The mean and standard deviation of the distribution of group assembly sums

An interesting problem in linear programming is the group assembly problem which is mathematically equivalent to the general transportation problem of economics. Computer programs designed for the determination of exact and approximate optimal group assemblies have been available for some time. This paper presents formulas for the mean and squared standard deviation of the distribution of all possible group assembly sums. Computational techniques are presented and the results are related to those of the analysis of variance of ak-factor problem withn levels of each factor.This research was supported in part by the United States Air Force under Project No. 7713, Task No. 77232, and Contract No. AF 18(600)-1050, monitored by the Crew Research Laboratory of the Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.