On general conditions for laws of large numbers in random linear programs

Numerical computations of large-scale linear programming problems often contain instability owing to modelling errors and accumulation of round-off errors. The question discussed here is whether the effect of these errors increases or decreases with the size of the problem. It is shown that the random errors in the original data have diminishing effects on the optimum as the number of variables increases. This result is stated in terms of the law of large numbers.