A Demand Estimation Algorithm for Inventory Management Systems Using Censored Data


  • A. Nikseresht Computer Science and Engineering Department, Shiraz University, Shiraz, Iran
  • K. Ziarati Computer Science and Engineering Department, Shiraz University, Shiraz, Iran
Volume: 7 | Issue: 6 | Pages: 2215-2221 | December 2017 | https://doi.org/10.48084/etasr.1517


During the selling time horizon of a product category, a number of products may become unavailable sooner than others and the customers may substitute their desired product with another or leave the system without purchase. So, the recorded sales do not show the actual demand of each product. In this paper, a nonparametric algorithm to estimate true demand using censored data is proposed. A customer choice model is employed to model the demand and then a nonlinear least square method is used to estimate the demand model parameters without assuming any distribution on customer’s arrival. A simple heuristic approach is applied to make the objective function convex, making the algorithm perform much faster and guaranteeing the convergence. Simulated dataset of different sizes are used to evaluate the proposed method. The results show a 23% improvement in root mean square error between estimated and simulated true demand, in contrast to alternate methods usually used in practice.


demand, estimation, inventory, revenue, management, control, unconstraining, uncensoring


Download data is not yet available.


N. Agrawal, S. A. Smith, “Estimating negative binomial demand for retail inventory management with unobservable lost sales”, Naval Research Logistics, Vol. 43, No. 6, pp. 839–861, 1996 DOI: https://doi.org/10.1002/(SICI)1520-6750(199609)43:6<839::AID-NAV4>3.0.CO;2-5

C. Eltze, S. Goergens, M. Loury, “Grocery store operations: Which improvements matter most?”, Akzente, Vol. 1, No. 1, pp. 74–81, 2013

C. Stefanescu,“Multivariate Demand: Modeling and Estimation from Censored Sales”, Available at: http://ssrn.com/abstract=1334353, 2009 DOI: https://doi.org/10.2139/ssrn.1334353

B. Tan, S. Karabati, “Retail inventory management with stock-out based dynamic demand substitution”, International Journal of Production Economics, Vol. 145, No. 1, pp. 78–87, 2013 DOI: https://doi.org/10.1016/j.ijpe.2012.10.002

J. Aastrup, H. Kotzab, “Analyzing out-of-stock in independent grocery stores: an empirical study”, International Journal of Retail & Distribution Management, Vol. 37, No. 9, pp. 765–789, 2009 DOI: https://doi.org/10.1108/09590550910975817

G. Xin, P. R. Messinger, J. Li, “Influence of soldout products on consumer choice”, Journal of Retailing, Vol. 85, No. 3, pp. 274–287, 2009 DOI: https://doi.org/10.1016/j.jretai.2009.05.009

S. Karmarkar, D. Goutam, B. Tathagata, “Revenue impacts of demand unconstraining and accounting for dependency”, Journal of Revenue and Pricing Management, Vol. 10, No. 4, pp. 367–381, 2011 DOI: https://doi.org/10.1057/rpm.2009.54

R. R. Wickham, Evaluation of forecasting techniques for short-term demand of air transportation, MSc Thesis, Massachusetts Institute Technology, 1995

K. T. Talluri, G. J. van Ryzin, I. Z. Karaesmen, G. J. Vulcano, “Revenue management: Models and methods”, 2008 Winter Simulation Conference, pp. 145–156, 2008 DOI: https://doi.org/10.1109/WSC.2008.4736064

L. R. Weatherford, “A review of optimization modeling assumptions in revenue management situations”, AGIFORS Reservations and Yield Management Study Group, 1997

W. L. Cooper, T. Homem-de-Mello, A. J. Kleywegt, “Models of the Spiral-Down Effect in Revenue Management”, Operations Research, Vol. 54, No. 5, pp. 968–987, 2006 DOI: https://doi.org/10.1287/opre.1060.0304

R. Saleh, “Estimating lost demand with imperfect availability indicators”, AGIFORS Reservations and Yield Management Study Group, 1997

R. J. A. Little, D. B. Rubin, Statistical Analysis with Missing Data, John Wiley & Sons, 2002 DOI: https://doi.org/10.1002/9781119013563

A. Nikseresht, K. Ziarati, “Review on the Newest Revenue Management Demand Forecasting Methods”, International Conference on Management, Economics and Industrial Engineering, Vol. 1, No. 1, 2015

P. Guo, B. Xiao, J. Li, “Unconstraining methods in revenue management systems: Research overview and prospects”, Advances in Operations Research, Vol. 2012, Article ID 270910, 2012 DOI: https://doi.org/10.1155/2012/270910

A. Nikseresht, K. Ziarati, “Estimating True Demand in Airline’s Revenue Management Systems using Observed Sales”, International Journal of Advanced Computer Science and Applications, Vol. 8, No. 7, pp. 361-369, 2017 DOI: https://doi.org/10.14569/IJACSA.2017.080748

K. T. Talluri, G. J. Van Ryzin, The Theory and Practice of Revenue Management, Springer Science & Business Media, 2005 DOI: https://doi.org/10.1007/b139000

A. Haensel, G. Koole, “Estimating unconstrained demand rate functions using customer choice sets”, Journal of Revenue and Pricing Management, Vol. 10, No. 5, pp. 438–454, 2011 DOI: https://doi.org/10.1057/rpm.2010.1

A. Haensel, G. Koole, J. Erdman, “Estimating unconstrained customer choice set demand: A case study on airline reservation data”, Journal of Choice Modelling, Vol. 4, No. 3, pp. 75–87, 2011 DOI: https://doi.org/10.1016/S1755-5345(13)70043-5

G. Vulcano, G. van Ryzin, R. Ratliff, “Estimating Primary Demand for Substitutable Products from Sales Transaction Data”, Operations Research, Vol. 60, No. 2, pp. 313–334, 2012 DOI: https://doi.org/10.1287/opre.1110.1012

C. C. Queenan, M. Ferguson, J. Higbie, R. Kapoor, “A Comparison of Unconstraining Methods to Improve Revenue Management Systems”, Production and Operations Management, Vol. 16, No. 404, pp. 729–746, 2007 DOI: https://doi.org/10.1111/j.1937-5956.2007.tb00292.x

V. F. Farias, S. Jagabathula, D. Shah, “A Nonparametric Approach to Modeling Choice with Limited Data”, Management Science, Vol. 59, No. 2, pp. 305-322, 2009 DOI: https://doi.org/10.1287/mnsc.1120.1610

A. G. Kok, M. L. Fisher, “Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application”, Operations Research, Vol. 55, No. 6, pp. 1001–1021, 2007 DOI: https://doi.org/10.1287/opre.1070.0409

A. Hubner, H. Kuhn, S. Kuhn, “An efficient algorithm for capacitated assortment planning with stochastic demand and substitution”, European Journal of Operational Research, Vol. 250, No. 2, pp. 505–520, 2016 DOI: https://doi.org/10.1016/j.ejor.2015.11.007

A. Jain, N. Rudi, T. Wang, “Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is (Almost) All You Need,” Operations Research, Vol. 63, No. 1, pp. 134–150, 2015 DOI: https://doi.org/10.1287/opre.2014.1326

L. G. Cooper, M. Nakanishi, Market-Share Analysis: Evaluating Competitive Marketing Effectiveness, Kluwer Academic Publishers, 1988 DOI: https://doi.org/10.1007/978-94-009-2681-3

S.-E. Andersson, “Passenger choice analysis for seat capacity control: A pilot project in Scandinavian Airlines”, International Transactions in Operational Research, Vol. 5, No. 6, pp. 471–486, 1998 DOI: https://doi.org/10.1111/j.1475-3995.1998.tb00130.x

S. Ja, S. Rao, B. V. Chandler, “Passenger recapture estimation in airline RM”, AGIFORS 41st Annual Symposium, 2001

T. S. Gruca, D. Sudharshan, “Equilibrium Characteristics of Multinomial Logit Market Share Models”, Journal of Marketing Research, Vol. 28, No. 4, pp. 480–482, 1991 DOI: https://doi.org/10.1177/002224379102800410

R. H. Zeni, Improved Forecast Accuracy in Airline Revenue Management by Unconstraining Demand Estimates from Censored Data, Universal-Publishers, 2001

Tarek Abdallah, G. Vulcano, “Demand Estimation under the Multinomial Logit Model from Sales Transaction”, working paper, Available at: https://www.researchgate.net/profile/Gustavo_Vulcano, 2016


How to Cite

A. Nikseresht and K. Ziarati, “A Demand Estimation Algorithm for Inventory Management Systems Using Censored Data”, Eng. Technol. Appl. Sci. Res., vol. 7, no. 6, pp. 2215–2221, Dec. 2017.


Abstract Views: 2739
PDF Downloads: 554

Metrics Information