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

  • 제22권1호
  • /
  • Pages.1-24
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  • 1997
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  • 1225-1119(pISSN)
  • /
  • 2733-4759(eISSN)
한국경영과학회 (The Korean Operations Research and Management Science Society)
권호 표지

A Study on Solution Methods of Two-stage Stochastic LP Problems

  • 발행 : 1997.03.01
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초록

In this paper, we have proposed new solution methods to solve TSLP (two-stage stochastic linear programming) problems. One solution method is to combine the analytic center concept with Benders' decomposition strategy to solve TSLP problems. Another method is to apply an idea proposed by Geoffrion and Graves to modify the L-shaped algorithm and the analytic center algorithm. We have compared the numerical performance of the proposed algorithms to that of the existing algorithm, the L-shaped algorithm. To effectively compare those algorithms, we have had computational experiments for seven test problems.

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참고문헌

  1. Manuscript Implementation and behavior of an interior point cutting plane algorithm for convex programming: An application to grometric programming Bahan, O.;J.L. Goffin;J.P. Vial;O. Du Merle
  2. Journal of the Royal Statistics Society v.B17 On minimizing a convex function subject to linear inequalities Beale, E.M.L.
  3. Operations Research v.33 Decomposition and partitioning methods for multistage stochastic linear programs Birge, J. R.
  4. European Journal of Operations Research v.34 A multicut algorithm for two-stage linear programs Birge, J.R.;F.V. Louveaux
  5. Mathematical Progrmming Study v.27 Designing approximation schemes for stochasic optimization problems, in particular for stochastic programs with recourse Birge, J.R.;R.J-B. Wets
  6. PH.D. thesis, Department of Industrial Engineering, University of Wisconsin-Madison Scenario analysis modeling and decompositon methods Chun, B.J.
  7. Technical Report 91-6 An Implementation of the bundle decomposition algorthm Chun, B.J.;S.J. Lee;S.M. Robinson
  8. Management Science v.1 Linear programming under uncertainty Dantzig, G.B.
  9. Technical Report SOL 88-8 Parallel processors for planning under uncertainty Danzig, G.B.;P.W. Glynn
  10. Technical Report SOL 91-11 Multi-stage stochastic linear programs for portfolio optimization Dantzig, G.B.;G. Infanger
  11. Numerical Techniques for Strochastic Optimization Facility location problem Ermoliev, Y.;Y. Ermoliev(ed.);R.J-B. Wets(ed.)
  12. Mathematical Programming v.47 MSLiP: a computer code for the multistage linear programming problems Gassmann, H.I.
  13. Management Science v.20 Multiconnodity distribution system design by Benders decomposition Geoffrion, A.M.;G.W. Graves
  14. Trends in mathematical Optimization Affine and projective transformations in nondifferentiable optimization Goffin, J.L.;K.H. Hoffmann(ed.);J.B. Hiriart-Urruty(ed.);C. Lemarechal(ed.);J. Zowe(ed.)
  15. Journal of Optimization Theroy and Applications v.65 Cutting planes and column generation techniques with the projective algorithm Goffin, J.L.;J.P. Vial
  16. Manuscript. Using central prices in the decomposition of linear programs Goffin, J.L.;A. Haurie;J.P. Vial;D.L. Zhu
  17. Management Science v.38 Decomposition and Nondifferentiable optimization with the projective algorithm Goffin, J.L.;A. Haurie;J.P. Vial
  18. Mathematical Programming v.20 A set of staircase limear programming test problems Ho, J.K.;E. Loute
  19. Technical Report SOL 89-13 Monte Carlo(importance) sampling within a Benders decomposition algorithm for stochastic limear programs Infanger, G.
  20. Journal of the SIAM v.8 The cutting-plane method for solving convex programs Kelly, J.E.
  21. Numerical Techniques for Stochastic Optimization Stochastic programming problems : Examples from the literature King, A. J.;Y. Ermoliec(ed.);R. J.-B Wets(ed.)
  22. Optimization v.23 A second order sffine scaling algorithm for the geometric programming dual with logarithmic barrier Kortanek, K. O.;H. No
  23. Optimization Theory For large Systems Lasdon, L. S.
  24. Ph. D. Thesis, School of Business, University of Wisconsin-Madison Parallel solution of multistage stochastic limear programming problems using the alahytic center method Lee, S. J.
  25. Annlas of Operations Research v.20 Stochastic network optimization models for investment planning Mulvey, J. M.;H. Vladimirou
  26. Annlas of Operations Research v.31 Applying the progressive hedging algorithm to stochastic generalized network Mulvey, J. M.;H. Vladimirou
  27. Report 90-09-08 A massively parallel algorithm for nonlimear stochastic network problems Nielson, S. S.;S. A. Zenios
  28. Mathematics of Operations Research v.16 Scenarios and aggregation in optimization under uncertainty Rockfellar, R. T.;R. J.-B. Wets
  29. Mathematical Programming v.35 A regularized decomposition method for minimizing a sum of polyhedral functions Ruszczynki, A.
  30. Aspiration Based Decision Support Systems, Lecture Notes in Economics and Mathematical Systems v.331 Modern techniques for linear dynamic and stochastic programs Ruszcynski, A.;A. Lewandowski(ed.);A. Wierzbicki(ed.)
  31. Aspiration Based Decision Support Systems, Lecture Notes in Economics and Mathematical Systems v.331 Regularized decomposition and augmented Lagrangian decompositon for angular limear programming problems Ruszcynski, A.;A. Lewandowski(ed.);A. Wierzbicki(ed.)
  32. Trends in Mathematical Optimization New algorithms in convex programming based on a notion of center for systems of analytic inequalities and on rational extrapolation Sonnevend, G.;K. H. Hoffmann(ed.);J. B. Hirianrt-Urruty(ed.);C. lemarechal(ed.);J. Zowe(ed.)
  33. Journal of Optimization Theory and Applications v.36 A cutting plane algorithm with linear and geometric rates of convergence Topkis, J. M.
  34. 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
  35. SIAM Journal on Applied Mathematics v.15 Stochastic progrmas with recourse Walkup, D. W.;R. J. -B. Wets
  36. SIAM Journal on Applied Mathematics v.14 Programming under uncertainty : The equivalent convex program Wets. R. J. -B.
  37. SIAM Journal on Applied Mathematics v.14 Programming under uncertainty : The solution set Wets. R. J. -B.
  38. Mathematical Programmig : 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.)
  39. Mathematical Programming v.39 Recovering optimal dual solution in Karmarkar's polynomial algorithm for linear programming Ye, Y.;M. Kojima
  40. Report 90-11-10 Massively parallel computations for financial planning under uncertainty Zenios, S. A.