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Pricing in Dynamic Marketing: The Cases of Piece-Wise Constant Sale and Retail Discounts

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

We consider a stylized distribution channel, where a manufacturer sells a single kind of good to a retailer. In classical setting, the profit of manufacturer is quadratic w.r.t. wholesales discount, while the profit of retailer is quadratic w.r.t. retail discount (pass-through). Thus, the wholesale prices and the retail prices are continuous. These results are elegant mathematically but not adequate economically. Therefore, we assume that wholesale discount and retail discounts are piece-wise constant. We show the strict concavity of retailer’s profits w.r.t. retail discount levels. As for the manufacturer’s profits w.r.t. wholesale discount levels, we show that strict concavity can be guaranteed only in the case when retail discount is constant and sufficiently large.

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Notes

  1. 1.

    It seems realistic, cf.  [12].

  2. 2.

    Parameter \(\overline{\alpha }\in [A_1, A_2]\) takes into account the fact that the retailer has some expectations about the wholesale discount: the motivation is reduced if the retailer is dissatisfied with the wholesale discount, i.e., if \(\alpha (t) <\overline{\alpha };\) on the contrary, the motivation increases if \(\alpha (t)> \overline{\alpha }\).

  3. 3.

    Note that \( x_{1}\left( \tau _{0}\right) =0\) while \(M_{1}\left( \tau _{0}\right) =\overline{M}\).

  4. 4.

    Due to (3), these formulas are well defined.

References

  1. Nerlove, M., Arrow, K.J.: Optimal advertising policy under dynamic conditions. Economica 29(144), 129–142 (1962)

    Article  Google Scholar 

  2. Vidale, M.L., Wolfe, H.B.: An Operations-Research Study of Sales Response to Advertising. Mathematical Models in Marketing. Lecture Notes in Economics and Mathematical Systems (Operations Research), vol. 132, pp. 223–225. Springer, Berlin, Heidelberg (1976). https://doi.org/10.1007/978-3-642-51565-1_72

    Chapter  Google Scholar 

  3. Bykadorov, I.A., Ellero, A., Moretti, E.: Minimization of communication expenditure for seasonal products. RAIRO Oper. Res. 36(2), 109–127 (2002)

    Article  MathSciNet  Google Scholar 

  4. Mosca, S., Viscolani, B.: Optimal goodwill path to introduce a new product. J. Optim. Theory Appl. 123(1), 149–162 (2004)

    Article  MathSciNet  Google Scholar 

  5. Giri, B.C., Bardhan, S.: Coordinating a two-echelon supply chain with price and inventory level dependent demand, time dependent holding cost, and partial backlogging. Int. J. Math. Oper. Res. 8(4), 406–423 (2016)

    MathSciNet  MATH  Google Scholar 

  6. Printezis, A., Burnetas, A.: The effect of discounts on optimal pricing under limited capacity. Int. J. Oper. Res. 10(2), 160–179 (2011)

    Article  MathSciNet  Google Scholar 

  7. Lu, L., Gou, Q., Tang, W., Zhang, J.: Joint pricing and advertising strategy with reference price effect. Int. J. Prod. Res. 54(17), 5250–5270 (2016)

    Article  Google Scholar 

  8. Zhang, S., Zhang, J., Shen, J., Tang, W.: A joint dynamic pricing and production model with asymmetric reference price effect. J. Ind. Manage. Optim. 15(2), 667–688 (2019)

    MathSciNet  MATH  Google Scholar 

  9. Bykadorov, I., Ellero, A., Moretti, E., Vianello, S.: The role of retailer’s performance in optimal wholesale price discount policies. Eur. J. Oper. Res. 194(2), 538–550 (2009)

    Article  MathSciNet  Google Scholar 

  10. Bykadorov, I.A., Ellero, A., Moretti, E.: Trade discount policies in the differential games framework. Int. J. Biomed. Soft Comput. Hum. Sci. 18(1), 15–20 (2013)

    Google Scholar 

  11. Bykadorov, I.: Dynamic marketing model: optimization of retailer’s role. Commun. Comput. Inf. Sci. 974, 399–414 (2019)

    Google Scholar 

  12. Bykadorov, I.: Dynamic marketing model: the case of piece-wise constant pricing. Commun. Comput. Inf. Sci. 1145, 150–163 (2020)

    Google Scholar 

Download references

Acknowledgments

The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0018) and within the framework of Laboratory of Empirical Industrial Organization, Economic Department of Novosibirsk State University. The work was supported in part by the Russian Foundation for Basic Research, projects 18-010-00728 and 19-010-00910 and by the Russian Ministry of Science and Education under the 5–100 Excellence Programme.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Koptyug Ave., 630090, Novosibirsk, Russia

    Igor Bykadorov

  2. Novosibirsk State University, 1 Pirogova St., 630090, Novosibirsk, Russia

    Igor Bykadorov

  3. Novosibirsk State University of Economics and Management, Kamenskaja street 56, 630099, Novosibirsk, Russia

    Igor Bykadorov

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  1. Igor Bykadorov
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Correspondence to Igor Bykadorov .

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Editors and Affiliations

  1. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Bykadorov, I. (2020). Pricing in Dynamic Marketing: The Cases of Piece-Wise Constant Sale and Retail Discounts. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_3

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