FALSA-facilities allocation by statistical analysis Part I. Further investigations on the cost distribution associated with the problem of facilities design

Abstract

The problem of facilities design involves the assignment of facilities to available locations so as to minimize the total cost. When N new facilities are to be added to an existing layout, there are N! feasible ways in which the assignment can be completed. Presented in this paper is a simple method to calculate the mean and the standard deviation of the total costs for the N! feasible layouts. The method is also useful for analysing the distribution of the total cost for the general facilities design problem when n' out of N facilities have been assigned to suitable locations and n (i.e. N-n') facilities are left for assignment. These parameters are of importance to the facilities design engineer who is solving the problem by any construction algorithm where the layout is completed by successive addition of facilities to locations. At any stage when the location of the first (n'- 1) facilities have been decided, the possible effect of assigning the n'th. facility to the jth location can be predicted by estimating the mean and variance of the distribution of the total cost associated with the assignment.