TY - JOUR

T1 - A simulation-based approach to two-stage stochastic programming with recourse

AU - Shapiro, Alexander

AU - Homem-de-Mello, Tito

N1 - Funding Information:
* Corresponding author. E-mail: ashapiro@isye.gatech.edu. ’ Supported by CNPq (Conselho National de Desenvolvimento Brazil. through a Doctoral Fellowship under grant 200595/93-8.

PY - 1998/5/1

Y1 - 1998/5/1

N2 - 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.

AB - 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.

KW - Confidence intervals

KW - Hypotheses testing

KW - Likelihood ratios

KW - Monte Carlo simulation

KW - Nonlinear programming

KW - Two-stage stochastic programming with recourse

KW - Validation analysis

KW - Variance reduction techniques

UR - http://www.scopus.com/inward/record.url?scp=0001762682&partnerID=8YFLogxK

U2 - 10.1007/BF01580086

DO - 10.1007/BF01580086

M3 - Article

AN - SCOPUS:0001762682

VL - 81

SP - 301

EP - 325

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 3

ER -