Conference Slide Presentations

ISMP 2000, Atlanta, Georgia, August 7-11, 2000



The 17th International Symposium on Mathematical Programming

Extending algebraic modelling languages for Stochastic Programming.

Abstract: The algebraic modelling languages (AML) have gained wide acceptance and use by researchers and practitioners of Mathematical Programming. At a simple level, stochastic programming (SP) models can be defined by a deterministic equivalent representation using an AML. Unfortunately, this leads to very large model data instances. We propose a direct approach in which the random values of the model coefficients and the stage structure of the decision variables and constraints are "overlaid" on the underlying algebraic (core) model of the SP problems. This leads to not only a natural definition of the SP model: the resulting generated instance is also a compact representation of the otherwise large explicit representation. This design is presented as SMPL: a stochastic extension of the MPL language. Our work in progress illustrates the generic aspect of this concept, whereby we are able introduce similar "stochastic" constructs to the AMPL syntax and thereby define an extension which we call SAMPL.


Author: Prof. Gautam Mitra

Brunel University
Department of Mathematical Sciences

Tel: (+44 (0)1895 274000 extension 2314

Email: mastggm@brunel.ac.uk
Home Page: http://www.brunel.ac.uk/depts/ma/

  1. Slides

  2. Outline
  3. Modelling with AMLs
  4. Modelling with AMLs
  5. Modelling SP
  6. Modelling SP
  7. Extending AMLs for SP (1)
  8. Extending AMLs for SP (2)
  9. Underlying deterministic
  10. Stochastic Information
  11. SP modelling object classes
  12. Syntax and structure
  13. Illustrative example: an asset allocation model
  14. Scenario generation
  15. Event tree
  16. Model entities
  17. Cash-flow constraints
  18. Security inventory balance
  19. Diversification constraint and objective function
  20. Formulation (Core)
  21. Model entities
  22. Formulation (Stoch)
  23. Chance-constrained
  24. SP modelling systems
  25. Current Developments
  26. System architecture
  27. Future directions
  28. Conclusions
  29. References
  30. SBRP stochastic info
  31. CCP stochastic info
  32. DBRP stochastic info
  33. Scenarios tree consistency
  34. SMPL (syntax)
  35. SMPL (syntax)
  36. SMPL (syntax)
  37. SMPL (syntax)
  38. SMPL (syntax)
  39. Example
  40. Aggregation
  41. Compact random values
  42. Expanded random values
  43. Sparse random values
  44. SMPL (DBRP)


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