The Sample Average Approximation Method for Stochastic Discrete Optimization

In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and consequently the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates and stopping rules of this procedure and present a numerical example of the stochastic knapsack problem. Key words. Stochastic programming, discrete optimization, Monte Carlo sampling, Law of Large Numbers, Large Deviations theory, sample average approximation, stopping rules, stochastic knapsack problem AMS subject classifications. 90C10, 90C15

• Type: Journal
• Year: 2002
• Where: SIAMJO
• Authors: Anton J. Kleywegt, Alexander Shapiro, Tito Homem-de-Mello
• Keywords: Monte Carlo, Sample Average, SIAMJO 2002, Stochastic Knapsack Problem