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