Economic theory and the world of practice: A celebration of the (S,s) model

Abstract

T he (S, s) model represents in ideal form the interplay between economic theory and the world of application. It was created during a period in which microeconomic theorists and applied mathematicians forged many of the tools that dominate economic analysis to this day, including linear programming, dynamic programming, and game theory. These conceptual advances resulted in large part from the desire to answer important practical questions. One such ques-tion of interest in both business and military circles concerned inventory control. For any stored good in more-or-less constant use, there is a need to keep stock on hand. It was the question of how best to balance the costs of ordering and of run-ning out of stock against the costs of holding excess inventory that inspired Arrow, Harris, and Marschak (1951) to introduce the (S, s) model. 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. We open the paper by providing a general overview of the essential features of the (S, s) model, concentrating on the original inventory theoretic setting. On one level, Arrow, Harris, and Marschak (1951) departed in only minor respects from existing models of inventory control, introducing uncertainty and discount-ing into inventory models with ordering costs. As the follow-up volume of Arrow, Karlin, and Scarf (1958) attests, this basic modeling theme can support a wid