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Optimal Policies and Approximations for a Bayesian Linear Regression Inventory Model

Department of Decision Sciences, College of Business, San Francisco State University, San Francisco, California 94132
Department of Decision Sciences, College of Business, San Francisco State University, San Francisco, California 94132
kazoury{at}sfsu.edu
jmiyaoka{at}sfsu.edu

In this paper, we consider a periodic review inventory problem where demand in each period is modeled by linear regression. We use a Bayesian formulation to update the regression parameters as new information becomes available. We find that a state-dependent base-stock policy is optimal and we give structural results. One interesting finding is that our structural results are not analogous to classical results in Bayesian inventory research. This departure from classical results is due to the role that the independent variables play in the Bayesian regression formulation. Because of the computational complexity of the optimal policy, we propose a combination of two heuristics that simplifies the Bayesian inventory problem. Through analytical and numerical evaluation, we find that the heuristics provide near-optimal results.

Key Words: Bayesian regression; inventory production; stochastic models; approximations heuristics
History: Received: July 27, 2006; accepted: November 24, 2008.