Abstract
In this paper, a new optimization model of competitive facility location and pricing is introduced. This model is an extension of the well-known (r|p)-centroid problem. In the model, two companies compete for the client’s demand. Each client has a finite budget and a finite demand. First, a company-leader determines a location of p facilities. Taking into account the location of leader’s facilities, the company-follower determines a location of its own r facilities. After that, each company assigns a price for each client. When buying a product, the client pays the price of the product and its transportation. A client buys everything from a company with lower total costs if their total costs do not exceed the budget of the client. If the cost of buying a product from both companies is the same, the demand of clients is distributed equally among them. The goal is to determine a location of leader’s facilities and set the prices in which the total income of the leader is maximal. Results about the computational complexity of the model are presented. Several special cases are considered. These cases can be divided into three categories: (1) polynomially solvable problems; (2) NP-hard problems; (3) problems related to the second level of the polynomial hierarchy. Finally, the complexity of the maxmin-2-Sat problem is discussed.
The research of the first author was supported by RFBR grant 17-07-00513 and the research of the second and third authors was supported by RFBR grant 16-07-00319.
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
References
Hotelling, H.: Stability in competition. Econ. J. 39(153), 41–57 (1929)
Eiselt, H.A., Laporte, G., Thisse, J.-F.: Competitive location models: a framework and bibliography. Transp. Sci. 27, 44–54 (1993)
Eiselt, H.A., Laporte, G.: Sequential location problems. Eur. J. Oper. Res. 96, 217–242 (1996)
Hamacher, H.W., Nickel, S.: Classification of location models. Locat. Sci. 6, 229–242 (1998)
Plastria, F.: Sequential location problems. Eur. J. Oper. Res. 129, 461–470 (2001)
Panin, A.A., Pashchenko, M.G., Plyasunov, A.V.: Bilevel competitive facility location and pricing problems. Autom. Remote Control 75(4), 715–727 (2014)
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-58412-1
Garcia, M.D., Fernandez, P., Pelegrin, B.: On price competition in location-price models with spatially separated markets. TOP 12, 351–374 (2004)
Pelegrin, B., Fernandez, P., Garcia, M.D., Cano, S.: On the location of new facilities for chain epansion under delivered pricing. Omega 40, 149–158 (2012)
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)
Alekseeva, E., Kochetov, Yu.: Matheuristics and exact methods for the discrete \((r\mid p)\)-centroid problem. In: Talbi, El.-G., Brotcorne, L. (eds.) Metaheuristics for Bi-level Optimization. SCI, vol. 482, pp. 189–219. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37838-6_7
Alekseeva, E., Kochetov, Yu., Plyasunov, A.: An exact method for the discrete \((r\mid p)\)-centroid problem. J. Global Optim. 63(3), 445–460 (2015)
Alekseeva, E., Kochetov, Yu., Plyasunov, A.: Complexity of local search for the p-median problem. Eur. J. Oper. Res. 191, 736–752 (2008)
Plyasunov, A.V., Panin, A.A.: The pricing problem. I: exact and approximate algorithms. J. Appl. Ind. Math. 7(2), 241–251 (2013)
Davydov, I.A., Kochetov, Y.A., Carrizosa, E.: A local search heuristic for the (rjp)-centroid problem in the plane. Comput. Oper. Res. 52, 334–340 (2014)
Lavlinskii, S.M., Panin, A.A., Plyasunov, A.V.: Comparison of models of planning public-private partnership. J. Appl. Ind. Math. 10(3), 356–369 (2016)
Kochetov, Yu.A., Panin, A.A., Plyasunov, A.V.: Comparison of metaheuristics for the bilevel facility location and mill pricing problem. J. Appl. Ind. Math. 19(3), 392–401 (2015)
Diakova, Z., Kochetov, Yu.: A double VNS heuristic for the facility location and pricing problem. Electron. Notes Discrete Math. 39, 29–34 (2012)
Iellamo, S., Alekseeva, E., Chen, L., Coupechoux, M., Kochetov, Yu.: Competitive location in cognitive radio networks. 4OR 13(1), 81–110 (2015)
Panin, A.A., Plyasunov, A.V.: On complexity of the bilevel location and pricing problems. J. Appl. Ind. Math. 8(4), 574–581 (2014)
Plyasunov, A.V., Panin, A.A.: The pricing problem. II: 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
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Kononov, A.V., Panin, A.A., Plyasunov, A.V. (2018). A New Model of Competitive Location and Pricing with the Uniform Split of the Demand. In: Eremeev, A., Khachay, M., Kochetov, Y., Pardalos, P. (eds) Optimization Problems and Their Applications. OPTA 2018. Communications in Computer and Information Science, vol 871. Springer, Cham. https://doi.org/10.1007/978-3-319-93800-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-93800-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93799-1
Online ISBN: 978-3-319-93800-4
eBook Packages: Computer ScienceComputer Science (R0)