The Multi-product Newsboy Problem with Price-Depended Demand and Fast Moving Items

  • Anna Kitaeva
  • Klimentii LivshitsEmail author
  • Ekaterina Ulyanova
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)


The present paper supposes that the newsboy sells multiple products, and in addition to determining optimal order quantities needs to determine the prices of each product. The demand for each product is a compound Poisson process that depends on the demands of other products. We suppose that the price-dependent intensity of the demand is large enough to use the normal approximation to the joint demand distribution. The goal of the retailer’s decision is to maximize his profit. Equations for optimal retail price under optimal order quantity are obtained and approximate solutions are proposed. Also approximate distribution of the selling time of a large order is found.


Newsboy problem Multiple products Fast moving items Selling time distribution 


  1. 1.
    Sharma, S.C.: Operation Research: Inventory Control and Queuing Theory. Series: DPH Mathematics. Discovery Publishing House Pvt. Ltd., New Delhi (2006)Google Scholar
  2. 2.
    Nazarov, A.A.: Asymptotic Analysis of Markovian Systems. Tom. State Univ. Publ. House, Tomsk (1991). (in Russian)Google Scholar
  3. 3.
    Schwarz, M., Daduna, H.: Queueing systems with inventory management with random lead times and with back ordering. Math. Meth. Oper. Res. 64, 383–414 (2006)CrossRefzbMATHGoogle Scholar
  4. 4.
    Krishnamoorthy, A., Lakshmy, B., Manikandan, R.: A survey on inventory models with positive service time. Opsearch 48(2), 153–169 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Manikandan, R., Sajeev, S.: Nair: M/M/1/1 queueing-inventory system with retail of unsatisfied customers. Commun. Appl. Anal. 21(2), 217–236 (2017)Google Scholar
  6. 6.
    Edgeworth, F.: The mathematical theory of banking. J. Roy. Statist. Soc. 51, 113–127 (1888)Google Scholar
  7. 7.
    Khouja, B.: The single period (news-vendor) problem: literature review and suggestions for future research. Omega 27, 537–553 (1999)CrossRefGoogle Scholar
  8. 8.
    Qin, Y., Wang, R., Vakharia, A., Chen, Y., Hanna-Seref, M.: The newsvendor problem: review and directions for future research. Eur. J. Oper. Res. 213, 361–374 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Turken, N., Tan, Y., Vakharia, A.J., Wang, L., et al.: The Multi-Product Newsvendor Problem: Review, Extension, and Directions for Future Research. In: Handbook of Newsvendor Problems: Models, Extensions and Applications, New York, vol. 176, pp. 3–39 (2012)Google Scholar
  10. 10.
    Whitin, T.M.: Inventory control and price theory. Manage. Sci. 2(1), 61–68 (1955)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Petruzzi, N.C., Dada, M.: Pricing and the newsvendor problem: a review with extensions. Oper. Res. 47(2), 183–194 (1999)CrossRefzbMATHGoogle Scholar
  12. 12.
    Yano, C.A., Gilbert, S.M.: Coordinated pricing and production/procurement decisions: a review. In: Eliashberg, J., Chakravarty, A. (eds.) Managing Business Interfaces: Marketing, Engineering, and Manufacturing Perspectives, pp. 63–103. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  13. 13.
    Chen, X., Simchi-Levi, D.: Joint pricing and inventory management. In: Özer, O., Phillips, R. (eds.) The Oxford Handbook of Pricing Management, pp. 784–822. Oxford University Press, London (2012)Google Scholar
  14. 14.
    Nahmias, S.: Demand estimation in lost sales inventory systems. Naval Res. Logist. 41, 739–757 (1994)CrossRefzbMATHGoogle Scholar
  15. 15.
    Kitaeva, A.V., Subbotina, V.I., Stepanova, N.V.: Estimating the compound poisson demand’s parameters for single period problem for large lot size. In: Dolgui, A., Sasiadek, J., Zaremba, M. (eds.) The 15th IFAC Symposium on Information Control in Manufacturing, Ottawa, Canada, 11–13 May 2015, vol. 48(3), pp. 1357–1361. Elsevier, IFAC-PapersOnLine (2015)Google Scholar
  16. 16.
    Kitaeva, A.V., Subbotina, V.I., Zhukovskiy, O.I.: Compound poisson demand inventory models with exponential batch size’s distribution. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) ITMM 2015. CCIS, vol. 564, pp. 240–249. Springer, Cham (2015). doi: 10.1007/978-3-319-25861-4_21 CrossRefGoogle Scholar
  17. 17.
    Kitaeva, A.V., Zhukovskaya, A.O., Zmeev, O.A.: Compound Poisson demand with price-dependent intensity for fast moving items: price optimisation and parameters estimation. Int. J. Prod. Res. 55(4), 4153–4163 (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Anna Kitaeva
    • 1
  • Klimentii Livshits
    • 1
    Email author
  • Ekaterina Ulyanova
    • 1
  1. 1.National Research Tomsk State UniversityTomskRussia

Personalised recommendations