A simulation-based approach to two-stage stochastic programming with recourse

Alexander Shapiro, Tito Homem-de-Mello

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202 Scopus citations


In this paper we consider stochastic programming problems where the objective function is given as an expected value function. We discuss Monte Carlo simulation based approaches to a numerical solution of such problems. In particular, we discuss in detail and present numerical results for two-stage stochastic programming with recourse where the random data have a continuous (multivariate normal) distribution. We think that the novelty of the numerical approach developed in this paper is twofold. First, various variance reduction techniques are applied in order to enhance the rate of convergence. Successful application of those techniques is what makes the whole approach numerically feasible. Second, a statistical inference is developed and applied to estimation of the error, validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm.

Original languageEnglish
Pages (from-to)301-325
Number of pages25
JournalMathematical Programming
Issue number3
StatePublished - 1 May 1998
Externally publishedYes


  • Confidence intervals
  • Hypotheses testing
  • Likelihood ratios
  • Monte Carlo simulation
  • Nonlinear programming
  • Two-stage stochastic programming with recourse
  • Validation analysis
  • Variance reduction techniques


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