Randomly generated polytopes are used frequently to test and compare algorithms for a variety of mathematical programming problems. These polytopes are constructed by generating linear inequality constraints with coefficients drawn independently from a distribution such as the uniform or the normal. It is noted that this class of 'random' polytopes has a special property: the angles between the hyperplanes, though dependent on the specific distribution used, tend to be equal when the dimension of the space increases. Obviously this structure of 'random' polytopes may bias test results.

--ZusammenfassungThe Asymptotic Behaviour of a Distributive Sorting Method. In the distributive sorting method of Dobosiewicz, both the interval between the minimum and the median of the numbers to be sorted and the interval between the median and the maximum are partitioned into n/2 subintervals of equal length; the procedure is then applied recursively on each subinterval containing more than three numbers. We refine and extend previous analyses of this method, e.g., by establishing its asymptotic linear behaviour under various probabilistic assumptions. AMS Subject Classifications

results for MP users in Section 3, results for LP models in Section 4, results for MP software in Section 5 and a summary and main conclusions in Section 6. Abstract.Results of an exhaustive survey of mathematical programming in the Netherlands held in 1982 are presented and, where applicable, compared to a survey held in 1976. It appears that the growth rate has levelled off, that about half of the largest one hundred industrial firms in the Netherlands now apply MP and that the users are quite satisfied with LP programs except for input, output and documentation.