Inventory Optimization using a Renewal Model for Sales

Abstract

Any optimization requires a realistic and simple model to predict future sales. The problem presenter had suggested that sales might arrive according to a Poisson distribution. We suggest that the company look at renewal theory for models of future sales orders. They have some very distinct advantages. They are powerful and easy to use, in fact the Poisson distribution is a special case. Renewal models are flexible enough to incorporate a variety of characteristics, such as clustering or regularity, upward or downward drift, and mean reversion. Also, some arguments can be made to justify the renewal models based on financial intuition. A realistic (albeit naive) problem is set up which has an analytic solution and other solution methods are discussed.