Abstract
Large-scale linear programming problems whose coefficients are random variables will be considered in this paper. Stability of the optimum solutions of these problems as the number of variables increases was shown in terms of the laws of large numbers by Kuhn and Quandt (on the weak law) and by Prékopa (on the strong law). The same conclusions were proved for a broader class of problems under weaker assumptions in the previous paper. Here, we prove the laws of large numbers under even weaker assumptions for independent and identically distributed (i.i.d.) random variables by applying an estimate by Brillinger and Petrov. We give a simple example which shows that the assumption r ≥ 2 associated with the moment condition given in Proposition 3.1 cannot be replaced by the weaker assumption 0 ＜ r ＜ 2.
