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A data-driven newsvendor problem: from data to decision. (English) Zbl 1430.90021
Summary: Retailers that offer perishable items are required to make ordering decisions for hundreds of products on a daily basis. This task is non-trivial because the risk of ordering too much or too little is associated with overstocking costs and unsatisfied customers. The well-known newsvendor model captures the essence of this trade-off. Traditionally, this newsvendor problem is solved based on a demand distribution assumption. However, in reality, the true demand distribution is hardly ever known to the decision maker. Instead, large datasets are available that enable the use of empirical distributions. In this paper, we investigate how to exploit this data for making better decisions. We identify three levels on which data can generate value, and we assess their potential. To this end, we present data-driven solution methods based on machine learning and quantile regression that do not require the assumption of a specific demand distribution. We provide an empirical evaluation of these methods with point-of-sales data for a large German bakery chain. We find that machine learning approaches substantially outperform traditional methods if the dataset is large enough. We also find that the benefit of improved forecasting dominates other potential benefits of data-driven solution methods.
MSC:
90B05 Inventory, storage, reservoirs
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[1] Ban, G.-Y.; Rudin, C., The big data newsvendor: practical insights from machine learning, Operations Research, 67, 1, 90-108, (2018)
[2] Barrow, D.; Crone, S.; Kourentzes, N., An evaluation of neural network ensembles and model selection for time series prediction, Proceedings of the 2010 international joint conference on neural networks (IJCNN), (2010)
[3] Barrow, D.; Kourentzes, N., The impact of special days in call arrivals forecasting: a neural network approach to modelling special days, European Journal of Operational Research, 264, 3, 967-977, (2018) · Zbl 1378.62097
[4] Ben-Tal, A.; Ghaoui, L. E.; Nemirovski, A., Robust optimization, (2009), Princeton University Press: Princeton University Press New Jersey
[5] Bergstra, J.; Bengio, Y., Random search for hyper-parameter optimization, Journal of Machine Learning Research, 13, 281-305, (2012) · Zbl 1283.68282
[6] Bertsimas, D.; Kallus, N., From predictive to prescriptive analytics, Management Science, forthcoming, (2018)
[7] Bertsimas, D.; Thiele, A., A robust optimization approach to inventory theory, Operations Research, 54, 1, 150-168, (2006) · Zbl 1167.90314
[8] Beutel, A. L.; Minner, S., Safety stock planning under causal demand forecasting, International Journal of Production Economics, 140, 2, 637-645, (2012)
[9] Breiman, L., Random forests, Machine Learning, 45, 1, 5-32, (2001) · Zbl 1007.68152
[10] Cannon, A. J., Quantile regression neural networks: Implementation in R and application to precipitation downscaling, Computers and Geosciences, 37, 9, 1277-1284, (2011)
[11] Carbonneau, R.; Laframboise, K.; Vahidov, R., Application of machine learning techniques for supply chain demand forecasting, European Journal of Operational Research, 184, 3, 1140-1154, (2008) · Zbl 1141.90441
[12] Conrad, S. A., Sales data and the estimation of demand, Operational Research Quarterly, 27, 1, 123-127, (1976) · Zbl 0318.90020
[13] Crone, S. F.; Hibon, M.; Nikolopoulos, K., Advances in forecasting with neural networks? Empirical evidence from the NN3 competition on time series prediction, International Journal of Forecasting, 27, 3, 635-660, (2011)
[14] Crone, S. F.; Kourentzes, N., Forecasting seasonal time series with multilayer perceptrons-an empirical evaluation of input vector specifications for deterministic seasonality, Proceedings of the 2009 international conference on data mining, 232-238, (2009)
[15] Friedman, J. H., Greedy function approximation: a gradient boosting machine, The Annals of Statistics, 29, 5, 1189-1232, (2001) · Zbl 1043.62034
[16] Gallego, G.; Moon, I., The distribution free newsboy problem: review and extensions, The Journal of the Operational Research Society, 44, 8, 825-834, (1993) · Zbl 0781.90029
[17] Godfrey, G. A.; Powell, W. B., An adaptive, distribution-free algorithm for the newsvendor problem with censored demands, with applications to inventory and distribution, Management Science, 47, 8, 1101-1112, (2001) · Zbl 1232.90053
[18] Hornik, K., Approximation capabilities of multilayer feedforward networks, Neural Networks, 4, 2, 251-257, (1991)
[19] Huber, J.; Gossmann, A.; Stuckenschmidt, H., Cluster-based hierarchical demand forecasting for perishable goods, Expert Systems with Applications, 76, 140-151, (2017)
[20] Hyndman, R. J.; Khandakar, Y., Automatic time series forecasting: the forecast package for R, Journal of Statistical Software, 26, 3, 1-22, (2008)
[21] Hyndman, R. J.; Koehler, A. B., Another look at measures of forecast accuracy, International journal of forecasting, 22, 4, 679-688, (2006)
[22] Hyndman, R. J.; Koehler, A. B.; Ord, J. K.; Snyder, R. D., Forecasting with exponential smoothing: The state space approach, (2008), Springer: Springer New York · Zbl 1211.62165
[23] Hyndman, R. J.; Koehler, A. B.; Snyder, R. D.; Grose, S., A state space framework for automatic forecasting using exponential smoothing methods, International Journal of Forecasting, 18, 3, 439-454, (2002)
[24] Ke, G.; Meng, Q.; Finley, T.; Wang, T.; Chen, W.; Ma, W.; Ye, Q.; Liu, T.-Y., LightGBM: A highly efficient gradient boosting decision tree, (Guyon, I.; Luxburg, U. V.; Bengio, S.; Wallach, H.; Fergus, R.; Vishwanathan, S.; Garnett, R., Advances in Neural Information Processing Systems 30, (2017), Curran Associates, Inc), 3146-3154
[25] Kingma, D. P.; Ba, J. L., Adam: A method for stochastic optimization, Proceedings of the international conference on learning representations 2015, (2015)
[26] Kleywegt, A. J.; Shapiro, A.; Homem-de Mello, T., The sample average approximation method for stochastic discrete optimization, SIAM Journal on Optimization, 12, 2, 479-502, (2002) · Zbl 0991.90090
[27] Koenker, R., Quantile regression, (2005), Cambridge University Press: Cambridge University Press New York · Zbl 1111.62037
[28] Kourentzes, N.; Barrow, D. K.; Crone, S. F., Neural network ensemble operators for time series forecasting, Expert Systems with Applications, 41, 9, 4235-4244, (2014)
[29] Lau, H.-S.; Lau, A. H.L., Estimating the demand distributions of single-period items having frequent stockouts, European Journal of Operational Research, 92, 2, 254-265, (1996) · Zbl 0912.90108
[30] Levi, R.; Perakis, G.; Uichanco, J., The data-driven newsvendor problem: new bounds and insights, Operations Research, 63, 6, 1294-1306, (2015) · Zbl 1333.90010
[31] Levi, R.; Roundy, R. O.; Shmoys, D. B., Provably near-optimal sampling-based policies for stochastic inventory control models, Mathematics of Operations Research, 32, 4, 821-839, (2007) · Zbl 1341.90005
[32] Oroojlooyjadid, A.; Snyder, L. V.; Takác, M., Applying deep learning to the newsvendor problem, CoRR, (2016)
[33] Perakis, G.; Roels, G., Regret in the newsvendor model with partial information, Operations Research, 56, 1, 188-203, (2008) · Zbl 1167.90350
[34] Prak, D.; Teunter, R., A general method for addressing forecasting uncertainty in inventory models, International Journal of Forecasting, In Press, (2018)
[35] Prak, D.; Teunter, R.; Syntetos, A., On the calculation of safety stocks when demand is forecasted, European Journal of Operational Research, 256, 2, 454-461, (2017) · Zbl 1394.90038
[36] Qin, Y.; Wang, R.; Vakharia, A. J.; Chen, Y.; Seref, M. M.H., The newsvendor problem: Review and directions for future research, European Journal of Operational Research, 213, 2, 361-374, (2011) · Zbl 1215.90005
[37] R Core Team, R: A language and environment for statistical computing, (2017), R Foundation for Statistical Computing: R Foundation for Statistical Computing Vienna, Austria
[38] Sachs, A. L.; Minner, S., The data-driven newsvendor with censored demand observations, International Journal of Production Economics, 149, 28-36, (2014)
[39] Scarf, H. E., A min-max solution of an inventory problem, (Arrow, K. J.; Karlin, S.; Scarf, H. E., Studies in the mathematical theory of inventory and production, (1958), Stanford University Press: Stanford University Press Stanford), 201-209
[40] Shapiro, A., Monte carlo sampling methods, (Ruszczynski, A.; Shapiro, A., Handbooks in operations research and management science, 10, (2003), Elsevier Science B.V: Elsevier Science B.V Boston, USA), 353-425
[41] Silver, E. A.; Pyke, D. F.; Thomas, D. J., Inventory and production management in supply chains, (2017), Taylor and Francis: Taylor and Francis New York
[42] Takeuchi, I.; Le, Q. V.; Sears, T. D.; Smola, A. J., Nonparametric quantile estimation, Journal of Machine Learning Research, 7, 1231-1264, (2006) · Zbl 1222.68316
[43] Taylor, J. W., A quantile regression approach to estimating the distribution of multiperiod returns, The Journal of Forecasting, 19, 299-311, (2000)
[44] Taylor, J. W., Forecasting daily supermarket sales using exponentially weighted quantile regression, European Journal of Operational Research, 178, 1, 154-167, (2007) · Zbl 1102.62103
[45] Thomassey, S.; Fiordaliso, A., A hybrid sales forecasting system based on clustering and decision trees, Decision Support Systems, 42, 1, 408-421, (2006)
[46] Trapero, J. R.; Cardós, M.; Kourentzes, N., Empirical safety stock estimation based on kernel and GARCH models, Omega, In Press, 1-13, (2018)
[47] Van Woensel, T.; Van Donselaar, K.; Broekmeulen, R.; Fransoo, J., Consumer responses to shelf out-of-stocks of perishable products, International Journal of Physical Distribution & Logistics Management, 37, 9, 704-718, (2007)
[48] Zhang, G.; Patuwo, B. E.; Hu, M. Y., Forecasting with artificial neural networks: the state of the art, International Journal of Forecasting, 14, 1, 35-62, (1998)
[49] Zhang, Y.; Gao, J., Assessing the performance of deep learning algorithms for newsvendor problem, Proceedings of the ICONIP 2017. Proceedings of the ICONIP 2017, LNCS, 10634, 912-921, (2017)
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