The Genesis of “Optimal Inventory Policy”

I have been asked to write on the steps leading to the paper by Theodore E. Harris, Jacob Marschak, and myself (1951), “Optimal Inventory Policy.” The account will be brief, for two reasons: (1) The origins are rather simple; (2) the event happened a long while ago, the details are not as clear in my memory as might be desired, and my records for the period appear to be nonexistent (I am not too sure that much of the relevant history ever got into my file, because most arrangements were made orally). Let me give a brief account of my whereabouts and affiliations during this period because they are relevant to the story. In fact, my involvement in inventory research could be described as a confluence of chance events. I had started my graduate study at Columbia University in 1940. My main interest was mathematical statistics; one of the few teachers was Harold Hotelling. However, there was then no Department of Statistics anywhere in the United States; Hotelling’s official position at Columbia was Professor of Economics. He had, of course, written several very famous papers on theoretical economics; in addition, Columbia did have the view that statistics was going to be very important in economic analysis. I first enrolled in the Department of Mathematics, but Hotelling made it clear to me that he had no influence in that department with regard to getting scholarship aid, and so I switched to the Department of Economics. Under Hotelling’s influence, the compulsory exposure to economics, and the evolution of my own interests, I became more involved in economic theory. I also had the pleasure and honor of taking courses with Abraham Wald, who had been hired by Hotelling with funds from outside the university. My studies were interrupted by World War II. I volunteered for military service and spent a little over three years on duty as a weather officer. While in the military, I received one of the first documents outlining the idea of sequential statistical analysis, as developed by Wald, and was excited by it both for practical reasons and for the intellectual horizons it opened up. I returned to graduate study in January 1946 and started work on a dissertation. None of my ideas seemed to me sufficiently good. In the meantime, I had acquired a reputation as a very good student, and I received an offer from Jacob Marschak, Director of the Cowles Commission for Research in Economics, then located at the University of Chicago though not formally a part of it. Marschak also had the position of Professor of Economics at Chicago. After stalling for a while, hoping to finish a thesis, I joined the Commission in April 1947. I met, almost immediately, a graduate student, Selma Schweitzer. Within a few months, we were married and are still enjoying our happiness. My wife had been a junior researcher at the United States Department of Agriculture; she worked there for the distinguished mathematical statistician Meyer A. Girshick, who had received his Ph.D. under Hotelling. His work overlapped the econometric research program of the Cowles Commission; he visited the Commission and Selma. He was leaving the Department of Agriculture to go to a project that developed into the RAND Corporation. After we met, he invited me to spend the summer of 1948 at RAND. He had also invited David Blackwell, and the three of us started trying to understand systematically sequential analysis from a decision-theoretic viewpoint. We wrote a paper in which was clearly displayed the recursive nature of the optimization problem (Arrow et al. 1949). That is, each stage involved a choice of actions and a random event, which together changed the prospects for the future. However, the problem at each stage was described in terms of a few parameters, and only these were altered by the outcome of the previous stage. Sequential analysis was a special case of what Richard Bellman a few years later termed, “dynamic programming” (Bellman 1957); indeed, he has credited our paper with suggesting the general formulation to him. (That summer was very fruitful in my research. As part of RAND’s efforts to understand the general concept of “military worth,” i.e., “national interest,” I was led to pose the problem of social choice and to demonstrate the impossibility of its general resolution. I had finally found a suitable dissertation topic.)