Using Dimensional Analysis to Teach Production/Operations/Supply Chain Management

Abstract

Scientists and engineers have been using the concept of dimensional homogeneity since it was introduced by Fourier (1822) "...every undetermined magnitude or constant has one dimension proper to itself, and the terms of one and the same equation could not be compared if they had not the same exponent of dimensions." The theory behind "dimensional homogeneity" was formalized by Edgar Buckingham (Buckingham, 1914), and it has become an integral part of the science and engineering curriculum ever since. While many business professors have some background in science and engineering, dimensional homogeneity or dimensional analysis is not a topic which is typically included in the business curriculum. This article examines some dimensional analysis approaches to some conventional operations management topics including capacity management, time value of money, breakeven/crossover analysis, and Economic Order Quantity (EOQ). The basic idea behind dimensional analysis is not "adding apples and oranges." This paper will look at some operations management applications of dimensional analysis and then try to restate some of the theory of dimensional analysis that will allow a broader application of the technique. Operations management applications will be given in a "before and after" format. Comparison of the before and after presentations will hopefully show some advantage to the dimensional analysis approach.