×

Newsvendor problems: an integrated method for estimation and optimisation. (English) Zbl 1495.90008

Summary: Newsvendor problems (NVP) form a classical and important family of stochastic optimisation problems. In this paper, we consider a data-driven method proposed recently by Ban and Rudin. We first examine it from a statistical viewpoint, and establish a connection with quantile regression. We then extend the approach to nonlinear NVP. Finally, we give extensive experimental results, on both simulated and real data. The results indicate that the approach performs as well as conventional ones when applied to linear NVP, but performs better when applied to nonlinear NVP. There is also evidence that the approach is more robust with respect to model misspecification.

MSC:

90B05 Inventory, storage, reservoirs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Al Thobaity, A.; Alshammari, F., Nurses on the frontline against the COVID-19 pandemic: An integrative review, Dubai Medical Journal, 3, 87-92 (2020)
[2] Arrow, K. J.; Harris, T.; Marschak, J., Optimal inventory policy, Econometrica, 19, 250-272 (1951) · Zbl 0045.23205
[3] Ban, G.-Y.; Rudin, C., The big data newsvendor: Practical insights from machine learning, Operations Research, 67, 90-108 (2019) · Zbl 1443.90093
[4] Bassok, Y.; Anupindi, R.; Akella, R., Single-period multiproduct inventory models with substitution, Operations Research, 47, 632-642 (1999) · Zbl 0979.90005
[5] Bertsimas, D.; Kallus, N., From predictive to prescriptive analytics, Management Science, 66, 1025-1044 (2020)
[6] Bertsimas, D.; Thiele, A., A Data-driven Approach to Newsvendor Problems, Technical Report (2005), Operations Research Center, MIT
[7] Beutel, A.-L.; Minner, S., Safety stock planning under causal demand forecasting, International Journal of Production Economics, 140, 637-645 (2012)
[8] Bruzda, J., Quantile forecasting in operational planning and inventory management—an initial empirical verification, Dynamic Econometric Models, 16, 5-20 (2016)
[9] Chen, S.-C.; Lai, Y.-H.; Tsay, S. L., Nursing perspectives on the impacts of COVID-19, Journal of Nursing Research, 28, 1682-3141 (2020)
[10] Choi, T. M., Handbook of newsvendor problems (2012), Springer: Springer New York
[11] Congzheng, L. (2020). Forecasting-and-newsvendor. https://github.com/Joshua960411/Forecasting-and-Newsvendor.
[12] Coronini-Cronberg, S.; Maile, E. J.; Majeed, A., Health inequalities: The hidden cost of COVID-19 in NHS hospital trusts?, Journal of the Royal Society of Medicine, 113, 179-184 (2020)
[13] Eeckhoudt, L.; Gollier, C.; Schlesinger, H., The risk-averse (and prudent) newsboy, Management Science, 41, 786-794 (1995) · Zbl 0843.90036
[14] Elmachtoub, A. N., & Grigas, P. Smart “predict, then optimize”. arXiv preprint arXiv:1710.08005
[15] Farrar, D. E.; Glauber, R. R., Multicollinearity in regression analysis: The problem revisited, Review of Economic and Statistics, 92-107 (1967)
[16] article 103637
[17] Hadley, G.; Whitin, T. M., Analysis of inventory systems (1963), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0133.42901
[18] Halman, N.; Orlin, J. B.; Simchi-Levi, D., Approximating the nonlinear newsvendor and single-item stochastic lot-sizing problems when data is given by an oracle, Operations Research, 60, 429-446 (2012) · Zbl 1248.90007
[19] He, B.; Dexter, F.; Macario, A.; Zenios, S., The timing of staffing decisions in hospital operating rooms: Incorporating workload heterogeneity into the newsvendor problem, Manufacturing and Service Operations Management, 14, 1, 99-114 (2012)
[20] Huber, J.; Müller, S.; Fleischmann, M.; Stuckenschmidt, H., A data-driven newsvendor problem: From data to decision, European Journal of Operational Research, 278, 904-915 (2019) · Zbl 1430.90021
[21] Hyndman, R., Athanasopoulos, G., Bergmeir, C., Caceres, G., Chhay, L., & O’Hara-Wild, M. et al. (2020). forecast: Forecasting functions for time series and linear models. R package version 8.13, https://pkg.robjhyndman.com/forecast/.
[22] Karlin, S.; Carr, C. R., Prices and optimal inventory policy, (Arrow, K. J.; Scarf, H., Studies in applied probability and management science (1962), Stanford University Press), 159-172 · Zbl 0142.17104
[23] Karmarkar, U. S., A robust forecasting technique for inventory and leadtime management, Journal of Operations Management, 12, 45-54 (1994)
[24] Kashefi, M. A., Effect of salvage market on strategic technology choice and capacity investment decision of firm under demand uncertainty, Facility Design eJournal, 17, 140-155 (2016)
[25] Khouja, M., The newsboy problem under progressive multiple discounts, European Journal of Operational Research, 84, 458-466 (1995) · Zbl 0909.90134
[26] Kim, G.; Wu, K.; Huang, E., Optimal inventory control in a multi-period newsvendor problem with non-stationary demand, Advanced Engineering Informatics, 29, 139-145 (2015)
[27] Kocherginsky, M.; He, X.; Mu, Y., Practical confidence intervals for regression quantiles, Journal of Computational and Graphical Statistics, 14, 41-55 (2005)
[28] Koenker, R., Quantile regression (2005), Cambridge University Press · Zbl 1111.62037
[29] Koenker, R.; Hallock, K. F., Quantile regression, Journal of Economic Perspectives, 15, 143-156 (2001)
[30] Koenker, R.; Machado, J. A.F., Goodness of fit and related inference processes for quantile regression, Journal of the American Statistical Association, 94, 1296-1310 (1999) · Zbl 0998.62041
[31] Korpela, J.; Tuominen, M., Inventory forecasting with a multiple criteria decision tool, International Journal of Production Economics, 45, 159-168 (1996)
[32] Kyparisis, G. J.; Koulamas, C., The price-setting newsvendor with nonlinear salvage revenue and shortage cost, Operations Research Letters, 46, 64-68 (2018) · Zbl 1525.90030
[33] Lau, A.; Lau, H., The newsstand problem: A capacitated multi-product single period inventory problem, Operations Research, 94, 29-42 (1996) · Zbl 0929.90003
[34] Liberopoulos, G.; Tsikis, I.; Delikouras, S., Backorder penalty cost coefficient “b”: What could it be?, International Journal of Production Economics, 123, 166-178 (2010)
[35] Liu, D. C.; Nocedal, J., On the limited memory BFGS method for large scale optimization, Mathematical Programming, 45, 503-528 (1989) · Zbl 0696.90048
[36] Liu, Q.; Luo, D.; Haase, J. E.; Guo, Q.; Wang, X. Q.; Liu, S., The experiences of health-care providers during the COVID-19 crisis in china: a qualitative study, The Lancet Global Health, 8, e790-e798 (2020)
[37] Liyanage, L. H.; Shanthikumar, J. G., A practical inventory control policy using operational statistics, Operations Research Letters, 33, 341-348 (2005) · Zbl 1090.90003
[38] Mills, E. S., Uncertainty and price theory, Quarterly Journal of Economics, 73, 116-130 (1959)
[39] Moon, I.; Silver, E. A., The multi-item newsvendor problem with a budget constraint and fixed ordering costs, Journal of the Operational Research Society, 51, 602-608 (2000) · Zbl 1055.90505
[40] Morse, P. M.; Kimball, G. E., Methods of operations research (1951), MIT Press · Zbl 0044.14204
[41] NHS England (2020). Statistics on COVID-19 hospital activity. Available at www.england.nhs.uk/statistics/statistical-work-areas/covid-19-hospital-activity.
[42] Pal, B.; Sana, S. S.; Chaudhuri, K., A distribution-free newsvendor problem with nonlinear holding cost, International Journal of Systems Science, 46, 1269-1277 (2015) · Zbl 1318.90009
[43] Pantumsinchai, P.; Knowles, T. W., Standard container size discounts and the single-period inventory problem, Decision Sciences, 22, 612-619 (1991)
[44] Petruzzi, N. C.; Dada, M., Pricing and the newsvendor problem: A review with extensions, Operations Research, 47, 183-194 (1999) · Zbl 1005.90546
[45] Porteus, E. L., Foundations of stochastic inventory theory (2002), Stanford University Press
[46] https://www.R-project.org/
[47] Scarf, H., Studies in the mathematical theory of inventory and production (1958), Stanford University Press · Zbl 0079.36003
[48] Silver, E. A.; Pyke, D. F.; Peterson, R., Inventory management and production planning and scheduling (1998), Wiley: Wiley New York
[49] Solis, F. J.; Wets, R., Minimization by random search techniques, Mathematics of Operations Research, 6, 19-30 (1981) · Zbl 0502.90070
[50] Syntetos, A. A.; Babai, Z.; Boylan, J. E.; Kolassa, S.; Nikolopoulos, K., Supply chain forecasting: Theory, practice, their gap and the future, European Journal of Operational Research, 252, 1-26 (2016) · Zbl 1346.90181
[51] Tashman, L. J., Out-of-sample tests of forecasting accuracy: An analysis and review, International Journal of Forecasting, 16, 4, 437-450 (2000)
[52] Zipkin, P. H., Foundations of inventory management (2000), McGraw-Hill · Zbl 1370.90005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.