Abstract
This article is dedicated to finding stable solutions to change input data on the example of pricing problems. In other words, we investigate stability analysis problems based on pricing problems.
Initial pricing problems can be described as the following Stackelberg game. There are a company and its potential clients. First, the company sets prices at own facilities for a homogeneous product. After that, each client chooses the facility in which the minimum of his costs is achieved. The cost consists of purchase and transportation prices. At the same time, clients can make a purchase only if their budget allows it. The goal is to establish prices at which the maximum profit of the company is achieved. In the generalized problem of competitive pricing, two companies compete with each other for the client demand. They set prices sequentially. Clients are also the last to decide.
For the pricing of one company, we discuss the computational complexity and algorithm solution of the stability analysis problem for three different pricing strategies. We also look at the competitive pricing problem with uniform pricing when the same price is set at all facilities. In conclusion, we discuss the relationship between the computational complexity of stability analysis problems and initial problems.
The research was supported by Russian Foundation for Basic Research (project No. 19-410-240003) (chapter 1,2) and the program of fundamental scientific researches of the SB RAS (project No. 0314-2019-0014) (chapter 3).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Carrizosa, E., Nickel, S.: Robust facility location. Math. Methods Oper. Res. 58(2), 331–349 (2003)
Carrizosa, E., Ushakov, A., Vasilyev, I.: Threshold robustness in discrete facility location problems: a bi-objective approach. Optim. Lett. 9(7), 1297–1314 (2015). https://doi.org/10.1007/s11590-015-0892-5
Davydov, I., Kochetov, Yu., Plyasunov, A.: On the complexity of the \((r\mid p)\)-centroid problem in the plane. TOP 22(2), 614–623 (2014)
Emelichev, V., Podkopaev, D.: Quantitative stability analysis for vector problems of 0–1 programming. Discrete Optim. 7(1–2), 48–63 (2010)
Emelichev, V.A., Podkopaev, D.P.: Stability and regularization of vector problems of integer linear programming. Diskretn. Anal. Issled. Oper. Ser. 2 8(1), 47–69 (2001)
Gordeev, E.N., Leont’ev, V.K.: A general approach to the study of the stability of solutions in discrete optimization problems. Zh. Vychisl. Mat. Mat. Fiz. 36(1), 66–72 (1996); Comput. Math. Math. Phys. 36(1), 53–58 (1996)
Hanjoul, P., Hansen, P., Peeters, D., Thisse, J.-F.: Uncapacitated plant location under alternative spatial price policies. Mark. Sci. 36, 41–57 (1990)
Kuzmin, K.G.: A united approach to finding the stability radii in a multicriteria problem of a maximum cut. Diskretn. Anal. Issled. Oper. 22(5), 30–51 (2015); Appl, J. Ind. Math. 9(4), 527–539 (2015)
Leont’ev, V.K.: Stability of the travelling salesman problem. Comput. Math. Math. Phys. 15(5), 199–213 (1975)
Leont’ev, V.K., Gordeev, E.N.: Qualitative analysis of trajectory problems. Kibernetika 5, 82–90 (1986)
Leont’ev, V.K., Gordeev, E.N.: Stability in bottleneck problems. Comput. Math. Math. Phys. 20(4), 275–280 (1980)
Plyasunov, A.V., Panin, A.A.: On three-level problem of competitive pricing. numerical computations: theory and algorithms. In: Proceedings of 2nd International Conference, Pizzo Calabro, Italy, 19–25 June 2016, pp. 050006-1–050006-5. AIP Publ., Melville (2016)
Plyasunov, A.V., Panin, A.A.: The pricing problem. I: exact and approximate algorithms. J. Appl. Ind. Math. 7(2), 241–251 (2013)
Plyasunov, A.V., Panin, A.A.: The pricing problem. I: computational complexity. J. Appl. Ind. Math. 7(3), 420–430 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Panin, A.A., Plyasunov, A.V. (2020). Stability Analysis for Pricing. In: Kochetov, Y., Bykadorov, I., Gruzdeva, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Communications in Computer and Information Science, vol 1275. Springer, Cham. https://doi.org/10.1007/978-3-030-58657-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-58657-7_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58656-0
Online ISBN: 978-3-030-58657-7
eBook Packages: Computer ScienceComputer Science (R0)