IIE Transactions

, Volume 31, Issue 5, pp 431–444 | Cite as

The newsboy problem with multiple demand classes

  • ALEX X. Zhang


We consider the single item newsboy problem, where the item can be sold to different demand classes at different prices. The demands are realized sequentially over time. That is, the newsboy purchases newspapers at the beginning of the day and sells them in the morning and in the afternoon with different prices. We analyze two cases where the prices are either decreasing or increasing; the former case applies, for example, to fashion goods retailing, while the latter to airlines and hotels. In the decreasing price case, we find the optimal order quantity to maximize the expected profit with independent multiple demands. We show numerically that aggregating the multiple demands with a single average price or applying the single demand newsboy model separately to multiple demand classes may lead to large sub-optimality. In the increasing price case, we analyze a two demand class model in which a fraction of the unsatisfied lower fare demand diverts to the high fare class, thus causing dependent sales. We follow a policy of protecting the sales in the higher fare class by limiting the sales in the lower fare class. We derive both the fare allocation limit and the initial capacity, and discuss managerial implications. For both models, we give bounds on the optimal order quantity.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Pfeifer, P.E. (1989) The airline discount fare allocation problem. Decision Sciences, 20, 149–157.Google Scholar
  2. [2]
    Bodily, S.E. and Weatherford, L.R. (1995) Perishable asset revenue management: generic and multiple-price yield management with diversion. Omega, 23, 173–185.Google Scholar
  3. [3]
    Belobaba, P.P. (1989) Application of a probabilistic decision model to airline seat inventory control. Operations Research, 37, 183–197.Google Scholar
  4. [4]
    Arrow, K.A., Harris, T.E. and Marschak, J. (1951) Optimal inventory policy. Econometrica, 19, 250–272.Google Scholar
  5. [5]
    Morse, M.P. and Kimball, G.E. (1951) Methods of Operations Research, M.I.T. Press, Cambridge, MA.Google Scholar
  6. [6]
    Ismail, B. and Louderback, J. (1979) Optimizing and satisfying in stochastic cost-volume profit analysis. Decision Sciences, 10, 205– 217.Google Scholar
  7. [7]
    Lau, H. (1980) The newsboy problem under alternative optimization objectives. Journal of the Operational Research Society, 31, 525–535.Google Scholar
  8. [7a]
    Eeckhoudt, E., Gollier, C. and Schlesinger, H. (1995) The risk-averse (and prudent) newsboy. Management Science, 41, 786–794.Google Scholar
  9. [8]
    Reyniers, D. (1990) A high-low search algorithm for a newsboy problem with delayed information feedback. Operations Research, 38, 838–846.Google Scholar
  10. [9]
    Gallego, G. and Moon, I. (1993) The distribution free newsboy problem: review and extensions. Journal of the Operational Research Society, 44, 825–834.Google Scholar
  11. [10]
    Jucker, J.V. and Rosenblatt, M.J. (1985) Single-period inventory models with demand uncertainty and quantity discounts: behavioral implications and a new solution procedure. Naval Research Logistics, 32, 537–550.Google Scholar
  12. [11]
    Khouja, M. (1995) The newsboy problem under progressive multiple discounts. European Journal of Operational Research, 84, 458–466.Google Scholar
  13. [12]
    Khouja, M. (1996) The newsboy problem with multiple discounts o.ered by suppliers and retailers. Decision Sciences, 27, 589–599.Google Scholar
  14. [13]
    Lau, A.H. and Lau, H. (1988) The newsboy problem with price-dependent demand distribution. IIE Transactions, 20, 168–175.Google Scholar
  15. [14]
    Silver, E.A. and Peterson, R. (1985) Decision Systems for Inventory Management and Production Planning, 2nd edn, Wiley, New York. Chapter 10.3, pp. 406–410.Google Scholar
  16. [15]
    Li, J., Lau, H. and Lau, A.H. (1991) A two-product newsboy problem with satisficing objective and independent exponential demands. IIE Transactions, 23, 29–39.Google Scholar
  17. [16]
    Kouvelis, P. and Gutierrez, G. (1997) The newsvendor problem in a global market: optimal centralized and decentralized policies for a two-market stochastic inventory system. Management Science, 43, 571–585.Google Scholar
  18. [17]
    Belobaba, P.P. (1987) Airline yield management: an overview of seat inventory control. Transportation Science, 20, 63–73.Google Scholar
  19. [18]
    Weatherford, L.R. and S.E. Bodily (1992) A taxonomy and research overview of perishable asset revenue management: yield management, overbooking, and pricing. Operations Research, 40, 831–844.Google Scholar
  20. [19]
    Belobaba, P.P. and Weatherford, L.R. (1996) Comparing decision rules that incorporate customer diversion in perishable asset revenue management situations. Decision Sciences, 27, 343–363.Google Scholar
  21. [20]
    Brumelle, S.L., McGill, J.I., Oum, T.H., Sawaki, K. and Tretheway, M.W. (1990) Allocation of airline seats between stochastically dependent demands. Transportation Science, 24, 183–192.Google Scholar
  22. [21]
    Gerchak, Y., Parlar, M. and Yee, T.K.M. (1985) Optimal rationing policies and production quantities for products with several demand classes. Canadian Journal of Administrative Sciences, 2, 161–176.Google Scholar
  23. [22]
    Lee, T.C. and Hersh, M. (1993) A model for dynamic airline seat inventory control with multiple seat bookings. Transportation Science, 27, 252–265.Google Scholar
  24. [23]
    Littlewood, K. (1972) Forecasting and control of passenger bookings. AGIFORS Symposium Proceedings, 12, 95–117.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

    • 1
  • ALEX X. Zhang
    • 1
  1. 1.Department of Information and Operations Management, Marshall School of BusinessUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations