한국경영과학회지 (Journal of the Korean Operations Research and Management Science Society)

  • 제27권3호
  • /
  • Pages.145-156
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  • 2002
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  • 1225-1119(pISSN)
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  • 2733-4759(eISSN)
한국경영과학회 (The Korean Operations Research and Management Science Society)
권호 표지

확률적 선형계획문제의 상한과 하한한계 분석

Analysis on Upper and Lower Bounds of Stochastic LP Problems

  • 발행 : 2002.09.01
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초록

Business managers are often required to use LP problems to deal with uncertainty inherent in decision making due to rapid changes in today＇s business environments. Uncertain parameters can be easily formulated in the two-stage stochastic LP problems. However, since solution methods are complex and time-consuming, a common approach has been to use modified formulations to provide upper and lower bounds on the two-stage stochastic LP problem. One approach is to use an expected value problem, which provides upper and lower bounds. Another approach is to use “walt-and-see” problem to provide upper and lower bounds. The objective of this paper is to propose a modified approach of “wait-and-see” problem to provide an upper bound and to compare the relative error of optimal value with various upper and lower bounds. A computing experiment is implemented to show the relative error of optimal value with various upper and lower bounds and computing times.

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참고문헌

  1. 경영과학 v.12 no.2 저장능력이 무한대인 장소입지문제에 벤더즈 분해기법과 GAMS의 적용 이상진
  2. 한국경영학회지 v.22 no.1 A study on solution methods of two-state stochastic LP problems 이상진
  3. 경영과학 v.15 no.1 요가 불확실한 경우의 장소입지 결정 모형 연구 이상진
  4. Operations Research v.18 The value of information and stochastic programming Avriel, M.;A.C. Williams
  5. Mathematical Programming Study v.27 Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse Birge, J.R.;R.J-B. Wets
  6. Mathematical Programming v.24 The value of the stochastic solution in stochastic linear programs with fixed recourse Birge, J.R.
  7. GAMS : A User's Guide Brooke, A.;D, Kendrick;A. Meeraus
  8. Linear Programming and Extensions Dantzig, G.B.
  9. Technical Report SOL 91-11 Multi-stage stochastic linear programs for portfolio optimization Dantzig, G.B.;G. Infanger
  10. Stochastic Optimization : A Statistical Method for Large Scale Stochastic LP Higle, Julia L.;Suvrajeet Sen
  11. Operations Research v.25 Sharp bounds on the value of perfect information Huang, C.C.;I. Vertinsky;W.T. Ziemba
  12. Journal of Optimization Theory and Application v.74 A sensitivity method for basis inverse representation in multistage stochastic LP problems Gondzio, J.;A. Ruszcznski
  13. Optimization Theory For Large Systems Lasdon, L.S.
  14. Numerical Techniques for Stochastic Optimization Optimal invstment for electricity generation : A stochastic model and a test problem Louveaux, F.V.;Y. Smeers;Y. Ermoliev(ed.);R. J-B. Wets(ed.)
  15. Operations Research v.35 Formulating Stochastic programs for interior point methods Lustig, I.J.;J.M. Mulvey;T.J. Carpenter
  16. Management Science v.6 Inequalities for stochastic linear program problems Madansky, A.
  17. Operations Research v.43 A new scenario decomposition method for large-scale stochastic optimization Mulvey, J.M.;A. Ruszczynski
  18. Annals of Operations Research v.31 Applying the progressive hedging algorithm to stochastic generalized networks Mulvey, J.M.;H. Vladimirou
  19. Management Science v.38 Stochastic network programming for financial planning problems Mulvey, J.M.;H. Vladimirou
  20. Mathematical Operations Research v.16 Scenarios and policy aggregation in optimization under uncertainty Rockafellar, R.T.;R. J-B. Wets
  21. SIAM Journal on Applied Mathematics v.17 L-shaped linear programs with application to optimal control and stochastic optimization Van Slyke, R.;R.J-B. Wets
  22. SIAM Journal on Applied Mathematics v.15 Stochastic programs with recourse Walkup, D.W.;R.J-B. Wets
  23. Mathematical Programming : The State of the Art Stochastic programming : Solution techniques and approximation schemes Wets, R.J-B.;A.Bachem(ed.);M. Grotschel(ed.);B.Korte(ed.)
  24. SIAM Journal on Applied Mathematics v.14 Programming under uncertainty : The equivalent convex program Wets, R.J-B.
  25. SIAM Journal on Applied Mathematics v.14 Programming under uncertainty : The solution set Wets, R.J-B.