CONFIDENCE REGION METHOD FOR A STOCHASTIC PROGRAMMING PROBLEM
確率計画問題における信頼域によるアプローチ

Hiroshi Morita, Hiroaki Ishii, Toshio Nishida
1987 Journal of the Operations Research Society of Japan  
We propose a minirnax model with a "quadratic" recourse. In stochastic linear programming models, a decision maker has been assumed to know the probability distribution of random variables. Here we consider the case that the parameters of distribution are unknown. We impose the restrictions on the unknown parameters from the view point of a confidence region, and then seek a minimax solution that minimizes the worst case of the parameters. This model reflects the situation minimizing the
more » ... nimizing the maximal possible damage. Especially, the independent normal distribution model is discussed in detail. The analysis for a sufficiently large sample size and a numerical result are given. m The unknown parameter 8 is imposed the restrictions estimated by the confidence region S witn a certain significance level. We consider the worst case of the parameter 8 among S, and then minimize the objective function of Copyright © by ORSJ. Unauthorized reproduction of this article is prohibited. where Uex is ex percentile of a standard normal distribution. Since lu I < 00,
doi:10.15807/jorsj.30.218 fatcat:qjvfg5hrfvf3hegzu4eozod3zy