Apolloni, Bruno; Pezzella, Ferdinando Confidence intervals in the solution of stochastic integer linear programming problems. (English) Zbl 0671.90058 Stochastics and optimization, Sel. Pap. ISSO Meet., Gorguano/Italy 1982, Ann. Oper. Res. 1, 67-78 (1984). Summary: [For the entire collection see Zbl 0673.00021.] A method is proposed to estimate confidence intervals for the solution of integer linear programming (ILP) problems where the technological coefficients matrix and the resource vector are made up of random variables whose distribution laws are unknown and only a sample of their values is available. This method, based on the theory of order statistics, only requires knowledge of the solution of the relaxed integer linear programming (RILP) problems which correspond to the sampled random parameter. The confidence intervals obtained in this way have proved to be more accurate than those estimaed by the current methods which use the integer solutions of the sampled ILP problems. Cited in 1 Document MSC: 90C15 Stochastic programming 90C10 Integer programming 62G30 Order statistics; empirical distribution functions 90C05 Linear programming 68Q25 Analysis of algorithms and problem complexity 62G15 Nonparametric tolerance and confidence regions Keywords:probabilistic analysis; confidence intervals; integer linear programming; order statistics; sampled random parameter Citations:Zbl 0673.00021 PDFBibTeX XML