Mean and standard deviation for the facilities design problem

Abstract

An important problem in facilities design to find an assignment of n facilities to n locations so that total materials handling cost is minimized. For problems of moderate size, suboptimal solutions must be accepted since optimal algorithms are computationally infeasible. If the mean and standard deviation of the layout cost distribution is known, then statistical methods may be used to measure and compare the efficiencies of various suboptimal solutions as well as to monitor the efficiency of the same assignment under changing production environments. In this paper a new, simple algorithm to calculate the exact value of the standard deviation of the layout cost distribution is presented (the mean is easy). This algorithm has a computational efficiency of O ( n 2 ) arithmetic operations for a problem of size n × n , an improvement over previous methods which are either inexact or have a computational efficiency of O ( n 4 ). Results of tests verifying the accuracy and claimed efficiency of this algorithm, as implemented on a microcomputer, are also presented (about 0.85 second for a 30 × 30 problem).