Dimensional Analysis in Operations Research

Abstract

Summary Dimensional Analysis is a general method of determining the form of solutions to physical problems. It is illustrated by an example from physics and descriptions of applications to some OR problems. The Ehrhardt power approximation for computing (s; S) inventory policies is examined from this point of view and found to be a wed. Dimensional Analysis (DA) is a technique that has been used by physicists and engineers for many years to obtain preliminary solutions to physical problems. Assuming that the phe- nomenon can be described by a dimensionally correct equation among a set of variables, DA quickly determines a general form of the solution form constraints put on it by their dimensions. DA is most useful where the derivation of an analytical solution is dicult but the variables that take part in the problem are understood or can be postulated. DA will not provide a complete solution, nor does it substitute for a knowledge of the working of the phenomenon involved. Newton, in proposing the principle of similitude in his Principia, recognised three primary distinct attributes, length, inertia (mass), and time from which other measures such as speed, force, and acceleration are derived. Fourier, in his work in the theory of heat, postulated them as \fundamental units, and suggested that every physical quantity has \dimensions derived from powers of these units. He introduced the idea of a \dimensional formula and showed that equations should have \dimensional homogeneity. From this requirement follows the constraints that DA uses to obtain the general form of a solution. Using the same method Lord Rayleigh later developed a range of solutions to physical problems such as the oscillation of liquid drops under surface tension. In the late 19th Century many of the great classical physicists used the

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