Demand fulfillment probability in a multi-item inventory system with limited historical data

ABSTRACT

In a budget-constrained multi-item inventory system with independent demands, we consider the case of unknown demand parameters that are estimated from limited amounts of historical demand data. In this situation, the probability of satisfying all item demands, as a measure of demand fulfillment, is a function of the finite-sample estimates of the unknown demand parameters; thus, the demand fulfillment probability is a random variable. First, we characterize the properties of an asymptotical approximation to the mean and variance of this random variable due to the use of limited data for demand parameter estimation. Second, we use the characterization of the variance of the demand fulfillment probability for quantifying the impact of demand parameter uncertainty on demand fulfillment via numerical experiments. Third, we propose an inventory optimization problem that minimizes the variance of the demand fulfillment probability due to demand parameter uncertainty subject to a budget constraint on the total inventory investment. Our numerical experiments demonstrate that, despite the availability of limited amounts of historical demand data, it is possible to manage inventory with significantly reduced variance in the demand fulfillment probability.

KEYWORDS:

• Demand fulfillment probability
• demand parameter uncertainty
• limited demand data

Acknowledgements

The authors thank the Department Editor, the Associate Editor, and the anonymous referees for their feedback that significantly improved the presentation in the article. A preliminary version of this article was published in the Proceedings of the 2016 Winter Simulation Conference.

Additional information

Notes on contributors

Canan G. Corlu

Canan G. Corlu is an Assistant Professor of administrative sciences in Metropolitan College at Boston University. She holds a Ph.D. in operations management from the Tepper School of Business at Carnegie Mellon University. Her research interests are in the areas of design and analysis of stochastic simulations with applications to operations management.

Bahar Biller

Bahar Biller is a Senior Research Scientist in the Software Sciences and Analytics organization of the General Electric Global Research Center. Her research lies in the area of quantitative risk management and advances the design and analysis of large-scale business system simulations to aid decision making under uncertainty.

Sridhar Tayur

Sridhar Tayor is the Ford Distinguished Research Chair and Professor of Operations Management at Carnegie Mellon University's Tepper School of Business. He received his Ph.D. in operations research and industrial engineering from Cornell University and his undergraduate degree in mechanical engineering from the Indian Institute of Technology at Madras. He is an INFORMS Fellow and Distinguished Fellow of MSOM and has been elected to the National Academy of Engineering. His research interests are in inventory modeling, supply chain management, and healthcare operations. He was founder (and CEO) of SmartOps Corporation, an enterprise supply chain software company, that was acquired by SAP.