The Big Data Newsvendor: Practical Insights from Machine Learning

References

• Akaike H (1974) A new look at the statistical model identification. IEEE Trans. Automat. Control 19(6):716–723.Crossref, Google Scholar
• Arrow KJ, KarlinS, Scarf H (1958) Studies in the Mathematical Theory of Inventory and Production, Vol. 1 (Stanford University Press, Stanford, CA).Google Scholar
• Azoury KS (1985) Bayes solution to dynamic inventory models under unknown demand distribution. Management Sci. 31(9):1150–1160.Link, Google Scholar
• Belloni A, Chernozhukov V (2011) ℓ1-penalized quantile regression in high-dimensional sparse models. Ann. Statist. 39(1):82–130.Crossref, Google Scholar
• Bousquet O, Elisseeff A (2002) Stability and generalization. J. Mach. Learn. Res. 2(Mar):499–526.Google Scholar
• Burnetas AN, Smith CE (2000) Adaptive ordering and pricing for perishable products. Oper. Res. 48(3):436–443.Link, Google Scholar
• Chaudhuri P (1991) Nonparametric estimates of regression quantiles and their local Bahadur representation. Ann. Statist. 19(2):760–777.Crossref, Google Scholar
• Chen X, Sim M, Sun P (2007) A robust optimization perspective on stochastic programming. Oper. Res. 55(6):1058–1071.Link, Google Scholar
• Chernozhukov V, Hansen C (2008) Instrumental variable quantile regression: A robust inference approach. J. Econom. 142(1):379–398.Crossref, Google Scholar
• Chernozhukov V, Fernández-Val I, Galichon A (2010) Quantile and probability curves without crossing. Econometrica 78(3):1093–1125.Crossref, Google Scholar
• Csörgö M (1983) Quantile Processes with Statistical Applications (SIAM, Philadelphia).Crossref, Google Scholar
• Devroye L, Wagner T (1979a) Distribution-free inequalities for the deleted and holdout error estimates. IEEE Trans. Inform. Theory 25(2):202–207.Crossref, Google Scholar
• Devroye L, Wagner T (1979b) Distribution-free performance bounds for potential function rules. IEEE Trans. Inform. Theory 25(5):601–604.Crossref, Google Scholar
• Donnelly L, Mulhern M (2012) NHS pays £1,600 a day for nurses as agency use soars. The Telegraph (July 14), http://www.telegraph.co.uk/news/9400079/NHS-_pays-_1600-_a-_day-_for-_nurses-_as-_agency-_use-_soars.html.Google Scholar
• Durrett R (2010) Probability: Theory and Examples, 4th edition (Cambridge University Press, New York).Crossref, Google Scholar
• Feldman RM (1978) A continuous review (s, s) inventory system in a random environment. J. Appl. Probab. 15(3):654–659.Crossref, Google Scholar
• Friedman J, Hastie T, Tibshirani R (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed., (Springer Science+Business Media, New York).Google Scholar
• Gallego G, Moon I (1993) The distribution free newsboy problem: Review and extensions. J. Oper. Res. Soc. 44(8):825–834.Crossref, Google Scholar
• Gallego G, Özer Ö (2001) Integrating replenishment decisions with advance demand information. Management Sci. 47(10):1344–1360.Link, Google Scholar
• Godfrey GA, Powell WB (2001) An adaptive, distribution-free algorithm for the newsvendor problem with censored demands, with applications to inventory and distribution. Management Sci. 47(8):1101–1112.Link, Google Scholar
• Grant M, Boyd S. CVX: Matlab software for disciplined convex programming, version 2.0 beta. Accessed September 2013, http://cvxr.com/cvx.Google Scholar
• Grant M, Boyd S (2008) Graph implementations for nonsmooth convex programs. Blondel V, Boyd S, Kimura H, eds. Recent Advances in Learning and Control, Lecture Notes in Control and Information Sciences (Springer, London), 95–110.Crossref, Google Scholar
• Graves SC, Meal HC, Dasu S, Qui Y (1986) Two-stage production planning in a dynamic environment. Multi-Stage Production Planning and Inventory Control (Springer, Berlin, Heidelberg), 9–43.Crossref, Google Scholar
• Green LV, Savin S, Savva N (2013) Nursevendor problem: Personnel staffing in the presence of endogenous absenteeism. Management Sci. 59(10):2237–2256.Link, Google Scholar
• Hannah L, Powell W, Blei DM (2010) Nonparametric density estimation for stochastic optimization with an observable state variable. Lafferty JD, Williams CKI, Shawe-Taylor J, Zemel RS, Culotta A, eds. Advances in Neural Information Processing Systems (NIPS 2010) (Curran Associates, Red Hook, NJ), 820–828.Google Scholar
• Heath DC, Jackson PL (1994) Modeling the evolution of demand forecasts ith application to safety stock analysis in production/distribution systems. IIE Trans. 26(3):17–30.Crossref, Google Scholar
• Hofmann T, Schölkopf B, Smola AJ (2008) Kernel methods in machine learning. Ann. Statist. 36(3):1171–1220.Crossref, Google Scholar
• HuhWT, Rusmevichientong P (2009) A nonparametric asymptotic analysis of inventory planning with censored demand. Math. Oper. Res. 34(1):103–123.Link, Google Scholar
• Iida T, Zipkin PH (2006) Approximate solutions of a dynamic forecast-inventory model. Manufacturing Service Oper. Management 8(4):407–425.Link, Google Scholar
• Koenker R (2005) Quantile Regression (Cambridge University Press, New York).Crossref, Google Scholar
• Kunnumkal S, Topaloglu H (2008) Using stochastic approximation methods to compute optimal base-stock levels in inventory control problems. Oper. Res. 56(3):646–664.Link, Google Scholar
• Levi R, Perakis G, Uichanco J (2015) The data-driven newsvendor problem: New bounds and insights. Oper. Res. 63(6):1294–1306.Link, Google Scholar
• Levi R, Roundy RO, Shmoys DB (2007) Provably near-optimal sampling-based policies for stochastic inventory control models. Math. Oper. Res. 32(4):821–839.Link, Google Scholar
• Liyanage LH, Shanthikumar JG (2005) A practical inventory control policy using operational statistics. Oper. Res. Lett. 33(4):341–348.Crossref, Google Scholar
• Lovejoy WS (1990) Myopic policies for some inventory models with uncertain demand distributions. Management Sci. 36(6):724–738.Link, Google Scholar
• Lovejoy WS (1992) Stopped myopic policies in some inventory models with generalized demand processes. Management Sci. 38(5):688–707.Link, Google Scholar
• Lu X, Song J-S, Regan A (2006) Inventory planning with forecast updates: Approximate solutions and cost error bounds. Oper. Res. 54(6):1079–1097.Link, Google Scholar
• Manton JH, Amblard P-O (2015) A primer on reproducing kernel Hilbert spaces. Found. Trends Signal Process. 8(1–2):1–126.Crossref, Google Scholar
• Nadaraya EA (1964) On estimating regression. Theory Probab. Appl. 9(1):141–142.Crossref, Google Scholar
• Parzen E (1979) Nonparametric statistical data modeling. J. Amer. Statist. Assoc. 74(365):105–121.Crossref, Google Scholar
• Perakis G, Roels G (2008) Regret in the newsvendor model with partial information. Oper. Res. 56(1):188–203.Link, Google Scholar
• Powell W, Ruszczyński A, Topaloglu H (2004) Learning algorithms for separable approximations of discrete stochastic optimization problems. Math. Oper. Res. 29(4):814–836.Link, Google Scholar
• Rockafellar RT (1997) Convex Analysis (Princeton University Press, Princeton, NJ).Google Scholar
• Rogers WH, Wagner TJ (1978) A finite sample distribution-free performance bound for local discrimination rules. Ann. Statist. 6(3):506–514.Crossref, Google Scholar
• Scarf H (1959a) Bayes solutions of the statistical inventory problem. Ann. Math. Statist. 30(2):490–508.Crossref, Google Scholar
• Scarf H (1959b) The optimality of (s,S) policies in the dynamic inventory problem. Mathematical Methods in the Social Science, Arrow KJ, Karlin S, Suppes P, eds. (Stanford University Press, Stanford, CA).Google Scholar
• Scarf H, Arrow KJ, Karlin S (1958) A min-max solution of an inventory problem. Studies in the Mathematical Theory of Inventory and Production, Vol. 10 (Stanford University Press, Stanford CA) 201–209.Google Scholar
• Schwarz G (1978) Estimating the dimension of a model. Ann. Statist. 6(2):461–464.Crossref, Google Scholar
• See C-T, Sim M (2010) Robust approximation to multiperiod inventory management. Oper. Res. 58(3):583–594.Link, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński AP (2009) Lectures on Stochastic Programming: Modeling and Theory, Vol. 9 (SIAM, Philadelphia).Crossref, Google Scholar
• Song J-S, Zipkin P (1993) Inventory control in a fluctuating demand environment. Oper. Res. 41(2):351–370.Link, Google Scholar
• Takeuchi I, Le QV, Sears TD, Smola AJ (2006) Nonparametric quantile estimation. J. Mach. Learn. Res. 7:(July): 1231–1264.Google Scholar
• Vapnik VN (1998) Statistical Learning Theory (Wiley, New York).Google Scholar
• Watson GS (1964) Smooth regression analysis. Sankhyā: Indian J. Statist. Ser. A. 26(4):359–372.Google Scholar