EVPI-based importance sampling solution procedures for multistage stochastic linear programmes on parallel MIMD architectures. Multistage stochastic linear programming has many practical applications for problems whose current decisions have to be made under future uncertainty. There are a variety of methods for solving the deterministic equivalent forms of these dynamic problems, including the simplex and interior-point methods and nested Benders decomposition, which decomposes the original problem into a set of smaller linear programming problems and has recently been shown to be superior to the alternatives for large problems. The Benders subproblems can be visualised as being attached to the nodes of a tree which is formed from the realisations of the random data process determining the uncertainty in the problem. This paper describes a parallel implementation of the nested Benders algorithm which employs a farming technique to parallelize nodal subproblem solutions. Differing structures of the test problems cause differing levels of speed-up on a variety of multicomputing platforms: problems with few variables and constraints per node do not gain from this parallelisation. We therefore employ stage aggregation to such problems to improve their parallel solution efficiency by increasing the size of the nodes and therefore the time spent calculating relative to the time spent communicating between processors. A parallel version of a sequential importance sampling solution algorithm based on local expected value of perfect information (EVPI) is developed which is applicable to extremely large multistage stochastic linear programmes which either have too many data paths to solve directly or a continuous distribution of possible realisations. It utilises the parallel nested Benders algorithm and a parallel version of an algorithm designed to calculate the local EVPI values for the nodes of the tree and achieves near linear speed-up.

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  1. Ekblom, J.; Blomvall, J.: Importance sampling in stochastic optimization: an application to intertemporal portfolio choice (2020)
  2. Mitra, Sovan; Ji, Tong: Optimisation of stochastic programming by hidden Markov modelling based scenario generation (2010)
  3. Heikkinen, T.; Pietola, K.: Investment and the dynamic cost of income uncertainty: the case of diminishing expectations in agriculture (2009)
  4. Herzog, Florian; Dondi, Gabriel; Keel, Simon; Schumann, Lorenz M.; Geering, Hans P.: Solving ALM problems via sequential stochastic programming (2009)
  5. Kuhn, D.: Convergent bounds for stochastic programs with expected value constraints (2009)
  6. Pennanen, Teemu: Epi-convergent discretizations of multistage stochastic programs via integration quadratures (2009)
  7. Wu, F.; Li, H. Z.; Chu, L. K.; Sculli, D.; Gao, K.: An approach to the valuation and decision of ERP investment projects based on real options (2009)
  8. Kuhn, Daniel: Aggregation and discretization in multistage stochastic programming (2008)
  9. Kaut, Michal; Wallace, Stein W.: Evaluation of scenario generation methods for stochastic programming (2007)
  10. Dempster, M. A. H.: Sequential importance sampling algorithms for dynamic stochastic programming (2006)
  11. Pennanen, Teemu; Koivu, Matti: Epi-convergent discretizations of stochastic programs via integration quadratures (2005)
  12. Dominguez-Ballesteros, B.; Mitra, G.; Lucas, C.; Koutsoukis, N.-S.: Modelling and solving environments for mathematical programming (MP): a status review and new directions (2002)
  13. Frauendorfer, Karl; Haarbr├╝cker, Gido: Test problems in stochastic multistage programming (2000)
  14. MirHassani, S. A.; Lucas, C.; Mitra, G.; Messina, E.; Poojari, C. A.: Computational solution of capacity planning models under uncertainty (2000)
  15. Zanghirati, G.; Cocco, F.; Paruolo, G.; Taddei, F.: A Cray T3E implementation of a parallel stochastic dynamic assets and liabilities management model (2000)
  16. Dempster, M. A. H.; Thompson, R. T.: EVPI-based importance sampling solution procedures for multistage stochastic linear programmes on parallel MIMD architectures (1999)
  17. Dentcheva, Darinka; R├Âmisch, Werner: Optimal power generation under uncertainty via stochastic programming (1998)
  18. Messina, E.; Mitra, G.: Modelling and analysis of multistage stochastic programming problems: A software environment (1997)