Economic Theory and the World of Practice: A Celebration of the (S,s) Model

It was the question of how best to balance the costs of ordering and of running out of stock against the costs of holding excess inventory that inspired Kenneth Arrow, Theodore Harris, and Jacob Marschak to introduce the ( S, s ) model in 1951. In this celebratory article, we show how this model not only answered important practical questions, but also opened the door to a quite startling range of important and challenging follow-up questions, many of great practical importance and analytic depth. The ( S, s ) model has become one of the touchstone models of economics, opening new vistas of applied economic theory to all who internalize its structure. Today it is universally applied to solve questions faced in inventory control. The core model elements, uncertainty and fixed costs of adjustment, are ubiquitous, which has resulted in its becoming the general purpose economic model of discrete adjustment. The ( S, s ) model has also become a profound source of inspiration for macroeconomists seeking to understand the role that discrete microeconomic adjustments play in macroeconomic fluctuations. Looking forward, we foresee rapid growth in the use of ( S, s ) modeling to aid households making complex and costly financial decisions, such as when and how to terminate a mortgage. In the projected era of "household operations research," new modeling challenges will arise due to enriched feedback from the world of practice.