A data-driven newsvendor problem: From data to decision

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.

[1]  Herbert E. Scarf,et al.  A Min-Max Solution of an Inventory Problem , 1957 .

[2]  David B. Shmoys,et al.  Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models , 2007, Math. Oper. Res..

[3]  Jc Jan Fransoo,et al.  Consumer responses to shelf out‐of‐stocks of perishable products , 2007 .

[4]  Dennis Prak,et al.  A general method for addressing forecasting uncertainty in inventory models , 2019, International Journal of Forecasting.

[5]  Dimitris Bertsimas,et al.  A Robust Optimization Approach to Inventory Theory , 2006, Oper. Res..

[6]  Nikolaos Kourentzes,et al.  An evaluation of neural network ensembles and model selection for time series prediction , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[7]  Stefan Minner,et al.  The data-driven newsvendor with censored demand observations , 2014 .

[8]  Dennis Prak,et al.  On the calculation of safety stocks when demand is forecasted , 2017, Eur. J. Oper. Res..

[9]  Georgia Perakis,et al.  Regret in the Newsvendor Model with Partial Information , 2008, Oper. Res..

[10]  S. A. Conrad,et al.  Sales Data and the Estimation of Demand , 1976 .

[11]  Cynthia Rudin,et al.  The Big Data Newsvendor: Practical Insights from Machine Learning Analysis , 2013 .

[12]  Rob J Hyndman,et al.  Forecasting with Exponential Smoothing: The State Space Approach , 2008 .

[13]  James W. Taylor,et al.  Forecasting daily supermarket sales using exponentially weighted quantile regression , 2007, Eur. J. Oper. Res..

[14]  Yoshua Bengio,et al.  Random Search for Hyper-Parameter Optimization , 2012, J. Mach. Learn. Res..

[15]  Warrren B Powell,et al.  An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution , 2001 .

[16]  Sébastien Thomassey,et al.  A hybrid sales forecasting system based on clustering and decision trees , 2006, Decis. Support Syst..

[17]  Heiner Stuckenschmidt,et al.  Cluster-based hierarchical demand forecasting for perishable goods , 2017, Expert Syst. Appl..

[18]  Junbin Gao,et al.  Assessing the Performance of Deep Learning Algorithms for Newsvendor Problem , 2017, ICONIP.

[19]  A. Shapiro Monte Carlo Sampling Methods , 2003 .

[20]  Nikolaos Kourentzes,et al.  Neural network ensemble operators for time series forecasting , 2014, Expert Syst. Appl..

[21]  Rob J Hyndman,et al.  Another look at measures of forecast accuracy , 2006 .

[22]  Rustam M. Vahidov,et al.  Application of machine learning techniques for supply chain demand forecasting , 2008, Eur. J. Oper. Res..

[23]  J. Friedman Greedy function approximation: A gradient boosting machine. , 2001 .

[24]  Sven F. Crone,et al.  Advances in forecasting with neural networks? Empirical evidence from the NN3 competition on time series prediction , 2011 .

[25]  Nikolaos Kourentzes,et al.  The impact of special days in call arrivals forecasting: A neural network approach to modelling special days , 2018, Eur. J. Oper. Res..

[26]  Alexander J. Smola,et al.  Nonparametric Quantile Estimation , 2006, J. Mach. Learn. Res..

[27]  Nikolaos Kourentzes,et al.  Forecasting Seasonal Time Series with Multilayer Perceptrons - An Empirical Evaluation of Input Vector Specifications for Deterministic Seasonality , 2009, DMIN.

[28]  Alex J. Cannon Quantile regression neural networks: Implementation in R and application to precipitation downscaling , 2011, Comput. Geosci..

[29]  Tie-Yan Liu,et al.  LightGBM: A Highly Efficient Gradient Boosting Decision Tree , 2017, NIPS.

[30]  Lawrence V. Snyder,et al.  Applying deep learning to the newsvendor problem , 2016, IISE Trans..

[31]  James W. Taylor A Quantile Regression Approach to Estimating the Distribution of Multiperiod Returns , 1999 .

[32]  Amy Hing-Ling Lau,et al.  Estimating the demand distributions of single-period items having frequent stockouts , 1996 .

[33]  Alexander Shapiro,et al.  The Sample Average Approximation Method for Stochastic Discrete Optimization , 2002, SIAM J. Optim..

[34]  Yuwen Chen,et al.  The newsvendor problem: Review and directions for future research , 2011, Eur. J. Oper. Res..

[35]  Stefan Minner,et al.  Safety Stock Planning Under Causal Demand Forecasting , 2012 .

[36]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[37]  Michael Y. Hu,et al.  Forecasting with artificial neural networks: The state of the art , 1997 .

[38]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[39]  G. Gallego,et al.  The Distribution Free Newsboy Problem: Review and Extensions , 1993 .

[40]  James W. Taylor A Quantile Regression Neural Network Approach to Estimating the Conditional Density of Multiperiod Returns , 2000 .

[41]  Rob J Hyndman,et al.  A state space framework for automatic forecasting using exponential smoothing methods , 2002 .

[42]  Georgia Perakis,et al.  The Data-Driven Newsvendor Problem: New Bounds and Insights , 2015, Oper. Res..

[43]  Dimitris Bertsimas,et al.  From Predictive to Prescriptive Analytics , 2014, Manag. Sci..

[44]  J. R. Trapero,et al.  Empirical safety stock estimation based on kernel and GARCH models , 2019, Omega.

[45]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[46]  David F. Pyke,et al.  Inventory and Production Management in Supply Chains , 2016 .

[47]  Rob J Hyndman,et al.  Automatic Time Series Forecasting: The forecast Package for R , 2008 .

[48]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.