Proceedings of the 2012 Winter Simulation Conference C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher, eds. A SIMULATION-BASED APPROACH TO CAPTURING AUTOCORRELATED DEMAND PARAMETER UNCERTAINTY IN INVENTORY MANAGEMENT Alp Akcay Bahar Biller Sridhar Tayur Tepper School of Business Carnegie Mellon University Pittsburgh, PA, 15213, USA ABSTRACT We consider a repeated newsvendor setting where the parameters of the demand distribution are unknown, and we study the problem of setting inventory targets using only a limited amount of historical demand data. We assume that the demand process is autocorrelated and represented by an Autoregressive-To-Anything time series. We represent the marginal demand distribution with the highly flexible Johnson translation system that captures a wide variety of distributional shapes. Using a simulation-based sampling algorithm, we quantify the expected cost due to parameter uncertainty as a function of the length of the historical demand data, the critical fractile, the parameters of the marginal demand distribution, and the autocorrelation of the demand process. We determine the improved inventory-target estimate accounting for this parameter uncertainty via sample-path optimization. 1 INTRODUCTION The common practice in production and inventory management is to estimate the unknown parameters of the demand distribution using a finite (and sometimes, very limited) amount of real-world data, and then to replace the unknown parameters in the inventory model with these estimates. This practice, however, ignores the uncertainty around the estimated demand parameters (i.e., parameter uncertainty), and accounts only for stochastic uncertainty (i.e., the uncertainty due to stochastic demand before the stocking decision). Consequently, the inventory manager often obtains inaccurate estimates that do not necessarily minimize the expected cost, which arises from the mismatch between demand and inventory. Hayes (1969), Liyanage and Shanthikumar (2005), and Akcay, Biller, and Tayur (2011a) discuss the shortcomings of ignoring demand parameter uncertainty (i.e., plugging the estimates of the demand parameters into the critical fractile solution formula) in a newsvendor setting when the demand process is independent over time. For the first time we study this problem considering an autocorrelated demand process. While parameter uncertainty is a considerable concern in effective management of inventories, it is indeed a general problem to be addressed in manufacturing and service settings when a finite amount of data is used to estimate the unknown parameters of a model. For example, Chick (2001) shows that accounting for parameter uncertainty in the simulation of an M/M/1 queueing system improves the estimates of the mean queue length and the expected percent availability of the server. Similarly, Zouaoui and Wilson (2004) demonstrate that the parameter uncertainty amounts up to 80% of the total uncertainty around the mean waiting time estimate of an M/G/1 queuing system. Our paper contributes to this literature by demonstrating the importance of parameter uncertainty in an inventory control setting and by minimizing the total cost function including not only the expected cost due to stochastic demand uncertainty but also the expected cost arising from the parameter uncertainty. However, this approach can be challenging as it is often not possible to express the total cost function in closed form unless the demand process is independent over 978-1-4673-4780-8/12/$31.00 ©2012 IEEE 3213 978-1-4673-4782-2/12/$31.00 ©2012 IEEE