Title

Using empirical Bayes for inventory problems with Poisson demand

Abstract

The fundamental problem for inventory management is to adjust inventory levels to achieve the right trade-off between the costs of holding inventory and the costs of a stockout. This requires knowledge of the distribution of demand, which is obtained through looking at the history of demand for this product. We are interested in how much inventory to hold for each of a large number of different items when each item has demand which occurs as a Poisson process, and where the rate parameter for each item is estimated on the basis of past demand. This problem matches that faced by a book retailer.  We will use an empirical Bayes approach that does not require a prior distribution for the demand rates to be specified in advance, but instead makes use of the entire set of observations to make deductions about the prior. We show the effectiveness of this approach, and by looking at some asymptotic cases we demonstrate the importance of making a full estimate of probabilities rather than just the rate parameter. There are a number of computational choices that need to be made when applying these ideas in practice and we make some recommendations. In practical inventory applications two questions naturally arise: should the data be grouped together according to characteristics of the items; and what should be done when there are trends over time.

Bio

Eddie Anderson is Professor of Analytics and Operations Management at Imperial College Business School. He is also Emeritus Professor at the University of Sydney Business School. Eddie has an honours degree in Mathematics from Cambridge, and a PhD in Operations Management, also from the University of Cambridge. During his career he has held Faculty positions at Cambridge, the University of New South Wales, and the University of Sydney.

Eddie has research interests in supply chain management; risk management; game theory and optimization. Much of his research involves the application of these ideas in energy markets. He has been Area Editor for Energy at the journal ‘Operations Research.