Skip to main content

Computer Support for Modeling in Stochastic Linear Programming

  • Chapter
Stochastic Programming

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 423))

Abstract

The purpose of the paper is to discuss the modeling process in stochastic linear programming (SLP) and to point out the SLP-specific features of computer support to this process.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Avriel and A. C. Williams. The value of information and stochastic programming. Operations Researc., 18:947–954, 1970.

    Article  Google Scholar 

  2. A. Bharadwaj, A. Lo. Choobineh, and B. Shetty. Model management systems: A survey. Annals of Operations Researc., 38:17–67, 1992.

    Article  Google Scholar 

  3. J. R. Birge. The value of stochastic solution in stochastic linear programs with fixed recourse. Mathematical Programmin., 24:314–325, 1982.

    Article  Google Scholar 

  4. J. R. Birge, M. A. H. Dempster, H. Gassmann, E. Gunn, A. J. King, and S. W. Wallace. A standard input format for multiperiod stochastic linear programs. Working Paper WP-87–118, IIASA, 1987.

    Google Scholar 

  5. J. Bisschop and A. Meeraus. On the development of a general algebraic modeling system in a strategic planning environment. Mathematical Programming Stud., 20:1–29, 1982.

    Article  Google Scholar 

  6. A. Brooke, D. Kendrick, and A. Meeraus. GAMS, A User’s Guide. The Scientific Press, 1988.

    Google Scholar 

  7. G. B. Dantzig and P. W. Glynn. Parallel processors for planning under uncertainty. Technical Report SOL 88–8R, Department for Operations Research, Stanford University, 1989.

    Google Scholar 

  8. D. R. Dolk. Model management systems for operations research: A prospectus. In G. Mitra, editor, Mathematical Methods for Decision Suppor., pages 347–373. Springer Verlag, 1988.

    Chapter  Google Scholar 

  9. Y. Ermoliev. Stochastic quasigradient methods and their application to systems optimization. Stochastic., 9:1–36, 1983.

    Article  Google Scholar 

  10. K. Frauendorfer and P. Kail. A solution method for SLP recourse problems with arbitrary multivariate distributions — the independent case. Problems of Control and Information Theor., 17:177–205, 1988.

    Google Scholar 

  11. K. Frauendorfer. Solving SLP recourse problems with arbitrary multivariate distributions — the dependent case. Mathematics of Operations Researc., 13:377–394, 1988.

    Article  Google Scholar 

  12. A. Gaivoronski. Stochastic quasigradient methods and their implementation. In Y. Ermoliev and R.J-B. Wets, editors, Numerical Techniques for Stochastic Optimizatio., pages 313–351. Springer Verlag, 1988.

    Chapter  Google Scholar 

  13. H. I. Gassmann and A. M. Ireland. Scenario formulation in an algebraic modelling language. Working Paper WP-92–7, School of Business Administration, Dalhousie University, Halifax, 1992.

    Google Scholar 

  14. A. M. Geoffrion. An introduction to structured modeling. Management Scienc., 33:547–588, 1987.

    Article  Google Scholar 

  15. A. M. Geoffrion. Computer-based modeling environments. European Journal on Operational Researc., 41:33–43, 1989.

    Article  Google Scholar 

  16. A. M. Geoffrion. FW/SM: A prototype structured modeling environment. Management Scienc., 37:1513–1538, 1991.

    Article  Google Scholar 

  17. H. J. Greenberg. RANDMOD: A system for randomizing modifications to an instance of a linear program. ORSA Journal on Computin., 3:173–175, 1991.

    Article  Google Scholar 

  18. H. J. Greenberg. Modeling by object-driven linear elemental relations: A user’s guide to MODLER. Kluwer Academic Publishers, 1993.

    Book  Google Scholar 

  19. H. J. Greenberg. A computer-assisted analysis system for mathematical programming models and solutions: A user’s guide to ANALYZE. Kluwer Academic Publishers, 1993.

    Book  Google Scholar 

  20. H. J. Greenberg and F. H. Murphy. A comparison of mathematical programming modeling systems. Annals of Operations Researc., 38:177–238, 1992.

    Article  Google Scholar 

  21. D. B. Hausch and W. T. Ziemba. Bounds on the value of information in uncertain decision problems II. Stochastic., 10:181–217, 1983.

    Article  Google Scholar 

  22. J. L. Higle and S. Sen. Stochastic decomposition: An algorithm for two-stage linear programs with recourse. Mathematics of Operations Researc., 16:650–669, 1991.

    Article  Google Scholar 

  23. P. Kall. Approximations to stochastic programs with complete fixed recourse. Numerische Mathemati., 22:333–339, 1974.

    Article  Google Scholar 

  24. P. Kall. Computational methods for solving two-stage stochastic linear programming problems. Zeitschrift für angewandte Mathematik und Physi., 30:261–271, 1979.

    Article  Google Scholar 

  25. P. Kall. Stochastic linear programming. Springer Verlag, 1976.

    Book  Google Scholar 

  26. P. Kall and D. Stoyan. Solving stochastic programming problems with recourse including error bounds. Mathematische Operationsforschung und Statistik, Ser. Optimizatio., 13:431–447, 1982.

    Article  Google Scholar 

  27. P. Kall. Towards computing the expected value of perfect information. In M. J. Beckmann, W. Eichhorn, and W. Krelle, editors, Mathematische Systeme in der Ökonomi., pages 277–287. Athenäum, 1983.

    Google Scholar 

  28. P. Kall. Stochastic programming with recourse: Upper bounds and moment problems — a review. In J. Guddat, B. Bank, H. Hollatz, P. Kall, D. Klatte, B. Kummer, K. Lommatzsch, K. Tammer, M. Vlach, and K. Zimmermann, editors, Advances in Mathematical Optimization (Dedicated to Prof. Dr.Dr.hc. F. Nožička., pages 86–103. Akademie-Verlag, Berlin, 1988.

    Google Scholar 

  29. P. Kall, A. Ruszczynski, and K. Frauendorfer. Approximation techniques in stochastic programming. In Y. Ermoliev and R.J-B. Wets, editors, Numerical Techniques for Stochastic Optimizatio., pages 33–64. Springer Verlag, 1988.

    Chapter  Google Scholar 

  30. P. Kall and J. Mayer. SLP-IOR: A model management system for stochastic linear programming — system design —. In A.J.M. Beulens and H.-J. Sebastian, editors, Optimization-Based Computer-Aided Modelling and Desig., pages 139–157. Springer Verlag, 1992.

    Chapter  Google Scholar 

  31. P. Kall and J. Mayer. A model management system for stochastic linear programming. In P. Kall, editor, System Modelling and Optimizatio., pages 580–587. Springer Verlag, 1992.

    Chapter  Google Scholar 

  32. P. Kall and J. Mayer. SLP-IOR: On the design of a workbench for testing SLP codes. Preprint, IOR, University of Zurich, 1992.

    Google Scholar 

  33. P. Kall and J. Mayer. Model management for stochastic linear programming. Mathematical Programming, Series., 1994. Submitted for publication.

    Google Scholar 

  34. E. Keller. GENSLP: A program for generating input for stochastic linear programs with complete fixed recourse. Manuscript, IOR, University of Zurich, 1984.

    Google Scholar 

  35. A. J. King. Stochastic programming problems: Examples from the literature. In Y. Ermoliev and R.J-B. Wets, editors, Numerical Techniques for Stochastic Optimizatio., pages 543–567. Springer Verlag, 1988.

    Chapter  Google Scholar 

  36. K. Marti. Konvexitätsaussagen zum linearen stochastischen opti-mierungsproblem. Zeitschrift für Wahrscheinlichkeitstheorie und verw. Geb., 18:159–166, 1971.

    Article  Google Scholar 

  37. J. Mayer. Probabilistic constrained programming: A reduced gradient algorithm implemented on PC. Working Paper WP-88–39, IIASA, 1988.

    Google Scholar 

  38. J. Mayer. Computational techniques for probabilistic constrained optimization problems. In K. Marti, editor, Stochastic Optimization: Numerical Methods and Technical Application., pages 141–164. Springer Verlag, 1992.

    Chapter  Google Scholar 

  39. C. van de Panne and W. Popp. Minimum cost cattle feed under probabilistic problem constraint. Management Scienc., 9:405–430, 1963.

    Article  Google Scholar 

  40. A. Prékopa. Logarithmic concave measures and related topics. In M. A. H. Dempster, editor, Stochastic Programmin., pages 63–82. Academic Press, 1980.

    Google Scholar 

  41. A. Prékopa. Numerical solution of probabilistic constrained programming problems. In Y. Ermoliev and R.J-B. Wets, editors, Numerical Techniques for Stochastic Optimizatio., pages 123–139. Springer Verlag, 1988.

    Chapter  Google Scholar 

  42. A. Ruszczynski. A regularized decomposition method for minimizing a sum of polyhedral functions. Mathematical Programmin., 35:309–333, 1986.

    Article  Google Scholar 

  43. K. Schittkowski. EMP: An expert system for mathematical programming. Technical report, Mathematisches Institut, Universitat Bayreuth, 1987.

    Google Scholar 

  44. K. Schittkowski. Some experiments on heuristic code selection versus numerical performance in nonlinear programming. European Journal on Operational Researc., 65:292–304, 1993.

    Article  Google Scholar 

  45. B. Strazicky. On an algorithm for solution of the two-stage stochastic programming problem. Methods of Operations Researc., XIX:142–156, 1974.

    Google Scholar 

  46. R. H. Sprague and E. D. Carlson. Building effective decision support systems. Prentice-Hall Publ. Co., 1982.

    Google Scholar 

  47. T. Szántai. A computer code for solution of probabilistic-constrained stochastic programming problems. In Y. Ermoliev and R.J-B. Wets, editors, Numerical Techniques for Stochastic Optimizatio., pages 229–235. Springer Verlag, 1988.

    Chapter  Google Scholar 

  48. R Van Slyke and R. J-B. Wets. L-shaped linear program with applications to optimal control and stochastic linear programs. SIAM J. Appl. Math., 17:638–663, 1969.

    Article  Google Scholar 

  49. S. W. Wallace and R. J-B. Wets. Preprocessing in stochastic programming: The case of uncapacitated networks. ORSA Journal on Computin., 1:252–270, 1989.

    Article  Google Scholar 

  50. S. W. Wallace and R. J-B. Wets. Preprocessing in stochastic programming: The case of linear programs. ORSA Journal on Computin., 4:45–59, 1992.

    Article  Google Scholar 

  51. R. J-B. Wets. Stochastic programming: Solution techniques and approximation schemes. In A. Bachern, M. Grötschel, and B. Korte, editors, Mathematical programming: The state of the ar., pages 566–603. Springer Verlag, 1983.

    Chapter  Google Scholar 

  52. R. J-B. Wets. Stochastic programming. In G. L. Nemhauser, editor, Handbooks in OR and MS, Vol., pages 573–629. Elsevier, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kall, P., Mayer, J. (1995). Computer Support for Modeling in Stochastic Linear Programming. In: Marti, K., Kall, P. (eds) Stochastic Programming. Lecture Notes in Economics and Mathematical Systems, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88272-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-88272-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58996-9

  • Online ISBN: 978-3-642-88272-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics