Optimization Letters

, Volume 13, Issue 2, pp 367–378 | Cite as

An efficient method for joint product line selection and pricing with fixed costs

  • Jungju Park
  • Jeonghoon MoEmail author
Original Paper


In this paper, we propose an exact solution approach to solve a joint product line selection and pricing problem with a fixed cost factor. We adopt the multinomial logit model to estimate the sales of each marketed product, and suppose that the introduction of each product to the market incurs some constant fixed costs. Utilizing an implicit function form of the optimal price, we transform the original problem into the one with the decision variables for the product introduction only. The efficiency of the proposed transformation approach is demonstrated through simulations. We further discuss its applicability to generalized problems.


Product line selection Pricing Fixed cost Convex integer programming 



This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) (No. NRF-2015R1A2A2A04007359).


  1. 1.
    Aydin, G., Ryan, J.K.: Product line selection and pricing under the multinomial logit choice model (2000)Google Scholar
  2. 2.
    Ben-Akiva, M.E., Lerman, S.R.: Discrete Choice Analysis: Theory and Application to Travel Demand, p. 9. MIT Press, Cambridge (1985)Google Scholar
  3. 3.
    Byrd, R.H., Nocedal, J., Waltz, R.A.: Knitro: an integrated package for nonlinear optimization. In: Pillo, G., Roma, M. (eds.) Large-Scale Nonlinear Optimization, pp. 35–59. Springer, Berlin (2006)CrossRefGoogle Scholar
  4. 4.
    Caro, F., Martínez-de Albéniz, V., Rusmevichientong, P.: The assortment packing problem: multiperiod assortment planning for short-lived products. Manag. Sci. 60(11), 2701–2721 (2014)CrossRefGoogle Scholar
  5. 5.
    Chhajed, D., Raman, N.: An integrated approach to product design and process selection. BEBR Faculty Working Paper; No. 92-0178 (1992)Google Scholar
  6. 6.
    Davis, J., Gallego, G., Topaloglu, H.: Assortment planning under the multinomial logit model with totally unimodular constraint structures. Cornell (2013)Google Scholar
  7. 7.
    Davis, J.M., Gallego, G., Topaloglu, H.: Assortment optimization under variants of the nested logit model. Oper. Res. 62(2), 250–273 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dence, T.P.: A brief look into the Lambert W function. Appl. Math. 4(6), 887 (2013)CrossRefGoogle Scholar
  9. 9.
    Dobson, G., Yano, C.A.: Product line and technology selection with shared manufacturing and engineering design resources. Simon School of Business Working Paper OP 95-01 (1995)Google Scholar
  10. 10.
    Gallego, G., Wang, R.: Multiproduct price optimization and competition under the nested logit model with product-differentiated price sensitivities. Oper. Res. 62(2), 450–461 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kunnumkal, S., Martnez-de-Albniz, V.: Tractable Models and Algorithms for Assortment Planning with Product Costs. Project Report. Indian School of Business, Hyderabad (2016)Google Scholar
  12. 12.
    Li, H., Huh, W.T.: Pricing multiple products with the multinomial logit and nested logit models: concavity and implications. Manuf. Serv. Oper. Manag. 13(4), 549–563 (2011)CrossRefGoogle Scholar
  13. 13.
    Li, H., Webster, S., Mason, N., Kempf, K.: Winner-2017 M&SOM practice-based research competition—product-line pricing under discrete mixed multinomial logit demand. Manuf. Serv. Oper, Manag (2018).
  14. 14.
    Maddah, B., Bish, E.K.: Joint pricing, assortment, and inventory decisions for a retailer’s product line. Naval Res. Logist. (NRL) 54(3), 315–330 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Méndez-Díaz, I., Miranda-Bront, J.J., Vulcano, G., Zabala, P.: A branch-and-cut algorithm for the latent-class logit assortment problem. Discrete Appl. Math. 164, 246–263 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Moorthy, K.S.: Market segmentation, self-selection, and product line design. Mark. Sci. 3(4), 288–307 (1984)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Rusmevichientong, P., Shen, Z.J.M., Shmoys, D.B.: Dynamic assortment optimization with a multinomial logit choice model and capacity constraint. Oper. Res. 58(6), 1666–1680 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Rusmevichientong, P., Shmoys, D., Tong, C., Topaloglu, H.: Assortment optimization under the multinomial logit model with random choice parameters. Prod. Oper. Manag. 23(11), 2023–2039 (2014)CrossRefGoogle Scholar
  19. 19.
    Rusmevichientong, P., Topaloglu, H.: Robust assortment optimization in revenue management under the multinomial logit choice model. Oper. Res. 60(4), 865–882 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Ryzin, G.V., Mahajan, S.: On the relationship between inventory costs and variety benefits in retail assortments. Manag. Sci. 45(11), 1496–1509 (1999)CrossRefzbMATHGoogle Scholar
  21. 21.
    Schön, C.: On the product line selection problem under attraction choice models of consumer behavior. Eur. J. Oper. Res. 206(1), 260–264 (2010)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Yonsei UniversitySeoulRepublic of Korea

Personalised recommendations