Some studies on distribution parameters for facilities design problems

Abstract

The assignment of n facilities to n locations, with the objective of minimizing the total cost of the design, is known as the facilities design problem. For a problem of size 𝓃, there are 𝓃! feasible solutions, which can be represented by a frequency distribution of total costs. Recent statistical analyses have indicated that these distributions can be adequately described as gamma, and for many practical purposes the log normal or normal distributions give good approximations. The absolute mean of all the 𝓃!assignments can be easily calculated.

For the assessment of the efficiencies of alternative layout designs, the knowledge of the standard deviation for total cost distributions associated with the facilities design problem is very useful to the facilities design engineer. A number of methods have been developed to compute the approximate value of the standard deviation from the basic data of flow and distance. This paper highlights the problem that such approximation may lead to a high level of errors. A computerized method for finding the exact value of the standard deviation has been presented.