The power of dimensional analysis in production systems design

Abstract

Dimensional Analysis (DA) is a well-known methodology in physics, chemistry and other traditional engineering areas. In its simplest form, DA is used to check the meaningfulness of a set of equations (dimensional homogeneity). In the last century, the dimensional theory has been profoundly investigated: its highest achievement is the Buckingham theorem (or pi-theorem), which states that any equation modelling a physical problem can be rearranged in terms of dimensionless ratios, thus saving variables to be handled, and especially enriching the inner physical knowledge of the studied phenomenon. In this paper we investigate how DA can be applied to Operations Management (OM) topics and which benefits it can bring to researchers in this area. A literature review is performed to clarify the main operative issues regarding DA application (assumptions and limitations); then existing applications of DA to OM are explored, pointing out that few researchers have tried to apply this methodology in the OM research field. Stemming from this analysis, we applied the pi-theorem to the design of a Flexible Manufacturing System. A complex problem, requiring 13 dimensional quantities to be expressed, is first studied via simulation; then DA is applied, reducing the number of variables to 9 dimensionless ratios. The reduced problem has a suitable size to be analytically explored and a regression model is formulated which, compared with the simulation study, offers the same precision in analysing the FMS behaviour, being more compact and powerful. This application shows the potential of DA in OM research, and will hopefully draw the attention of researches to this powerful, but unfamiliar and therefore neglected, methodology.