • ) pp
    • A. Gupta, R. Ravi, and A. Sinha, “LP rounding approximation algorithms for stochastic network design,” Mathematics of Operations Research 32 (2007) pp. 345–364.
    • (2007) Mathematics of Operations Research , vol.32 , pp. 345-364
    • Gupta, A.1    Ravi, R.2    Sinha, A.3
  • 184
    • 0029304830 scopus 로고
    • Discounted linear exponential quadratic gaussian control
    • ) pp
    • L.P. Hansen and T. Sargent, “Discounted linear exponential quadratic gaussian control,” IEEE Transactions on Automatic Control 40 (1995) pp. 968-971.
    • (1995) IEEE Transactions on Automatic Control , vol.40 , pp. 968-971
    • Hansen, L.P.1    Sargent, T.2
  • 186
    • 38649141305 scopus 로고
    • Martingales and arbitrage in multiperiod securities markets
    • ) pp
    • J.M. Harrison and D.M. Kreps, “Martingales and arbitrage in multiperiod securities markets,” Journal of Economic Theory 20 (1979) pp. 381–408.
    • (1979) Journal of Economic Theory , vol.20 , pp. 381-408
    • Harrison, J.M.1    Kreps, D.M.2
  • 187
    • 0025511612 scopus 로고
    • Scheduling networks of queues:Heavy traffic analysis of a two-station closed network
    • ) pp
    • J.M. Harrison and L.M. Wein, “Scheduling networks of queues:Heavy traffic analysis of a two-station closed network,” Operations Research 38 (1990) pp. 1052–1064.
    • (1990) Operations Research , vol.38 , pp. 1052-1064
    • Harrison, J.M.1    Wein, L.M.2
  • 188
    • 0024136280 scopus 로고
    • Solving many linear programs that differ only in the righthand side
    • ) pp
    • D. Haugland and S.W. Wallace, “Solving many linear programs that differ only in the righthand side,” European Journal of Operational Research 37 (1988) pp. 318–324.
    • (1988) European Journal of Operational Research , vol.37 , pp. 318-324
    • Haugland, D.1    Wallace, S.W.2
  • 190
    • 1542276923 scopus 로고    scopus 로고
    • Decomposition of test sets in stochastic integer programming
    • ) pp
    • R. Hemmecke and R. Schultz, “Decomposition of test sets in stochastic integer programming,” Mathematical Programming 94 (2003) pp. 323–341.
    • (2003) Mathematical Programming , vol.94 , pp. 323-341
    • Hemmecke, R.1    Schultz, R.2
  • 192
    • 0011044859 scopus 로고
    • Statistical verification of optimality conditions for stochastic programs with recourse
    • ) pp
    • J. Higle and S. Sen, “Statistical verification of optimality conditions for stochastic programs with recourse,” Annals of Operations Research 30 (1991a) pp. 215–240.
    • (1991) Annals of Operations Research , vol.30 , pp. 215-240
    • Higle, J.1    Sen, S.2
  • 193
    • 0000800872 scopus 로고
    • Stochastic decomposition: An algorithm for two stage linear programs with recourse
    • ) pp
    • J. Higle and S. Sen, “Stochastic decomposition: an algorithm for two stage linear programs with recourse,” Mathematics of Operations Research 16 (1991b) pp. 650–669.
    • (1991) Mathematics of Operations Research , vol.16 , pp. 650-669
    • Higle, J.1    Sen, S.2
  • 195
    • 23844512693 scopus 로고
    • Conditions nécessaires d’optimalité pour un programme stochastique avec recours
    • ) pp
    • J.-B. Hiriart-Urruty, “Conditions nécessaires d’optimalité pour un programme stochastique avec recours,” SIAM Journal on Control and Optimization 16 (1978) pp. 317–329.
    • (1978) SIAM Journal on Control and Optimization , vol.16 , pp. 317-329
    • Hiriart-Urruty, J.-B.1
  • 196
    • 0033414695 scopus 로고    scopus 로고
    • New optimality cuts for a single vehicle stochastic routing problem
    • ), pp
    • C. Hjörring and J. Holt, “New optimality cuts for a single vehicle stochastic routing problem,” Annals of Operations Research 86 (1999), pp. 569–584.
    • (1999) Annals of Operations Research , vol.86 , pp. 569-584
    • Hjörring, C.1    Holt, J.2
  • 197
    • 0016047946 scopus 로고
    • Nested decomposition for dynamic models
    • ) pp
    • J.K. Ho and A.S. Manne, “Nested decomposition for dynamic models,” Mathematical Programming 6 (1974) pp. 121–140.
    • (1974) Mathematical Programming , vol.6 , pp. 121-140
    • Ho, J.K.1    Manne, A.S.2
  • 198
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • ) pp
    • W. Hoeffding, “Probability inequalities for sums of bounded random variables,” Journal of the American Statistical Association 58 (1963) pp. 13–30.
    • (1963) Journal of the American Statistical Association , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 199
    • 0346356531 scopus 로고
    • Decision problems under risk and chance constrained programming: Dilemmas in the transition
    • ) pp
    • A. Hogan, J. Morris, and H. Thompson, “Decision problems under risk and chance constrained programming: dilemmas in the transition,” Management Science 27 (1981) pp. 698– 716.
    • (1981) Management Science , vol.27 , pp. 698-716
    • Hogan, A.1    Morris, J.2    Thompson, H.3
  • 200
    • 78651464316 scopus 로고
    • Reply to Professors Charnes and Cooper concerning their response to ‘Decision problems under risk and chance constrained programming: Dilemmas in the transition
    • ) pp
    • A. Hogan, J. Morris, and H. Thompson, “Reply to Professors Charnes and Cooper concerning their response to ‘Decision problems under risk and chance constrained programming: dilemmas in the transition’,” Management Science 30 (1984) pp. 258–259.
    • (1984) Management Science , vol.30 , pp. 258-259
    • Hogan, A.1    Morris, J.2    Thompson, H.3
  • 202
    • 0035261934 scopus 로고    scopus 로고
    • Generating Scenario Trees for Multistage Decision Problems
    • ) pp
    • K. Høyland and S.W. Wallace, “Generating Scenario Trees for Multistage Decision Problems,” Management Science 47 (2001) pp. 295-307.
    • (2001) Management Science , vol.47 , pp. 295-307
    • Høyland, K.1    Wallace, S.W.2
  • 203
    • 0017468990 scopus 로고
    • Bounds on the expectation of a convex function of a random variable: With applications to stochastic programming
    • ) pp
    • C.C. Huang, W.T. Ziemba, and A. Ben-Tal, “Bounds on the expectation of a convex function of a random variable: with applications to stochastic programming,” Operations Research 25 (1977) pp. 315–325.
    • (1977) Operations Research , vol.25 , pp. 315-325
    • Huang, C.C.1    Ziemba, W.T.2    Ben-Tal, A.3
  • 207
    • 0011486381 scopus 로고
    • Monte Carlo (Importance) sampling within a Benders decomposition algorithm for stochastic linear programs; Extended version: Including results of large-scale problems
    • Systems Optimization Laboratory, Stanford University (Stanford, CA
    • G. Infanger, “Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs; Extended version: including results of large-scale problems,” Technical Report SOL 91-6, Systems Optimization Laboratory, Stanford University (Stanford, CA, 1991).
    • (1991) Technical Report SOL , vol.91-6
    • Infanger, G.1
  • 209
    • 0005037941 scopus 로고
    • A minimax procedure for a class of linear programs under uncertainty
    • ) pp
    • R. Jagganathan, “A minimax procedure for a class of linear programs under uncertainty,” Operations Research 25 (1977) pp. 173–177.
    • (1977) Operations Research , vol.25 , pp. 173-177
    • Jagganathan, R.1
  • 210
    • 0021850995 scopus 로고
    • Use of sample information in stochastic recourse and chance-constrained programming models
    • ) pp
    • R. Jagganathan, “Use of sample information in stochastic recourse and chance-constrained programming models,” Management Science 31 (1985) pp. 96–108.
    • (1985) Management Science , vol.31 , pp. 96-108
    • Jagganathan, R.1
  • 211
    • 0012306929 scopus 로고
    • Linear programming with stochastic processes as parameters as applied to production planning
    • ) pp
    • R. Jagganathan, “Linear programming with stochastic processes as parameters as applied to production planning,” Annals of Operations Research 30 (1991) pp. 107–114.
    • (1991) Annals of Operations Research , vol.30 , pp. 107-114
    • Jagganathan, R.1
  • 212
    • 0024107816 scopus 로고
    • A priori solution of a traveling salesman problem in which a random subset of the customers are visited
    • ) pp
    • P. Jaillet, “A priori solution of a traveling salesman problem in which a random subset of the customers are visited,” Operations Research 36 (1988) pp. 929–936.
    • (1988) Operations Research , vol.36 , pp. 929-936
    • Jaillet, P.1
  • 215
    • 34250609333 scopus 로고
    • Sur les fonctions convexes et les inégalités entre les valeurs moyennes
    • ) pp
    • J.L. Jensen, “Sur les fonctions convexes et les inégalités entre les valeurs moyennes,” Acta. Math. 30 (1906) pp. 175–193.
    • (1906) Acta. Math. , vol.30 , pp. 175-193
    • Jensen, J.L.1
  • 217
    • 0003343577 scopus 로고
    • Computational methods for solving two-stage stochastic linear programming problems
    • ) pp
    • P. Kall, “Computational methods for solving two-stage stochastic linear programming problems,” Journal of Applied Mathematics and Physics 30 (1979) pp. 261–271.
    • (1979) Journal of Applied Mathematics and Physics , vol.30 , pp. 261-271
    • Kall, P.1
  • 218
    • 0023218747 scopus 로고
    • Stochastic programs with recourse: An upper bound and the related moment problem
    • ) pp
    • P. Kall, “Stochastic programs with recourse: an upper bound and the related moment problem,” Zeitschrift für Operations Research 31 (1987) pp. A119–A141.
    • (1987) Zeitschrift für Operations Research , vol.31 , pp. A119-A141
    • Kall, P.1
  • 219
    • 9944226444 scopus 로고
    • An upper bound for stochastic linear programming using first and total second moments
    • ) pp
    • P. Kall, “An upper bound for stochastic linear programming using first and total second moments,” Annals of Operations Research 30 (1991) pp. 267–276.
    • (1991) Annals of Operations Research , vol.30 , pp. 267-276
    • Kall, P.1
  • 220
    • 0012234873 scopus 로고    scopus 로고
    • SLP-IOR: An interactive model management system for stochastic linear programs
    • ) pp
    • P. Kall and J. Mayer, “SLP-IOR: an interactive model management system for stochastic linear programs,” Mathematical Programming 75 (1996) pp. 221–240.
    • (1996) Mathematical Programming , vol.75 , pp. 221-240
    • Kall, P.1    Mayer, J.2
  • 221
    • 0004914713 scopus 로고
    • Solving stochastic programming problems with recourse including error bounds
    • ) pp
    • P. Kall and D. Stoyan, “Solving stochastic programming problems with recourse including error bounds,” Math. Operationsforsch. Statist. Ser. Optim. 13 (1982) pp. 431–447.
    • (1982) Math. Operationsforsch. Statist. Ser. Optim. , vol.13 , pp. 431-447
    • Kall, P.1    Stoyan, D.2
  • 223
    • 0005577586 scopus 로고
    • Short term financial planning under uncertainty
    • ) pp
    • J.G. Kallberg, R.W. White, and W.T. Ziemba, “Short term financial planning under uncertainty,” Management Science 28 (1982) pp. 670–682.
    • (1982) Management Science , vol.28 , pp. 670-682
    • Kallberg, J.G.1    White, R.W.2    Ziemba, W.T.3
  • 224
    • 0000624306 scopus 로고
    • Comparison of alternative utility functions in portfolio selection problems
    • ) pp
    • J.G. Kallberg and W.T. Ziemba, “Comparison of alternative utility functions in portfolio selection problems,” Management Science 29 (1983) pp. 1257–1276.
    • (1983) Management Science , vol.29 , pp. 1257-1276
    • Kallberg, J.G.1    Ziemba, W.T.2
  • 225
    • 34250291854 scopus 로고
    • Decomposition of arborescent linear programs
    • ) pp
    • M. Kallio and E. Porteus, “Decomposition of arborescent linear programs,” Mathematical Programming 13 (1977) pp. 348–356.
    • (1977) Mathematical Programming , vol.13 , pp. 348-356
    • Kallio, M.1    Porteus, E.2
  • 227
    • 0001483058 scopus 로고
    • Budgeting costs of nursing in a hospital
    • ) pp
    • E. Kao and M. Queyranne, “Budgeting costs of nursing in a hospital,” Management Science 31 (1985) pp. 608–621.
    • (1985) Management Science , vol.31 , pp. 608-621
    • Kao, E.1    Queyranne, M.2
  • 228
    • 51249181779 scopus 로고
    • A new polynomial-time algorithm for linear programming
    • ) pp
    • N. Karmarkar, “A new polynomial-time algorithm for linear programming,” Combinatorica 4 (1984) pp. 373–395.
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.1
  • 229
    • 0020707907 scopus 로고
    • Extreme points of certain sets of probability measure, with applications
    • ) pp
    • A. Karr, “Extreme points of certain sets of probability measure, with applications,” Mathematics of Operations Research 8 (1983) pp. 74–85.
    • (1983) Mathematics of Operations Research , vol.8 , pp. 74-85
    • Karr, A.1
  • 230
    • 0002515295 scopus 로고
    • The general moment problem, a geometric approach
    • ) pp
    • J. Kemperman, “The general moment problem, a geometric approach,” Annals of Mathematical Statistics 39 (1968) pp. 93–122.
    • (1968) Annals of Mathematical Statistics , vol.39 , pp. 93-122
    • Kemperman, J.1
  • 232
    • 0346867081 scopus 로고
    • Guaranteeing approach to solving quantile optimization problems
    • ) pp
    • A.I. Kibzun and V.Yu. Kurbakovskiy, “Guaranteeing approach to solving quantile optimization problems,” Annals of Operations Research 30 (1991) pp. 81–93.
    • (1991) Annals of Operations Research , vol.30 , pp. 81-93
    • Kibzun, A.I.1    Kurbakovskiy, V.Y.2
  • 233
    • 0040133871 scopus 로고
    • Finite generation method
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • A. King, “Finite generation method” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988a) pp. 295–312.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 295-312
    • King, A.1
  • 234
    • 0002279598 scopus 로고
    • Stochastic programming problems:Examples from the literature
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • A. King, “Stochastic programming problems:Examples from the literature” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988b) pp. 543–567.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 543-567
    • King, A.1
  • 235
    • 0001659305 scopus 로고
    • Asymptotic theory for solutions in generalized M-estimation and stochastic programming
    • ) pp
    • A. King and R.T. Rockafellar, “Asymptotic theory for solutions in generalized M-estimation and stochastic programming,” Mathematics of Operations Research 18 (1993) pp. 148–162.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 148-162
    • King, A.1    Rockafellar, R.T.2
  • 237
    • 0020912156 scopus 로고
    • An aggregate subgradient method for nonsmooth convex minimization
    • ) pp
    • K.C. Kiwiel, “An aggregate subgradient method for nonsmooth convex minimization,” Mathematical Programming 27 (1983) pp. 320–341.
    • (1983) Mathematical Programming , vol.27 , pp. 320-341
    • Kiwiel, K.C.1
  • 238
    • 0031678181 scopus 로고    scopus 로고
    • Financial asset-pricing theory and stochastic programming models for asset/liability managment: A synthesis
    • ) pp
    • P. Klaassen, “Financial asset-pricing theory and stochastic programming models for asset/liability managment: a synthesis,” Management Science 44 (1998) pp. 31–48.
    • (1998) Management Science , vol.44 , pp. 31-48
    • Klaassen, P.1
  • 240
    • 0022698724 scopus 로고
    • Robustness against dependence in PERT: An application of duality and distributions with known marginals
    • ) pp
    • W.K. Klein Haneveld, “Robustness against dependence in PERT: an application of duality and distributions with known marginals,” Mathematical Programming Study 27 (1986) pp. 153–182.
    • (1986) Mathematical Programming Study , vol.27 , pp. 153-182
    • Klein Haneveld, W.K.1
  • 241
    • 33745698308 scopus 로고    scopus 로고
    • Two-stage integer programs with stochastic right-hand sides-A superadditive dual approach
    • ) pp
    • N. Kong, A.J. Schaefer, and B.K. Hunsaker, “Two-stage integer programs with stochastic right-hand sides-A superadditive dual approach,” Mathematical Programming 108 (2006) pp. 275–296.
    • (2006) Mathematical Programming , vol.108 , pp. 275-296
    • Kong, N.1    Schaefer, A.J.2    Hunsaker, B.K.3
  • 242
    • 0035900037 scopus 로고    scopus 로고
    • Scenario generation and stochastic programming models for asset-liability management
    • ) pp
    • R. Kouwenberg, “Scenario generation and stochastic programming models for asset-liability management,” European Journal of Operations Research 134 (2001) pp. 279–292.
    • (2001) European Journal of Operations Research , vol.134 , pp. 279-292
    • Kouwenberg, R.1
  • 244
    • 0002009278 scopus 로고
    • Temporal von Neumann-Morgenstern and Induced Preferences
    • ) pp
    • D.M. Kreps and E.L. Porteus, “Temporal von Neumann-Morgenstern and Induced Preferences,” Journal Of Economic Theory 20(1979) pp. 81–10.
    • (1979) Journal of Economic Theory , vol.20 , pp. 81-10
    • Kreps, D.M.1    Porteus, E.L.2
  • 245
    • 38349190492 scopus 로고    scopus 로고
    • Daniel Kuhn,“ Aggregation and Discretization in Multistage Stochastic Programming,”Mathematical Programming A 113 (2008) pp. 61–94
    • Daniel Kuhn,“ Aggregation and Discretization in Multistage Stochastic Programming,”Mathematical Programming A 113 (2008) pp. 61–94.
  • 247
    • 0022715033 scopus 로고
    • A bank asset and liability management model
    • ) pp
    • M. Kusy and W.T. Ziemba, “A bank asset and liability management model,” Operations Research 34 (1986) pp. 356–376.
    • (1986) Operations Research , vol.34 , pp. 356-376
    • Kusy, M.1    Ziemba, W.T.2
  • 249
    • 0000415520 scopus 로고
    • The integer L-shaped method for stochastic integer programs with complete recourse
    • ) pp
    • G. Laporte and F.V. Louveaux, “The integer L-shaped method for stochastic integer programs with complete recourse,” Operations Research Letters 13 (1993) pp. 133–142.
    • (1993) Operations Research Letters , vol.13 , pp. 133-142
    • Laporte, G.1    Louveaux, F.V.2
  • 250
    • 0024962821 scopus 로고
    • Models and exact solutions for a class of stochastic location-routing problems
    • ) pp
    • G. Laporte, F.V. Louveaux, and H. Mercure, “Models and exact solutions for a class of stochastic location-routing problems,” European Journal of Operational Research 39 (1989) pp. 71–78.
    • (1989) European Journal of Operational Research , vol.39 , pp. 71-78
    • Laporte, G.1    Louveaux, F.V.2    Mercure, H.3
  • 251
    • 0000967180 scopus 로고
    • An exact solution for the a priori optimization of the probabilistic traveling salesman problem
    • ) pp
    • G. Laporte, F.V. Louveaux, and H. Mercure, “An exact solution for the a priori optimization of the probabilistic traveling salesman problem,” Operations Research 42 (1994) pp. 543– 549.
    • (1994) Operations Research , vol.42 , pp. 543-549
    • Laporte, G.1    Louveaux, F.V.2    Mercure, H.3
  • 252
    • 0001840045 scopus 로고
    • Exact solution to a location problem with stochastic demands
    • ) pp
    • G. Laporte, F.V. Louveaux, and L. Van Hamme, “Exact solution to a location problem with stochastic demands,” Transportation Science 28 (1994) pp. 95–103.
    • (1994) Transportation Science , vol.28 , pp. 95-103
    • Laporte, G.1    Louveaux, F.V.2    van Hamme, L.3
  • 253
    • 0036563024 scopus 로고    scopus 로고
    • An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands
    • ) pp
    • G. Laporte, F.V. Louveaux and L. Van hamme, “An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands,” Operations Research 50 (2002) pp. 415–423.
    • (2002) Operations Research , vol.50 , pp. 415-423
    • Laporte, G.1    Louveaux, F.V.2    van hamme, L.3
  • 255
    • 0001796318 scopus 로고
    • Bundle methods in nonsmooth optimization” in: Nonsmooth optimization
    • Pergamon, Oxford-Elmsford, New York, NY, ) pp
    • C. Lemaréchal, “Bundle methods in nonsmooth optimization” in: Nonsmooth optimization (Proc. IIASA Workshop) (Pergamon, Oxford-Elmsford, New York, NY, 1978) pp. 79–102.
    • (1978) Proc. IIASA Workshop) , pp. 79-102
    • Lemaréchal, C.1
  • 256
    • 0037319402 scopus 로고    scopus 로고
    • Decomposition algorithms for stochastic programming on a computational grid
    • ) pp
    • J. Linderoth and S. Wright, “Decomposition algorithms for stochastic programming on a computational grid,” Computational Optimization and its Applications 24 (2003) pp. 207– 250.
    • (2003) Computational Optimization and Its Applications , vol.24 , pp. 207-250
    • Linderoth, J.1    Wright, S.2
  • 257
    • 45949116982 scopus 로고
    • Semi-parametric upper bounds for option prices and expected payoffs
    • ) pp
    • A.W. Lo, “Semi-parametric upper bounds for option prices and expected payoffs,” Journal of Financial Economics 19 (1987) pp. 373–387.
    • (1987) Journal of Financial Economics , vol.19 , pp. 373-387
    • Lo, A.W.1
  • 258
    • 33645326816 scopus 로고
    • Piecewise convex programs
    • ) pp
    • F.V. Louveaux, “Piecewise convex programs,” Mathematical Programming 15 (1978) pp. 53–62.
    • (1978) Mathematical Programming , vol.15 , pp. 53-62
    • Louveaux, F.V.1
  • 259
    • 0019035580 scopus 로고
    • A solution method for multistage stochastic programs with recourse with application to an energy investment problem
    • ) pp
    • F.V. Louveaux, “A solution method for multistage stochastic programs with recourse with application to an energy investment problem,” Operations Research 28 (1980) pp. 889–902.
    • (1980) Operations Research , vol.28 , pp. 889-902
    • Louveaux, F.V.1
  • 260
    • 0022696503 scopus 로고
    • Multistage stochastic programs with block-separable recourse
    • ) pp
    • F.V. Louveaux, “Multistage stochastic programs with block-separable recourse,” Mathematical Programming Study 28 (1986) pp. 48–62.
    • (1986) Mathematical Programming Study , vol.28 , pp. 48-62
    • Louveaux, F.V.1
  • 261
    • 0001711127 scopus 로고
    • A dual-based procedure for stochastic facility location
    • ) pp
    • F.V. Louveaux and D. Peeters, “A dual-based procedure for stochastic facility location,” Operations Research 40 (1992) pp. 564–573.
    • (1992) Operations Research , vol.40 , pp. 564-573
    • Louveaux, F.V.1    Peeters, D.2
  • 262
    • 77950485307 scopus 로고    scopus 로고
    • Stochastic integer programming
    • A. Ruszczyński and A. Shapiro, Eds., Elsevier, Amsterdam, ) pp
    • F. Louveaux and R. Schultz, “Stochastic integer programming,” in: A. Ruszczyński and A. Shapiro, Eds., Handbooks in Operations Research and Management Science 10, (Elsevier, Amsterdam, 2003) pp. 213–266.
    • (2003) Handbooks in Operations Research and Management Science , vol.10 , pp. 213-266
    • Louveaux, F.1    Schultz, R.2
  • 264
    • 85098111240 scopus 로고    scopus 로고
    • Stochastic optimization for the introduction of a new energy technology
    • to appear
    • F.V. Louveaux and Y. Smeers, “Stochastic optimization for the introduction of a new energy technology,” Stochastics (to appear) (2011).
    • (2011) Stochastics
    • Louveaux, F.V.1    Smeers, Y.2
  • 265
    • 34250079346 scopus 로고
    • Stochastic programming with simple integer recourse
    • ) pp
    • F.V. Louveaux and M. van der Vlerk, “Stochastic programming with simple integer recourse,” Mathematical Programming 61 (1993) pp. 301–325.
    • (1993) Mathematical Programming , vol.61 , pp. 301-325
    • Louveaux, F.V.1    van der Vlerk, M.2
  • 266
    • 67649566847 scopus 로고    scopus 로고
    • A sample approximation approach for optimization with probabilistic constraints
    • ) pp
    • J. Luedtke and S. Ahmed, “A sample approximation approach for optimization with probabilistic constraints,” SIAM Journal on Optimization 19 (2008) pp. 674–699.
    • (2008) SIAM Journal on Optimization , vol.19 , pp. 674-699
    • Luedtke, J.1    Ahmed, S.2
  • 267
    • 0012335591 scopus 로고
    • Bounds on the expectation of a convex function of a multivariate random variable
    • ) pp
    • A. Madansky, “Bounds on the expectation of a convex function of a multivariate random variable,” Annals of Mathematical Statistics 30 (1959) pp. 743–746.
    • (1959) Annals of Mathematical Statistics , vol.30 , pp. 743-746
    • Madansky, A.1
  • 268
    • 0000000764 scopus 로고
    • Inequalities for stochastic linear programming problems
    • ) pp
    • A. Madansky, “Inequalities for stochastic linear programming problems,” Management Science 6 (1960) pp. 197–204.
    • (1960) Management Science , vol.6 , pp. 197-204
    • Madansky, A.1
  • 269
    • 85098159679 scopus 로고    scopus 로고
    • Technical Report, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1991)
    • M. Maddox and J.R. Birge, “Bounds on the distribution of tardiness in a PERT network,” Technical Report, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1991).
    • Bounds on the Distribution of Tardiness in a PERT Network
    • Maddox, M.1    Birge, J.R.2
  • 270
    • 0032632474 scopus 로고    scopus 로고
    • Monte Carlo bounding techniques for determining solution quality in stochastic programs
    • ) pp
    • W. Mak, D.P. Morton, and R.K.Wood, “Monte Carlo bounding techniques for determining solution quality in stochastic programs,” Operations Research Letters 24 (1999) pp. 47–56.
    • (1999) Operations Research Letters , vol.24 , pp. 47-56
    • Mak, W.1    Morton, D.P.2    Wood, R.K.3
  • 271
    • 0013240063 scopus 로고
    • Inequalities for stochastic nonlinear programming problems
    • ) pp
    • O. Mangasarian and J.B. Rosen, “Inequalities for stochastic nonlinear programming problems,” Operations Research 12 (1964) pp. 143–154.
    • (1964) Operations Research , vol.12 , pp. 143-154
    • Mangasarian, O.1    Rosen, J.B.2
  • 274
    • 84863089800 scopus 로고
    • Portfolio Selection; Efficient Diversification of Investments
    • H.M. Markowitz, Portfolio Selection; Efficient Diversification of Investments (John Wiley, Inc., New York, NY, 1959).
    • (1959) John Wiley, Inc., New York, NY
    • Markowitz, H.M.1
  • 278
    • 0001050498 scopus 로고
    • Turnpike theory
    • ) pp
    • L. McKenzie, “Turnpike theory,” Econometrica 44 (1976) pp. 841–864.
    • (1976) Econometrica , vol.44 , pp. 841-864
    • McKenzie, L.1
  • 279
    • 85098194154 scopus 로고    scopus 로고
    • R.C. Merton, “On the pricing of corporate debt: the risk structure of interest rates,” The Journal of Finance 29 (1974) pp. 449-470 (Papers and Proceedings of the Thirty-Second Annual Meeting of the American Finance Association, New York, New York, December 28-30, 1973)
    • R.C. Merton, “On the pricing of corporate debt: the risk structure of interest rates,” The Journal of Finance 29 (1974) pp. 449-470 (Papers and Proceedings of the Thirty-Second Annual Meeting of the American Finance Association, New York, New York, December 28-30, 1973).
  • 281
    • 0001155110 scopus 로고
    • Chance-constrained programming with joint chance constraints
    • ) pp
    • J. Miller and H. Wagner, “Chance-constrained programming with joint chance constraints,” Operations Research 12 (1965) pp. 930–945.
    • (1965) Operations Research , vol.12 , pp. 930-945
    • Miller, J.1    Wagner, H.2
  • 282
    • 0000531094 scopus 로고
    • On the maximal domain of a ‘monotone’ function
    • ) pp
    • G.J. Minty, “On the maximal domain of a ‘monotone’ function,” Michigan Mathematics Journal 8 (1961) pp. 135–137.
    • (1961) ” Michigan Mathematics Journal , vol.8 , pp. 135-137
    • Minty, G.J.1
  • 283
    • 4043137849 scopus 로고
    • Adaptive step-size control for stochastic optimization algorithm
    • ) pp. , (in Russian)
    • F. Mirzoachmedov and S. Uriasiev, “Adaptive step-size control for stochastic optimization algorithm,” Zhurnal vicisl. mat. i mat. fiz. 6 (1983) pp. 1314–1325 (in Russian).
    • (1983) Zhurnal Vicisl. Mat. I Mat. Fiz. , vol.6 , pp. 1314-1325
    • Mirzoachmedov, F.1    Uriasiev, S.2
  • 284
    • 85098159311 scopus 로고
    • Approximation methods and extremum conditions in nonsmooth control systems
    • ) pp
    • B. Mordukhovich, “Approximation methods and extremum conditions in nonsmooth control systems,” Soviet Mathematics Doklady 36 (1988) pp. 164–168.
    • (1988) Soviet Mathematics Doklady , vol.36 , pp. 164-168
    • Mordukhovich, B.1
  • 285
    • 21344469142 scopus 로고    scopus 로고
    • An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling
    • ) pp
    • D.P. Morton, “An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling,” Annals of Operations Research64 (1996) pp. 211–235.
    • (1996) Annals of Operations Research , vol.64 , pp. 211-235
    • Morton, D.P.1
  • 286
    • 0032155337 scopus 로고    scopus 로고
    • Stopping rules for a class of sampling-based stochastic programming algorithms
    • ) pp
    • D.P. Morton, “Stopping rules for a class of sampling-based stochastic programming algorithms,” Operations Research 46 (1998) pp. 710–718.
    • (1998) Operations Research , vol.46 , pp. 710-718
    • Morton, D.P.1
  • 287
    • 0000937493 scopus 로고
    • A new scenario decomposition method for large scale stochastic optimization
    • ) pp
    • J.M. Mulvey and A. Ruszczyński, “A new scenario decomposition method for large scale stochastic optimization,” Operations Research 43 (1995) pp. 477–490.
    • (1995) Operations Research , vol.43 , pp. 477-490
    • Mulvey, J.M.1    Ruszczyński, A.2
  • 288
    • 0000301396 scopus 로고
    • Stochastic network optimization models for investment planning
    • ) pp
    • J.M. Mulvey and H. Vladimirou, “Stochastic network optimization models for investment planning,” Annals of Operations Research 20 (1989) pp. 187–217.
    • (1989) Annals of Operations Research , vol.20 , pp. 187-217
    • Mulvey, J.M.1    Vladimirou, H.2
  • 289
    • 0006115292 scopus 로고
    • Applying the progressive hedging algorithm to stochastic generalized networks
    • ) pp
    • J.M. Mulvey and H. Vladimirou, “Applying the progressive hedging algorithm to stochastic generalized networks,” Annals of Operations Research 31 (1991a) pp. 399–424.
    • (1991) Annals of Operations Research , vol.31 , pp. 399-424
    • Mulvey, J.M.1    Vladimirou, H.2
  • 290
    • 84986946902 scopus 로고
    • Solving multistage stochastic networks: An application of scenario aggregation
    • ) pp
    • J.M. Mulvey and H. Vladimirou, “Solving multistage stochastic networks: an application of scenario aggregation,” Networks 21 (1991b) pp. 619–643.
    • (1991) Networks , vol.21 , pp. 619-643
    • Mulvey, J.M.1    Vladimirou, H.2
  • 291
    • 0000114960 scopus 로고
    • Stochastic network programming for financial planning problems
    • ) pp
    • J.M. Mulvey and H. Vladimirou, “Stochastic network programming for financial planning problems,” Management Science 38 (1992) pp. 1642–1664.
    • (1992) Management Science , vol.38 , pp. 1642-1664
    • Mulvey, J.M.1    Vladimirou, H.2
  • 292
    • 34250509257 scopus 로고
    • Linear programming under uncertainty: A basic property of the optimal solution
    • ) pp
    • K.G. Murty, “Linear programming under uncertainty: a basic property of the optimal solution,” Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 10 (1968) pp. 284–288.
    • (1968) Z. Wahrscheinlichkeitstheorie Und Verw. Gebiete , vol.10 , pp. 284-288
    • Murty, K.G.1
  • 293
  • 294
    • 0022698797 scopus 로고
    • Algorithms for stochastic programs: The case of nonstochastic tenders
    • ) pp
    • J.L. Nazareth and R.J-B Wets, “Algorithms for stochastic programs: the case of nonstochastic tenders,” Mathematical Programming Study 28 (1986) pp. 1–28.
    • (1986) Mathematical Programming Study , vol.28 , pp. 1-28
    • Nazareth, J.L.1    Wets, R.J.-B.2
  • 296
    • 36248992411 scopus 로고    scopus 로고
    • Convex approximations of chance constrained programs
    • A. Nemirovksi and A. Shapiro, “Convex approximations of chance constrained programs,” SIAM Journal on Optimization 17 (2006) 969-996.
    • (2006) SIAM Journal on Optimization , vol.17 , pp. 969-996
    • Nemirovksi, A.1    Shapiro, A.2
  • 297
    • 44349128988 scopus 로고    scopus 로고
    • Confidence level solutions for stochastic programming
    • Yu. Nesterov and J.-Ph. Vial, “Confidence level solutions for stochastic programming,” Automatica 44 (2008), 1559–1568.
    • (2008) Automatica , vol.44 , pp. 1559-1568
    • Nesterov, Y.1    Vial, J.-P.2
  • 298
  • 299
    • 0027555591 scopus 로고
    • A massively parallel algorithm for nonlinear stochastic network problems
    • ) pp
    • S.S. Nielsen and S.A. Zenios, “A massively parallel algorithm for nonlinear stochastic network problems,” Operations Research 41 (1993a) pp. 319–337.
    • (1993) Operations Research , vol.41 , pp. 319-337
    • Nielsen, S.S.1    Zenios, S.A.2
  • 300
    • 84973818637 scopus 로고
    • Proximal minimizations with D-functions and the massively parallel solution of linear stochastic network programs
    • ) pp
    • S.S. Nielsen and S.A. Zenios, “Proximal minimizations with D-functions and the massively parallel solution of linear stochastic network programs,” International Journal of Supercomputing and Applications 7 (1993b) pp. 349–364.
    • (1993) International Journal of Supercomputing and Applications , vol.7 , pp. 349-364
    • Nielsen, S.S.1    Zenios, S.A.2
  • 301
    • 0023312728 scopus 로고
    • Nested decomposition of multistage nonlinear programs with recourse
    • ) pp
    • M.-C. Noël and Y. Smeers, “Nested decomposition of multistage nonlinear programs with recourse,” Mathematical Programming 37 (1987) pp. 131–152.
    • (1987) Mathematical Programming , vol.37 , pp. 131-152
    • Noël, M.-C.1    Smeers, Y.2
  • 302
    • 0001565276 scopus 로고    scopus 로고
    • On optimal allocation of indivisibles under uncertainty
    • ) pp
    • V.I. Norkin, Y.M. Ermoliev, and A. Ruszczyński, “On optimal allocation of indivisibles under uncertainty,” Operations Research 46 (1998) pp. 381–395.
    • (1998) Operations Research , vol.46 , pp. 381-395
    • Norkin, V.I.1    Ermoliev, Y.M.2    Ruszczyński, A.3
  • 303
    • 0001454014 scopus 로고    scopus 로고
    • A branch and bound method for stochastic global optimization
    • ) pp
    • V.I. Norkin, G.Ch. Pflug, and A. Ruszczyński, “A branch and bound method for stochastic global optimization,” Mathematical Programming 83 (1998) pp. 425–450.
    • (1998) Mathematical Programming , vol.83 , pp. 425-450
    • Norkin, V.I.1    Pflug, G.C.2    Ruszczyński, A.3
  • 304
    • 49149089526 scopus 로고    scopus 로고
    • A Branch-and-Cut algorithm for two-stage stochastic mixed-binary programs with continuous first-stage variables
    • ) pp
    • L. Ntaimo and S. Sen,“ A Branch-and-Cut algorithm for two-stage stochastic mixed-binary programs with continuous first-stage variables,” International Journal of Computational Science and Engineering 3 (2008a) pp. 231–241.
    • (2008) International Journal of Computational Science and Engineering , vol.3 , pp. 231-241
    • Ntaimo, L.1    Sen, S.2
  • 305
    • 45749093779 scopus 로고    scopus 로고
    • A comparative study of decomposition algorithms for stochastic combinatorial optimization
    • ) pp
    • L. Ntaimo and S. Sen, “A comparative study of decomposition algorithms for stochastic combinatorial optimization,” Computational Optimization and Applications 40 (2008b) pp. 299–319.
    • (2008) Computational Optimization and Applications , vol.40 , pp. 299-319
    • Ntaimo, L.1    Sen, S.2
  • 307
    • 0022185792 scopus 로고
    • Stochastic optimization of a multireservoir hydroelectric system—A decomposition approach
    • ) pp
    • M.V.F. Pereira and L.M.V.G. Pinto, “Stochastic optimization of a multireservoir hydroelectric system—A decomposition approach,” Water Resources Research 21 (1985) pp. 779–792.
    • (1985) Water Resources Research , vol.21 , pp. 779-792
    • Pereira, M.V.F.1    Pinto, L.M.V.G.2
  • 308
    • 34249928584 scopus 로고
    • Multistage Stochastic Optimization Applied to Energy Planning
    • ) pp
    • M.V.F. Pereira and L.M.V.G. Pinto, “Multistage Stochastic Optimization Applied to Energy Planning,” Mathematical Programming 52 (1991) pp. 359-375.
    • (1991) Mathematical Programming , vol.52 , pp. 359-375
    • Pereira, M.V.F.1    Pinto, L.M.V.G.2
  • 309
    • 0002015332 scopus 로고
    • Stepsize rules, stopping times and their implementation in stochastic quasigradient algorithms
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • G.Ch. Pflug, “Stepsize rules, stopping times and their implementation in stochastic quasigradient algorithms” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988) pp. 353–372.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 353-372
    • Pflug, G.C.1
  • 310
    • 0013270047 scopus 로고    scopus 로고
    • Scenario tree generation for multiperiod financial optimization by optimal discretization
    • G.Ch. Pflug, “Scenario tree generation for multiperiod financial optimization by optimal discretization,” Mathematical Programming, Ser. B 89 (2001) pp. 251271.
    • (2001) Mathematical Programming, Ser. B , vol.89
    • Pflug, G.C.1
  • 311
    • 0037321489 scopus 로고    scopus 로고
    • A note on the recursive and parallel structure of the Birge and Qi factorization
    • ) pp
    • G.Ch. Pflug and L. Halada, “A note on the recursive and parallel structure of the Birge and Qi factorization,” Computational Optimization and Applications 24 (2003) pp. 251–265.
    • (2003) Computational Optimization and Applications , vol.24 , pp. 251-265
    • Pflug, G.C.1    Halada, L.2
  • 312
    • 0042769481 scopus 로고
    • Deterministic approximations of probability inequalities,” ZOR—Methods and Models of Operations Research, Series
    • ) pp
    • J. Pintér, “Deterministic approximations of probability inequalities,” ZOR—Methods and Models of Operations Research, Series Theory 33 (1989) pp. 219–239.
    • (1989) Theory , vol.33 , pp. 219-239
    • Pintér, J.1
  • 313
    • 46449109930 scopus 로고    scopus 로고
    • On the convergence of stochastic dual dynamic programming and related methods
    • ) pp
    • A.B. Philpott and Z. Guan, “On the convergence of stochastic dual dynamic programming and related methods,” Operations Research Letters 36 (2008) pp. 450-455.
    • (2008) Operations Research Letters , vol.36 , pp. 450-455
    • Philpott, A.B.1    Guan, Z.2
  • 314
    • 0001621211 scopus 로고    scopus 로고
    • Sample-path optimization of convex stochastic performance functions
    • ) pp
    • E.L. Plambeck, B-R. Fu, S.M. Robinson, and R. Suri, “Sample-path optimization of convex stochastic performance functions,” Mathematical Programming 75 (1996) pp. 137–176.
    • (1996) Mathematical Programming , vol.75 , pp. 137-176
    • Plambeck, E.L.1    Fu, B.-R.2    Robinson, S.M.3    Suri, R.4
  • 315
    • 0000553271 scopus 로고
    • A comparative review of alternative algorithms for the dynamic vehicle allocation program
    • B. Golden and A. Assad, Eds., North-Holland, Amsterdam
    • W.B. Powell, “A comparative review of alternative algorithms for the dynamic vehicle allocation program” in: B. Golden and A. Assad, Eds., Vehicle Routing: Methods and Studies (North-Holland, Amsterdam, 1988).
    • (1988) Vehicle Routing: Methods and Studies
    • Powell, W.B.1
  • 317
    • 0000485147 scopus 로고
    • Logarithmic concave measures with application to stochastic programming
    • ) pp
    • A. Prékopa, “Logarithmic concave measures with application to stochastic programming,” Acta. Sci. Math. (Szeged) 32 (1971) pp. 301–316.
    • (1971) Acta. Sci. Math. (Szeged) , vol.32 , pp. 301-316
    • Prékopa, A.1
  • 318
    • 0000678433 scopus 로고
    • Contributions to the theory of stochastic programs
    • ) pp
    • A. Prékopa, “Contributions to the theory of stochastic programs,” Mathematical Programming 4 (1973) pp. 202–221.
    • (1973) Mathematical Programming , vol.4 , pp. 202-221
    • Prékopa, A.1
  • 319
    • 0012233996 scopus 로고
    • Programming under probabilistic constraints with a random technology matrix
    • ) pp
    • A. Prékopa, “Programming under probabilistic constraints with a random technology matrix,” Mathematische Operationsforschung und Statistik 5 (1974) pp. 109–116.
    • (1974) Mathematische Operationsforschung Und Statistik , vol.5 , pp. 109-116
    • Prékopa, A.1
  • 320
    • 0003312808 scopus 로고
    • Logarithmically concave measures and related topics
    • M.A.H. Dempster, Ed., Academic Press, New York, NY
    • A. Prékopa, “Logarithmically concave measures and related topics” in: M.A.H. Dempster, Ed., Stochastic Programming (Academic Press, New York, NY, 1980).
    • (1980) Stochastic Programming
    • Prékopa, A.1
  • 321
    • 0023817936 scopus 로고
    • Boole-Bonferroni inequalities and linear programming
    • ) pp
    • A. Prékopa, “Boole-Bonferroni inequalities and linear programming,” Operations Research 36 (1988) pp. 145–162.
    • (1988) Operations Research , vol.36 , pp. 145-162
    • Prékopa, A.1
  • 322
    • 0003410675 scopus 로고
    • Kluwer Academic Publishers, Dordrecht, Netherlands
    • A. Prékopa, Stochastic Programming (Kluwer Academic Publishers, Dordrecht, Netherlands, 1995).
    • (1995) Stochastic Programming
    • Prékopa, A.1
  • 324
    • 0021717883 scopus 로고
    • On the practical importance of asymptotic optimality in certain heuristic algorithms
    • ) pp
    • H.N. Psaraftis, “On the practical importance of asymptotic optimality in certain heuristic algorithms,” Networks (1984) pp. 587–596.
    • (1984) Networks , pp. 587-596
    • Psaraftis, H.N.1
  • 325
    • 0022135659 scopus 로고
    • Forest iteration method for stochastic transportation problem
    • ) pp
    • L. Qi, “Forest iteration method for stochastic transportation problem,” Mathematical Programming Study (1985) pp. 142–163.
    • (1985) Mathematical Programming Study , pp. 142-163
    • Qi, L.1
  • 326
    • 0022699061 scopus 로고
    • An alternating method for stochastic linear programming with simple recourse
    • ) pp
    • L. Qi, “An alternating method for stochastic linear programming with simple recourse,” Stochastic Processes and Their Applications 841 (1986) pp. 183–190.
    • (1986) Stochastic Processes and Their Applications , vol.841 , pp. 183-190
    • Qi, L.1
  • 327
  • 329
    • 33646750383 scopus 로고    scopus 로고
    • Hedging uncertainty: Approximation algorithms for stochastic optimization problems
    • ) pp
    • R. Ravi and A. Sinha, “Hedging uncertainty: Approximation algorithms for stochastic optimization problems,” Mathematical Programming Ser. A 108 (2006) pp. 97-114.
    • (2006) Mathematical Programming Ser. A , vol.108 , pp. 97-114
    • Ravi, R.1    Sinha, A.2
  • 333
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R.T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, NJ, 1969).
    • (1969) Convex Analysis
    • Rockafellar, R.T.1
  • 334
    • 0003450909 scopus 로고
    • Society for Industrial and Applied Mathematics, Philadelphia, PA
    • R.T. Rockafellar, Conjugate Duality and Optimization (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1974).
    • (1974) Conjugate Duality and Optimization
    • Rockafellar, R.T.1
  • 335
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • ) pp
    • R.T. Rockafellar, “Monotone operators and the proximal point algorithm,” SIAM Journal on Control and Optimization 14 (1976a) pp. 877–898.
    • (1976) SIAM Journal on Control and Optimization , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 337
    • 0002062038 scopus 로고    scopus 로고
    • Optimization of Conditional Value-At-Risk
    • ) pp
    • R.T. Rockafellar and S. Uryasev, “Optimization of Conditional Value-At-Risk,” The Journal of Risk 2:3 (2000) pp. 21–41.
    • (2000) The Journal of Risk , vol.2 , Issue.3 , pp. 21-41
    • Rockafellar, R.T.1    Uryasev, S.2
  • 338
    • 0036076694 scopus 로고    scopus 로고
    • Conditional Value-at-Risk for general loss distributions
    • ) pp
    • R.T. Rockafellar and S. Uryasev, “Conditional Value-at-Risk for general loss distributions,” Journal of Banking and Finance 26 (2002) pp. 1443–1471.
    • (2002) Journal of Banking and Finance , vol.26 , pp. 1443-1471
    • Rockafellar, R.T.1    Uryasev, S.2
  • 340
    • 0016949808 scopus 로고
    • Stochastic convex programming, relatively complete recourse and induced feasibility
    • ) pp
    • R.T. Rockafellar and R.J-B Wets, “Stochastic convex programming, relatively complete recourse and induced feasibility,” SIAM Journal on Control and Optimization 14 (1976b) pp. 574–589.
    • (1976) SIAM Journal on Control and Optimization , vol.14 , pp. 574-589
    • Rockafellar, R.T.1    Wets, R.J.-B.2
  • 341
    • 0022699539 scopus 로고
    • A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming
    • ) pp
    • R.T. Rockafellar and R.J-B Wets, “A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming,” Mathematical Programming Study 28 (1986) pp. 63–93.
    • (1986) Mathematical Programming Study , vol.28 , pp. 63-93
    • Rockafellar, R.T.1    Wets, R.J.-B.2
  • 342
    • 0000514655 scopus 로고
    • Scenarios and policy aggregation in optimization under uncertainty
    • ) pp
    • R.T. Rockafellar and R.J-B Wets, “Scenarios and policy aggregation in optimization under uncertainty,” Mathematics of Operations Research 16 (1991) pp. 119–147.
    • (1991) Mathematics of Operations Research , vol.16 , pp. 119-147
    • Rockafellar, R.T.1    Wets, R.J.-B.2
  • 344
    • 34249921301 scopus 로고
    • Distribution sensitivity in stochastic programming
    • ) pp
    • W. Römisch and R. Schultz, “Distribution sensitivity in stochastic programming,” Mathematical Programming 50 (1991a) pp. 197–226.
    • (1991) Mathematical Programming , vol.50 , pp. 197-226
    • Römisch, W.1    Schultz, R.2
  • 345
    • 0000269246 scopus 로고
    • Stability analysis for stochastic programs
    • ) pp
    • W. Römisch and R. Schultz, “Stability analysis for stochastic programs,” Annals of Operations Research 31 (1991b) pp. 241–266.
    • (1991) Annals of Operations Research , vol.31 , pp. 241-266
    • Römisch, W.1    Schultz, R.2
  • 350
    • 0022751475 scopus 로고
    • A regularized decomposition for minimizing a sum of polyhedral functions
    • ) pp
    • A. Ruszczyński, “A regularized decomposition for minimizing a sum of polyhedral functions,” Mathematical Programming 35 (1986) pp. 309–333.
    • (1986) Mathematical Programming , vol.35 , pp. 309-333
    • Ruszczyński, A.1
  • 351
    • 0001060664 scopus 로고
    • Parallel decomposition of multistage stochastic programming problems
    • ) pp
    • A. Ruszczyński, “Parallel decomposition of multistage stochastic programming problems,” Mathematical Programming 58 (1993a) pp. 201–228.
    • (1993) Mathematical Programming , vol.58 , pp. 201-228
    • Ruszczyński, A.1
  • 353
    • 10044271668 scopus 로고    scopus 로고
    • Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra
    • ) pp
    • A. Ruszczyński, “Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra,” Mathematical Programming 93 (2002) pp.195–215.
    • (2002) Mathematical Programming , vol.93 , pp. 195-215
    • Ruszczyński, A.1
  • 354
    • 0006699794 scopus 로고
    • Approximations for chance constrained programming problems
    • ) pp
    • G. Salinetti, “Approximations for chance constrained programming problems,” Stochastics 10 (1983) pp. 157–169.
    • (1983) Stochastics , vol.10 , pp. 157-169
    • Salinetti, G.1
  • 356
    • 0010183458 scopus 로고
    • Inequalities for the probability of the occurrence of at least m out of n events
    • ) pp
    • Y.S. Sathe, M. Pradhan, and S.P. Shah, “Inequalities for the probability of the occurrence of at least m out of n events,” Journal of Applied Probability 17 (1980) pp. 1127–1132.
    • (1980) Journal of Applied Probability , vol.17 , pp. 1127-1132
    • Sathe, Y.S.1    Pradhan, M.2    Shah, S.P.3
  • 357
    • 0002693448 scopus 로고
    • A minimax solution of an inventory problem
    • K.J. Arrow, S. Karlin, and H. Scarf, Eds., Stanford University Press, Stanford, CA
    • H. Scarf, “A minimax solution of an inventory problem” in: K.J. Arrow, S. Karlin, and H. Scarf, Eds., Studies in the Mathematical Theory of Inventory and Production (Stanford University Press, Stanford, CA, 1958).
    • (1958) Studies in the Mathematical Theory of Inventory and Production
    • Scarf, H.1
  • 358
    • 0013258601 scopus 로고
    • Continuity properties of expectation functionals in stochastic integer programming
    • ) pp
    • R. Schultz, “Continuity properties of expectation functionals in stochastic integer programming,” Mathematics of Operations Research 18 (1993) pp. 578–589.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 578-589
    • Schultz, R.1
  • 359
    • 0000151690 scopus 로고    scopus 로고
    • Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis reductions
    • ) pp
    • R. Schultz, L. Stougie and M.H. van der Vlerk, “Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis reductions,” Mathematical Programming 83 (1998) pp. 229–252.
    • (1998) Mathematical Programming , vol.83 , pp. 229-252
    • Schultz, R.1    Stougie, L.2    van der Vlerk, M.H.3
  • 360
    • 61449101310 scopus 로고    scopus 로고
    • Reoptimization approaches for the vehicle-routing problem with stochastic demands
    • ) pp
    • N. Secomandi and F. Margot, “Reoptimization approaches for the vehicle-routing problem with stochastic demands,” Operations Research 57 (2009) pp. 214–230.
    • (2009) Operations Research , vol.57 , pp. 214-230
    • Secomandi, N.1    Margot, F.2
  • 361
    • 43249104456 scopus 로고    scopus 로고
    • Algorithms for stochastic mixed-integer programming”
    • in: K. Aardal, G.L. Nemhauser, R. Weismantel, Eds., Elsevier, Amsterdam, ) pp
    • S. Sen, “Algorithms for stochastic mixed-integer programming”, in: K. Aardal, G.L. Nemhauser, R. Weismantel, Eds., Handbooks in Operations Research and Management Science (Elsevier, Amsterdam, 2005) pp. 515–558.
    • (2005) Handbooks in Operations Research and Management Science , pp. 515-558
    • Sen, S.1
  • 362
    • 24044484404 scopus 로고    scopus 로고
    • 2 algorithm for large scale stochastic mixed-integer programming
    • ) pp
    • 2 algorithm for large scale stochastic mixed-integer programming,” Mathematical Programming 104 (2005) pp. 1–20.
    • (2005) Mathematical Programming , vol.104 , pp. 1-20
    • Sen, S.1    Higle, J.L.2
  • 363
    • 31744441041 scopus 로고    scopus 로고
    • Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming
    • ) pp
    • S. Sen and H.D. Sherali, “Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming,” Mathematical Programming 106 (2006) pp. 203– 223
    • (2006) Mathematical Programming , vol.106 , pp. 203-223
    • Sen, S.1    Sherali, H.D.2
  • 364
    • 33847159232 scopus 로고    scopus 로고
    • An approximation scheme for stochastic linear programming and its application to stochastic integer programs
    • ) pp
    • D.B. Shmoys and C. Swamy, “An approximation scheme for stochastic linear programming and its application to stochastic integer programs,” Journal of the ACM 53 (2006) pp. 978– 1012.
    • (2006) Journal of the ACM , vol.53 , pp. 978-1012
    • Shmoys, D.B.1    Swamy, C.2
  • 365
    • 0001530774 scopus 로고
    • Asymptotic analysis of stochastic programs
    • ) pp
    • A. Shapiro, “Asymptotic analysis of stochastic programs,” Annals of Operations Research 30 (1991) pp. 169–186.
    • (1991) Annals of Operations Research , vol.30 , pp. 169-186
    • Shapiro, A.1
  • 366
    • 21044447935 scopus 로고    scopus 로고
    • Inference of statistical bounds for multistage stochastic programming problems
    • ) pp
    • A. Shapiro, “Inference of statistical bounds for multistage stochastic programming problems,” Mathematical Methods of Operations Research 58 (2003) pp. 57–68.
    • (2003) Mathematical Methods of Operations Research , vol.58 , pp. 57-68
    • Shapiro, A.1
  • 367
    • 0034550507 scopus 로고    scopus 로고
    • On the rate of convergence of optimal solutions of Monte Carlo approximations of stochastic programs
    • ) pp
    • A. Shapiro and T. Homem-de-Mello, “On the rate of convergence of optimal solutions of Monte Carlo approximations of stochastic programs,” SIAM Journal on Optimization 11 (2000) pp. 70–86.
    • (2000) SIAM Journal on Optimization , vol.11 , pp. 70-86
    • Shapiro, A.1    Homem-De-mello, T.2
  • 368
    • 84980092818 scopus 로고
    • Capital asset prices: A theory of market equilibrium under conditions of risk
    • ) pp
    • W.F. Sharpe, “Capital asset prices: a theory of market equilibrium under conditions of risk,” Journal of Finance 19 (1964) pp. 425–442.
    • (1964) Journal of Finance , vol.19 , pp. 425-442
    • Sharpe, W.F.1
  • 369
    • 33847159232 scopus 로고    scopus 로고
    • An approximation scheme for stochastic linear programming and its application to stochastic integer programs
    • ) pp
    • D.B. Shmoys and C. Swamy,“ An approximation scheme for stochastic linear programming and its application to stochastic integer programs,” Journal of the ACM 53 (2006) pp. 978– 1012.
    • (2006) Journal of the ACM , vol.53 , pp. 978-1012
    • Shmoys, D.B.1    Swamy, C.2
  • 371
    • 0024083859 scopus 로고
    • Stochastic optimization models for lake eutrophication management
    • ) pp
    • L. Somlyódi and R.J-B Wets, “Stochastic optimization models for lake eutrophication management,” Operations Research 36 (1988) pp. 660–681.
    • (1988) Operations Research , vol.36 , pp. 660-681
    • Somlyódi, L.1    Wets, R.J.-B.2
  • 372
    • 84960591048 scopus 로고
    • The cost of subsistence
    • G.J. Stigler, “The cost of subsistence,” Journal of Farm Economics 27 (1945), 303–314.
    • (1945) Journal of Farm Economics , vol.27 , pp. 303-314
    • Stigler, G.J.1
  • 374
    • 0038885223 scopus 로고
    • Some results concerning an algorithm for the discrete recourse problem
    • M.A.H. Dempster, Ed., Academic Press, New York, NY
    • B. Strazicky, “Some results concerning an algorithm for the discrete recourse problem,” in: M.A.H. Dempster, Ed., Stochastic Programming (Academic Press, New York, NY, 1980).
    • (1980) Stochastic Programming
    • Strazicky, B.1
  • 376
    • 0346147749 scopus 로고
    • A simplex method for network programs with convex separable piecewise linear costs and its application to stochastic transshipment problems
    • in: D.Z. Du and P.M. Pardalos, Eds., World Scientific Publishing Co., London, ) pp
    • J. Sun, L. Qi, and K-H. Tsai, “A simplex method for network programs with convex separable piecewise linear costs and its application to stochastic transshipment problems,” in: D.Z. Du and P.M. Pardalos, Eds., Network Optimization Problems: Algorithms, Applications and Complexity (World Scientific Publishing Co., London, 1993) pp. 281–300.
    • (1993) Network Optimization Problems: Algorithms, Applications and Complexity , pp. 281-300
    • Sun, J.1    Qi, L.2    Tsai, K.-H.3
  • 377
    • 33748620926 scopus 로고    scopus 로고
    • Sampling-based approximation algorithms for multistage stochastic optimization
    • IEEE Computer Society, Los Alamitos, CA, ) pp
    • C. Swamy and D.B. Shmoys, “Sampling-based approximation algorithms for multistage stochastic optimization, in: Proceedings of FOCS 2005 (IEEE Computer Society, Los Alamitos, CA, 2005) pp. 357–366.
    • (2005) Proceedings of FOCS 2005 , pp. 357-366
    • Swamy, C.1    Shmoys, D.B.2
  • 378
    • 38149072053 scopus 로고    scopus 로고
    • Approximation Algorithms for 2-Stage Stochastic Optimization Problems
    • pp
    • C. Swamy and D.B. Shmoys, “Approximation Algorithms for 2-Stage Stochastic Optimization Problems,” ACM SIGACT News 37:March (2006) pp. 33–46.
    • (2006) ACM SIGACT News 37:March , pp. 33-46
    • Swamy, C.1    Shmoys, D.B.2
  • 379
    • 84913724605 scopus 로고
    • Chance-constrained equivalents of stochastic programming problems
    • ) pp
    • G.H. Symonds, “Chance-constrained equivalents of stochastic programming problems,” Operations Research 16 (1968) pp. 1152–1159.
    • (1968) Operations Research , vol.16 , pp. 1152-1159
    • Symonds, G.H.1
  • 380
    • 0022694634 scopus 로고
    • Evaluation of a special multivariate gamma distribution function
    • ) pp
    • T. Szántai, “Evaluation of a special multivariate gamma distribution function,” Mathematical Programming Study 27 (1986) pp. 1–16.
    • (1986) Mathematical Programming Study , vol.27 , pp. 1-16
    • Szántai, T.1
  • 381
    • 85098189091 scopus 로고    scopus 로고
    • Introduction to Quality Engineering (Asian Productivity Center, Tokyo, Japan, 1986)
    • G. Taguchi, Introduction to Quality Engineering (Asian Productivity Center, Tokyo, Japan, 1986).
    • Taguchi, G.1
  • 384
    • 77950486395 scopus 로고
    • Ph.D. Dissertation, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI
    • S. Takriti, “On-line Solution of Linear Programs with Varying Right-Hand Sides,” Ph.D. Dissertation, Department of Industrial and Operations Engineering, University of Michigan (Ann Arbor, MI, 1994).
    • (1994) On-Line Solution of Linear Programs with Varying Right-Hand Sides
    • Takriti, S.1
  • 385
    • 0034138665 scopus 로고    scopus 로고
    • Using integer programming to refine Lagrangian-based unit commitment solutions
    • ), pp
    • S. Takriti and J.R. Birge, “Using integer programming to refine Lagrangian-based unit commitment solutions,” IEEE Transactions on Power Systems 15 (2000a), pp. 151-156.
    • (2000) IEEE Transactions on Power Systems , vol.15 , pp. 151-156
    • Takriti, S.1    Birge, J.R.2
  • 386
    • 0033703331 scopus 로고    scopus 로고
    • Lagrangian solution techniques and bounds for loosely-coupled mixed-integer stochastic programs
    • ) pp
    • S. Takriti and J.R. Birge, “Lagrangian solution techniques and bounds for loosely-coupled mixed-integer stochastic programs,” Operations Research 48 (2000b) pp. 91–98.
    • (2000) Operations Research , vol.48 , pp. 91-98
    • Takriti, S.1    Birge, J.R.2
  • 388
    • 52449148039 scopus 로고
    • An extension of Karmarkar’s algorithm for linear programming using dual variables
    • ) pp
    • M.J. Todd and B.P. Burrell, “An extension of Karmarkar’s algorithm for linear programming using dual variables,” Algorithmica 1 (1986) pp. 409–424.
    • (1986) Algorithmica , vol.1 , pp. 409-424
    • Todd, M.J.1    Burrell, B.P.2
  • 389
    • 0001555742 scopus 로고
    • On the convergence of some feasible Eddirection algorithms for nonlinear programming
    • ) pp
    • D.M. Topkis and A.F. Veinott, Jr., “On the convergence of some feasible Eddirection algorithms for nonlinear programming,” SIAM Journal on Control 5 (1967) pp. 268–279.
    • (1967) SIAM Journal on Control , vol.5 , pp. 268-279
    • Topkis, D.M.1    Veinott, A.F.2
  • 391
    • 0002783313 scopus 로고
    • Adaptive stochastic quasigradient methods
    • Y. Ermoliev and R. Wets, Eds., Springer-Verlag, Berlin, ) pp
    • S. Uriasiev, “Adaptive stochastic quasigradient methods” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988) pp. 373– 384.
    • (1988) Numerical Techniques for Stochastic Optimization , pp. 373-384
    • Uriasiev, S.1
  • 392
    • 0004148624 scopus 로고
    • McGraw-Hill Inc., New York, NY
    • F.A. Valentine, Convex Sets (McGraw-Hill Inc., New York, NY, 1964).
    • (1964) Convex Sets
    • Valentine, F.A.1
  • 393
    • 21044440737 scopus 로고    scopus 로고
    • Convex approximations for complete integer recourse models
    • ) pp
    • M. H. van der Vlerk, “Convex approximations for complete integer recourse models,” Mathematical Programming 99 (2004) pp. 297–310.
    • (2004) Mathematical Programming , vol.99 , pp. 297-310
    • van der Vlerk, M.H.1
  • 395
    • 0014534894 scopus 로고
    • L-shaped linear programs with application to optimal control and stochastic programming
    • ) pp
    • R. Van Slyke and R.J-B Wets, “L-shaped linear programs with application to optimal control and stochastic programming,” SIAM Journal on Applied Mathematics 17 (1969) pp. 638– 663.
    • (1969) SIAM Journal on Applied Mathematics , vol.17 , pp. 638-663
    • van Slyke, R.1    Wets, R.J.-B.2
  • 396
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite Programming
    • ) pp
    • L. Vandenberghe and S. Boyd,“ Semidefinite Programming,” SIAM Review 38 (1996) pp. 49–95.
    • (1996) SIAM Review , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 397
    • 85098121953 scopus 로고    scopus 로고
    • P. Varaiya and R.J-B Wets, “Stochastic dynamic optimization approaches and computation” in: M. Iri and K. Tanabe, Eds., Mathematical Programming: Recent Developments and Applications (Kluwer, Dordrecht, Netherlands, 1989) pp. 309–332
    • P. Varaiya and R.J-B Wets, “Stochastic dynamic optimization approaches and computation” in: M. Iri and K. Tanabe, Eds., Mathematical Programming: Recent Developments and Applications (Kluwer, Dordrecht, Netherlands, 1989) pp. 309–332.
  • 398
    • 1642500005 scopus 로고
    • Probability of loss on loan portfolio
    • Technical Report (San Francisco, CA
    • O. Vasiček, “Probability of loss on loan portfolio,” KMV Corporation, Technical Report (San Francisco, CA, 1987); available at: www.moodyskmv.com/research/files/wp/Probability of Loss on Loan Portfolio.pdf.
    • (1987) KMV Corporation
    • Vasiček, O.1
  • 400
    • 23744491457 scopus 로고    scopus 로고
    • Loan portfolio value
    • ) pp
    • O. Vasiček, “Loan portfolio value,” Risk 15:12 (2002) pp. 160-162.
    • (2002) Risk , vol.15 , Issue.12 , pp. 160-162
    • Vasiček, O.1
  • 401
    • 0027554515 scopus 로고
    • Restricted simplicial decomposition for convex constrained problems
    • ) pp
    • J.A. Ventura and D.W. Hearn, “Restricted simplicial decomposition for convex constrained problems,” Mathematical Programming 59 (1993) pp. 71–85.
    • (1993) Mathematical Programming , vol.59 , pp. 71-85
    • Ventura, J.A.1    Hearn, D.W.2
  • 406
    • 0346985250 scopus 로고
    • Stochastic programs with recourse II: On the continuity of the objective
    • ) pp
    • D. Walkup and R.J-B Wets, “Stochastic programs with recourse II: on the continuity of the objective,” SIAM Journal on Applied Mathematics 17 (1969) pp. 98–103.
    • (1969) SIAM Journal on Applied Mathematics , vol.17 , pp. 98-103
    • Walkup, D.1    Wets, R.J.-B.2
  • 407
    • 0022695397 scopus 로고
    • Decomposing the requirement space of a transportation problem into polyhedral cones
    • ) pp
    • S.W. Wallace, “Decomposing the requirement space of a transportation problem into polyhedral cones,” Mathematical Programming Study 28 (1986a) pp. 29–47.
    • (1986) Mathematical Programming Study , vol.28 , pp. 29-47
    • Wallace, S.W.1
  • 408
    • 0022781673 scopus 로고
    • Solving stochastic programs with network recourse
    • ) pp
    • S.W. Wallace, “Solving stochastic programs with network recourse,” Networks 16 (1986b) pp. 295–317.
    • (1986) Networks , vol.16 , pp. 295-317
    • Wallace, S.W.1
  • 409
    • 84987041118 scopus 로고
    • A piecewise linear upper bound on the network recourse function
    • ) pp
    • S.W. Wallace, “A piecewise linear upper bound on the network recourse function,” Networks 17 (1987) pp. 87–103.
    • (1987) Networks , vol.17 , pp. 87-103
    • Wallace, S.W.1
  • 410
    • 0033684759 scopus 로고    scopus 로고
    • Decision making under uncertainty: Is sensitivity analysis of any use?
    • ) pp
    • S.W. Wallace, “Decision making under uncertainty: is sensitivity analysis of any use?” Operations Research 48 (2000) pp. 20–25.
    • (2000) Operations Research , vol.48 , pp. 20-25
    • Wallace, S.W.1
  • 411
    • 0027105298 scopus 로고
    • Preprocessing in stochastic programming: The case of linear programs
    • ) pp
    • S.W. Wallace and R.J-B Wets, “Preprocessing in stochastic programming: the case of linear programs,” ORSA Journal on Computing 4 (1992) pp. 45–59.
    • (1992) ORSA Journal on Computing , vol.4 , pp. 45-59
    • Wallace, S.W.1    Wets, R.J.-B.2
  • 412
    • 0027646393 scopus 로고
    • Bounding multi-stage stochastic programs from above
    • ) pp
    • S.W. Wallace and T.C. Yan, “Bounding multi-stage stochastic programs from above,” Mathematical Programming 61 (1993) pp. 111–129.
    • (1993) Mathematical Programming , vol.61 , pp. 111-129
    • Wallace, S.W.1    Yan, T.C.2
  • 414
    • 0005010428 scopus 로고
    • Programming under uncertainty: The equivalent convex program
    • ) pp
    • R.J-B Wets, “Programming under uncertainty: the equivalent convex program,” SIAM Journal on Applied Mathematics 14 (1966) pp. 89–105.
    • (1966) SIAM Journal on Applied Mathematics , vol.14 , pp. 89-105
    • Wets, R.J.-B.1
  • 415
    • 34250455156 scopus 로고
    • Characterization theorems for stochastic programs
    • ) pp
    • R.J-B Wets, “Characterization theorems for stochastic programs,” Mathematical Programming 2 (1972) pp. 166–175.
    • (1972) Mathematical Programming , vol.2 , pp. 166-175
    • Wets, R.J.-B.1
  • 416
    • 0016084468 scopus 로고
    • Stochastic programs with fixed recourse: The equivalent deterministic problem
    • ) pp
    • R.J-B Wets, “Stochastic programs with fixed recourse: the equivalent deterministic problem,” SIAM Review 16 (1974) pp. 309–339.
    • (1974) SIAM Review , vol.16 , pp. 309-339
    • Wets, R.J.-B.1
  • 417
    • 0010677475 scopus 로고
    • R.W. Cottle, F. Giannessi and J.-L. Lions, Eds., Variational Inequalities and Complementarity Problems (John Wiley, Inc., New York, NY, ) pp
    • R.J-B Wets, “Convergence of convex functions, variational inequalities and convex optimization problems” in: R.W. Cottle, F. Giannessi and J.-L. Lions, Eds., Variational Inequalities and Complementarity Problems (John Wiley, Inc., New York, NY, 1980a) pp. 375–404.
    • (1980) Convergence of Convex Functions, Variational Inequalities and Convex Optimization Problems , pp. 375-404
    • Wets, R.J.-B.1
  • 418
    • 5744249393 scopus 로고
    • Stochastic multipliers, induced feasibility and nonanticipativity in stochastic programming
    • M.A.H. Dempster, Ed., Academic Press, New York, NY
    • R.J-B Wets, “Stochastic multipliers, induced feasibility and nonanticipativity in stochastic programming” in: M.A.H. Dempster, Ed., Stochastic Programming (Academic Press, New York, NY, 1980b).
    • (1980) Stochastic Programming
    • Wets, R.J.-B.1
  • 419
    • 0001332013 scopus 로고
    • Solving stochastic programs with simple recourse
    • ) pp
    • R.J-B Wets, “Solving stochastic programs with simple recourse,” Stochastics 10 (1983a) pp. 219–242.
    • (1983) Stochastics , vol.10 , pp. 219-242
    • Wets, R.J.-B.1
  • 420
    • 0012660094 scopus 로고
    • Stochastic programming: Solution techniques and approximation schemes
    • in: A. Bachem, M. Grötschel, and B. Korte, Eds., Springer-Verlag, Berlin, ) pp
    • R.J-B Wets, “Stochastic programming: solution techniques and approximation schemes” in: A. Bachem, M. Grötschel, and B. Korte, Eds., Mathematical Programming: State-of-the-Art 1982 (Springer-Verlag, Berlin, 1983b) pp. 560–603.
    • (1983) Mathematical Programming: State-Of-The-Art , vol.1982 , pp. 560-603
    • Wets, R.J.-B.1
  • 421
    • 0002975395 scopus 로고
    • Large-scale linear programming techniques in stochastic programming
    • in: Y. Ermoliev and R. Wets, Eds., SpringerVerlag, Berlin
    • R.J-B Wets, “Large-scale linear programming techniques in stochastic programming” in: Y. Ermoliev and R. Wets, Eds., Numerical Techniques for Stochastic Optimization (SpringerVerlag, Berlin, 1988).
    • (1988) Numerical Techniques for Stochastic Optimization
    • Wets, R.J.-B.1
  • 422
    • 77957099013 scopus 로고
    • Stochastic programming
    • in: G.L. Nemhauser, A.H.G. Rinnooy Kan, and M.J. Todd, Eds., North–Holland, Amsterdam, Netherlands
    • R.J-B Wets, “Stochastic programming” in: G.L. Nemhauser, A.H.G. Rinnooy Kan, and M.J. Todd, Eds., Optimization (Handbooks in Operations Research and Management Science; Vol. 1, North–Holland, Amsterdam, Netherlands, 1990).
    • (1990) Optimization (Handbooks in Operations Research and Management Science; Vol , pp. 1
    • Wets, R.J.-B.1
  • 425
    • 0004686884 scopus 로고
    • A stochastic transportation problem
    • ) pp
    • A.C. Williams, “A stochastic transportation problem,” Operations Research 11 (1963) pp. 759–770.
    • (1963) Operations Research , vol.11 , pp. 759-770
    • Williams, A.C.1
  • 426
    • 84882225276 scopus 로고
    • Approximation formulas for stochastic linear programming
    • ) pp
    • A.C. Williams, “Approximation formulas for stochastic linear programming,” SIAM Journal on Applied Mathematics 14 (1966) pp. 668–677.
    • (1966) SIAM Journal on Applied Mathematics , vol.14 , pp. 668-677
    • Williams, A.C.1
  • 429
    • 0000877462 scopus 로고
    • Two stage linear programming under uncertainty with 0-1 integer first stage variables
    • ) pp
    • R. Wollmer, “Two stage linear programming under uncertainty with 0-1 integer first stage variables,” Mathematical Programming 19 (1980) pp. 279–288.
    • (1980) Mathematical Programming , vol.19 , pp. 279-288
    • Wollmer, R.1
  • 430
  • 432
    • 0007724010 scopus 로고
    • Primal-dual aggregation and disaggregation for stochastic linear programs
    • ) pp
    • S.E. Wright, “Primal-dual aggregation and disaggregation for stochastic linear programs,” Mathematics of Operations Research 19 (1994) pp. 893–908.
    • (1994) Mathematics of Operations Research , vol.19 , pp. 893-908
    • Wright, S.E.1
  • 433
    • 0030715517 scopus 로고    scopus 로고
    • A scalable parallel interior point algorithm for stochastic linear programming and robust optimization
    • A. Murli and G. Toraldo, Eds., Springer, New York, ) pp
    • D. Yang and S.A. Zenios, “A scalable parallel interior point algorithm for stochastic linear programming and robust optimization,” in: A. Murli and G. Toraldo, Eds., Computational Issues in High Performance Software for Nonlinear Optimization (Springer, New York, 1997) pp. 143–158.
    • (1997) Computational Issues in High Performance Software for Nonlinear Optimization , pp. 143-158
    • Yang, D.1    Zenios, S.A.2
  • 435
    • 33644599009 scopus 로고    scopus 로고
    • A stochastic programming approach to the airline crew scheduling Problem
    • ) pp
    • J.W. Yen and J.R. Birge, “A stochastic programming approach to the airline crew scheduling Problem,” Transportation Science 40 (2006) pp. 3–14.
    • (2006) Transportation Science , vol.40 , pp. 3-14
    • Yen, J.W.1    Birge, J.R.2
  • 436
    • 0005078389 scopus 로고
    • On minimax solutions of stochastic linear programming problems
    • ) pp
    • J. Žáčková, “On minimax solutions of stochastic linear programming problems,” Časopis pro Pěstování Matematiky 91 (1966) pp. 423–430.
    • (1966) Časopis Pro Pěstování Matematiky , vol.91 , pp. 423-430
    • Žáčková, J.1
  • 437
    • 0003718989 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • S.A. Zenios, Financial Optimization (Cambridge University Press, Cambridge, UK, 1993).
    • (1993) Financial Optimization
    • Zenios, S.A.1
  • 438
    • 0342618578 scopus 로고
    • Computational algorithms for convex stochastic programs with simple recourse
    • ) pp
    • W.T. Ziemba, “Computational algorithms for convex stochastic programs with simple recourse,” Operations Research 18 (1970) pp. 414–431.
    • (1970) Operations Research , vol.18 , pp. 414-431
    • Ziemba, W.T.1
  • 441
    • 0019032977 scopus 로고
    • Bounds for row-aggregation in linear programming
    • ) pp
    • P. Zipkin, “Bounds for row-aggregation in linear programming,” Operations Research 28 (1980a) pp. 903–916.
    • (1980) Operations Research , vol.28 , pp. 903-916
    • Zipkin, P.1
  • 442
    • 0018998304 scopus 로고
    • Bounds on the effect of aggregating variables in linear programs
    • ) pp
    • P. Zipkin, “Bounds on the effect of aggregating variables in linear programs,” Operations Research 28 (1980b) pp. 403–418.
    • (1980) Operations Research , vol.28 , pp. 403-418
    • Zipkin, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.