Abstract
We investigate the impact of the sample size in the non-stationary newsvendor problem when the underlying demand distribution is not known, and performance is measured by the decision-maker’s average regret. The approach we propose is entirely data-driven, in the sense that we do not estimate the probability distribution of the demand and instead rely exclusively on historical data. We propose an iterative algorithm to determine the number of past observations that should be included in the decision-making process, provide insights into the optimal sample size and perform extensive computational experiments.
Research partially supported by the National Science Foundation, grant DMI-0540143.
Research partially supported by the National Science Foundation, grant DMI-0540143. Corresponding author.
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References
Bertsimas, Dimitris, and Aurélie Thiele. (2004). A data-driven approach to newsvendor problems. Technical report, Massachusetts Institute of Technology, Cambridge, MA.
Brumelle, Shelby, and Jeffrey McGill. (1993). Airline seat allocation with multiple nested fare classes. Operations Research, 41 127–137.
Ferguson, Thomas. (1996). A Course in Large Sample Theory, Chapman & Hall/CRC, Boca Raton, FL.
Gallego, Guillermo, and Ilkyeong Moon. (1993). The distribution-free newsboy problem: Review and extensions. Journal of the Operational Research Society, 44 825–834.
Godfrey, Gregory, and Warren Powell. (2001). An adaptive, distribution-free algorithm for the newsvendor problem with censored demands, with applications to inventory and distribution. Management Science, 47 1101–1112.
Levi, Retsef, Robin Roundy, and David Shmoys. (2006). Provably near-optimal sampling-based policies for stochastic inventory control models. Proceedings of the 38 th annual ACM Symposium on the Theory of Computing (STOC), to appear.
Metan, Gokhan, and Aurélie Thiele. (2006). The data-driven newsvendor problem. Technical report, Lehigh University, Bethlehem, PA.
Porteus, Evan. (2002). Stochastic Inventory Theory, Stanford University Press, Palo Alto, CA.
Robbins, Herbert, and Sutton Monro (1951). A stochastic approximation method. Ann. Math. Statis. 22 400–407.
Scarf, Herbert. (1958). A min-max solution of an inventory problem, in Studies in the mathematical theory of inventory and production, pages 201–209, Stanford University Press, Palo Alto, CA.
van Ryzin, Garrett, and Jeffrey McGill (2000). Revenue management without forecasting or optimization: An adaptive algorithm for determining airline seat protection levels. Management Science, 46 760–775.
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Metan, G., Thiele, A. (2007). An Adaptive Algorithm for the Optimal Sample Size in the Non-Stationary Data-Driven Newsvendor Problem. In: Baker, E.K., Joseph, A., Mehrotra, A., Trick, M.A. (eds) Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies. Operations Research/Computer Science Interfaces Series, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-48793-9_6
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DOI: https://doi.org/10.1007/978-0-387-48793-9_6
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