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Mslip: A computer code for the multistage stochastic linear programming problem

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Abstract

This paper describes an efficient implementation of a nested decomposition algorithm for the multistage stochastic linear programming problem. Many of the computational tricks developed for deterministic staircase problems are adapted to the stochastic setting and their effect on computation times is investigated. The computer code supports an arbitrary number of time periods and various types of random structures for the input data. Numerical results compare the performance of the algorithm to MINOS 5.0.

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References

  1. P.G. Abrahamson, “A nested decomposition approach for solving staircase linear programs,” Technical Report SOL 83-4, Systems Optimization Laboratory, Stanford University (Stanford, CA, 1983).

    Google Scholar 

  2. J.F. Benders, “Partitioning procedures for solving mixed-variables programming problems,”Numerische Mathematik 4 (1962) 238–252.

    Google Scholar 

  3. J.R. Birge, “Solution methods for stochastic dynamic linear programs,” Technical Report SOL 80-29, Systems Optimization Laboratory, Stanford University (Stanford, CA, 1980).

    Google Scholar 

  4. J.R. Birge, “Decomposition and partitioning methods for multistage stochastic linear programs,”Operations Research 33 (1985) 989–1007.

    Google Scholar 

  5. J.R. Birge, “NDSP User's manual,” in: J. Edwards, ed.,Documentation for the ADO/SDS collection of stochastic programming codes, Working Paper WP-85-02, International Institute for Applied Systems Analysis (Laxenburg, Austria, 1985).

    Google Scholar 

  6. J.R. Birge, M.A.H. Dempster, H.I. Gassmann, E.A. Gunn, A.J. King and S.W. Wallace, “A standard input format for multiperiod stochastic linear programs,”COAL Newsletter 17 (1987) 1–20.

    Google Scholar 

  7. J.R. Birge and F.V. Louveaux, “A multicut algorithm for two-stage linear programs,”European Journal of Operational Research 34 (1988) 384–392.

    Google Scholar 

  8. P. Birge, “A research bibliography in stochastic programming,” Working Paper, International Institute for Applied Systems Analysis (Laxenburg, Austria, 1988).

    Google Scholar 

  9. J. Bisschop and A. Meeraus, “Matrix augmentation and partitioning in the updating of the basis inverse,”Mathematical Programming 13 (1977) 241–254.

    Google Scholar 

  10. S.P. Bradley and D.B. Crane, “A dynamic model for bond portfolio management,”Management Science 19 (1972) 139–151.

    Google Scholar 

  11. V. Chvatál,Linear Programming (Freeman, New York, 1983).

    Google Scholar 

  12. G.B. Dantzig,Linear Programming and Extensions (Princeton University Press, Princeton, NJ, 1963).

    Google Scholar 

  13. G.B. Dantzig and P. Wolfe, “Decomposition principle for linear programs,”Operations Research 8 (1960), 101–111.

    Google Scholar 

  14. H.I. Gassmann, “Optimal harvest of a forest in the presence of uncertainty,”Canadian Journal of Forest Research 19 (1989) 1267–1274.

    Google Scholar 

  15. S. Garstka and D. Rutenberg, “Computation in discrete stochastic programs with recourse,”Operations Research 21 (1973) 112–122.

    Google Scholar 

  16. C.R. Glassey, “Nested decomposition and multi-stage linear programs,”Management Science 20 (1973) 282–292.

    Google Scholar 

  17. D. Haugland and S.W. Wallace, “Solving many linear programs that differ only in the righthand side,” Working Paper #372102-1, Christian Michelsen Institute (Bergen, Norway, 1986).

    Google Scholar 

  18. J.K. Ho, “Convergence behavior of decomposition algorithms for linear programs,”Operations Research Letters 2 (1984) 91–94.

    Google Scholar 

  19. J.K. Ho and E. Loute, “A set of staircase linear programming test problems,”Mathematical Programming 20 (1981) 245–250.

    Google Scholar 

  20. J.K. Ho and A.S. Manne, “Nested decomposition for dynamic models,”Mathematical Programming 6 (1974) 121–140.

    Google Scholar 

  21. J.G. Kallberg and W.T. Ziemba, “An algorithm for portfolio revision: Theory, Computational Algorithm and empirical results,” in: R.A. Schultz, ed.,Applications of Management Science, Vol. I (JAI Press, Greenwich, CT, 1981) pp. 267–292.

    Google Scholar 

  22. F.V. Louveaux, “A solution method for multistage stochastic programs with application to an energy investment problem,”Operations Research 28 (1980) 889–902.

    Google Scholar 

  23. R.R. Merkovsky, “Near-linear convergent procedures for convex and large scale optimization based on linear programming: Theory and Applications,” Ph.D. Thesis, Dalhousie University (Halifax, N.S., 1987).

    Google Scholar 

  24. F. Mirzoakhmedov and M.V. Mikhalevich, “Modelling of optimal cultivated land distribution by means of a multistage stochastic programming problem,”Ekonomicheski i matematicheskie metody 18 (1982) 918–922 (in Russian).

    Google Scholar 

  25. B.A. Murtagh and M.A. Saunders, “MINOS 5.0 user's guide,” Technical Report SOL 83-20, Systems Optimization Laboratory, Stanford University (Stanford, CA, 1983).

    Google Scholar 

  26. M.-C. Noël and Y. Smeers, “Nested decomposition of multistage nonlinear programs with recourse,” CORE Working Paper #8505, Université Catholique de Louvain (Louvain-la-Neuve, Belgium, 1985).

    Google Scholar 

  27. R.P. O'Neill, “Nested decomposition of multistage convex programs,”SIAM Journal of Control and Optimization 14 (1976) 409–418.

    Google Scholar 

  28. C.E. Pfefferkorn and J.A. Tomlin, “Design of a linear programming system for ILLIAC IV,” Technical Report SOL 76-8, Systems Optimization Laboratory, Stanford University (Stanford, CA,. 1976).

    Google Scholar 

  29. A.N. Rae, “Stochastic programming, utility and sequential decision problems in farm management,”American Journal of Agricultural Economics 53 (1971) 625–638.

    Google Scholar 

  30. R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, NJ, 1970).

    Google Scholar 

  31. D.M. Scott, “A dynamic programming approach to time staged convex programs,” Technical Report SOL 85-3, Systems Optimization Laboratory, Stanford University (Stanford, CA, 1985).

    Google Scholar 

  32. S.B. Smith, “Planning transistor production by linear programming,”Operations Research 13 (1965) 132–139.

    Google Scholar 

  33. R. Van Slyke and R.J.-B. Wets, “L-shaped linear programs with application to optimal control and stochastic optimization,”SIAM Journal on Applied Mathematics 17 (1969) 638–663.

    Google Scholar 

  34. D. Walkup and R.J.-B. Wets, “Lifting projections of convex polyhedra,”Pacific Journal of Mathematics 28 (1969) 465–475.

    Google Scholar 

  35. R.J.-B. Wets, “Large scale linear programming techniques in stochastic programming,” in: Yu. Ermoliev and R.J.-B. Wets, eds.,Numerical Methods in Stochastic Optimization, Lecture Notes in Mathematics (Springer, Berlin, 1988).

    Google Scholar 

  36. R.J. Wittrock, “Advances in a nested decomposition algorithm for solving staircase linear programs,” Technical Report SOL 83-2, Systems Optimization Laboratory, Stanford University (Stanford, CA, 1983).

    Google Scholar 

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Gassmann, H.I. Mslip: A computer code for the multistage stochastic linear programming problem. Mathematical Programming 47, 407–423 (1990). https://doi.org/10.1007/BF01580872

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  • DOI: https://doi.org/10.1007/BF01580872

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