Abstract
In this paper, the question of interest is estimating true demand of a product at a given store location and time period in the retail environment based on a single noisy and potentially censored observation. To address this question, we introduce a %non-parametric framework to make inference from multiple time series. Somewhat surprisingly, we establish that the algorithm introduced for the purpose of "matrix completion" can be used to solve the relevant inference problem. Specifically, using the Universal Singular Value Thresholding (USVT) algorithm [7], we show that our estimator is consistent: the average mean squared error of the estimated average demand with respect to the true average demand goes to 0 as the number of store locations and time intervals increase to $\infty$. We establish naturally appealing properties of the resulting estimator both analytically as well as through a sequence of instructive simulations. Using a real dataset in retail (Walmart), we argue for the practical relevance of our approach.
- 2014. (2014). https://www.kaggle.com/c/walmart-recruiting-store-sales-forecastingGoogle Scholar
- Oren Anava, Elad Hazan, and Assaf Zeevi. 2015. Online Time Series Prediction with Missing Data. In Proceedings of the 32nd International Conference on Machine Learning (ICML-15), David Blei and Francis Bach (Eds.). JMLR Workshop and Conference Proceedings, 2191--2199. http://jmlr.org/proceedings/papers/v37/anava15.pdf Google Scholar
Digital Library
- Ravi Anupindi, Maqbool Dada, and Sachin Gupta. 1998. Estimation of Consumer Demand with Stock-Out Based Substitution: An Application to Vending Machine Products. Marketing Science 17, 4 (1998), 406--423. Google Scholar
Digital Library
- Katy S. Azoury. 1985. Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution. Management Science 31, 9 (2017/01/07 1985), 1150--1160.Google Scholar
- Gah-Yi Ban. 2015. The data-driven (s, S) policy: The data-driven (s, S) policy: The data driven (s, S) policy: why you can have confidence in censored demand data. Available at SSRN: https://ssrn.com/abstract=2654014 (2015).Google Scholar
- Apostolos N. Burnetas and Craig E. Smith. 2000. Adaptive Ordering and Pricing for Perishable Products. Operations Research 48, 3 (2017/01/07 2000), 436--443. Google Scholar
Digital Library
- Sourav Chatterjee. 2015. Matrix estimation by Universal Singular Value Thresholding. Ann. Statist. 43 (2015), 177--214.Google Scholar
Cross Ref
- Li Chen and Adam J. Mersereau. 2015. Analytics for Operational Visibility in the Retail Store: The Cases of Censored Demand and Inventory Record Inaccuracy. Springer US, Boston, MA, 79--112.Google Scholar
- Zhe Chen and Andrzej Cichocki. 2005. Nonnegative matrix factorization with temporal smoothness and/or spatial decorrelation constraints. Laboratory for Advanced Brain Signal Processing, RIKEN, Tech. Rep 68 (2005).Google Scholar
- Christopher T. Conlon and Julie Holland Mortimer. 2013. Demand Estimation under Incomplete Product Availability. American Economic Journal: Microeconomics 5, 4 (November 2013), 1--30.Google Scholar
Cross Ref
- S. A. Conrad. 1976. Sales Data and the Estimation of Demand. Operational Research Quarterly (1970--1977) 27, 1 (1976), 123--127. http://www.jstor.org/stable/3009217Google Scholar
- Gregory A. Godfrey and Warren B. Powell. 2001. An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution. Management Science 47, 8 (2017/01/07 2001), 1101--1112. Google Scholar
Digital Library
- Woonghee Tim Huh and Paat Rusmevichientong. 2009. A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand. Mathematics of Operations Research 34, 1 (2017/01/07 2009), 103--123. Google Scholar
Digital Library
- Sumit Kunnumkal and Huseyin Topaloglu. 2008. Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control Problems. Operations Research 56, 3 (2017/01/07 2008), 646--664. Google Scholar
Digital Library
- Retsef Levi, Robin O. Roundy, and David B. Shmoys. 2007. Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models. Mathematics of Operations Research 32, 4 (2017/01/07 2007), 821--839. Google Scholar
Digital Library
- L. Massoulié M. Lelarge and J. Xu. 2014. Edge label inference in generalized stochastic block model: from spectral theory to impossibility results. Conference on Learning Theory (COLT) (2014).Google Scholar
- Rahul Mazumder, Trevor Hastie, and Robert Tibshirani. 2010. Spectral regularization algorithms for learning large incomplete matrices. Journal of machine learning research 11, Aug (2010), 2287--2322. Google Scholar
Digital Library
- Andrés Musalem, Marcelo Olivares, Eric T. Bradlow, Christian Terwiesch, and Daniel Corsten. 2010. Structural Estimation of the Effect of Out-of-Stocks. Management Science 56, 7 (2017/01/07 2010), 1180--1197. Google Scholar
Digital Library
- Steven Nahmias. 1994. Demand estimation in lost sales inventory systems. Naval Research Logistics (NRL) 41, 6 (1994), 739--757.Google Scholar
Cross Ref
- Warren Powell, Andrzej Ruszczyński, and Huseyin Topaloglu. 2004. Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems. Mathematics of Operations Research 29, 4 (2017/01/07 2004), 814--836. Google Scholar
Digital Library
- Swati Rallapalli, Lili Qiu, Yin Zhang, and Yi-Chao Chen. 2010. Exploiting Temporal Stability and Low-rank Structure for Localization in Mobile Networks. In Proceedings of the Sixteenth Annual International Conference on Mobile Computing and Networking (MobiCom '10). ACM, New York, NY, USA, 161--172. Google Scholar
Digital Library
- Matthew Roughan, Yin Zhang,Walter Willinger, and Lili Qiu. 2012. Spatio-temporal Compressive Sensing and Internet Traffic Matrices. IEEE/ACM Trans. Netw. 20, 3 (June 2012), 662--676. Google Scholar
Digital Library
- Ruslan Salakhutdinov and Andriy Mnih. 2007. Probabilistic matrix factorization. In NIPS, Vol. 20. 1--8. Google Scholar
Digital Library
- Ruslan Salakhutdinov and Andriy Mnih. 2008. Bayesian probabilistic matrix factorization using Markov chain Monte Carlo. In Proceedings of the 25th international conference on Machine learning. ACM, 880--887. Google Scholar
Digital Library
- Catalina Stefanescu. 2009. Multivariate Customer Demand: Modeling and Estimation from Censored Sales. Available at SSRN: https://ssrn.com/abstract=1334353 (2009).Google Scholar
- Gustavo Vulcano, Garrett van Ryzin, and Richard Ratliff. 2012. Estimating Primary Demand for Substitutable Products from Sales Transaction Data. Operations Research 60, 2 (2012), 313--334. Google Scholar
Digital Library
- William E. Wecker. 1978. Predicting Demand from Sales Data in the Presence of Stockouts. Management Science 24, 10 (1978), 1043--1054. http://www.jstor.org/stable/2630558Google Scholar
Digital Library
- Liang Xiong, Xi Chen, Tzu-Kuo Huang, Jeff Schneider, and Jaime G. Carbonell. 2010. Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization. 211--222.Google Scholar
- Hsiang-Fu Yu, Nikhil Rao, and Inderjit S. Dhillon. 2015. Temporal Regularized Matrix Factorization. CoRR abs/1509.08333 (2015).Google Scholar
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Censored Demand Estimation in Retail
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Censored Demand Estimation in Retail
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