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Journal of Applied and Industrial Mathematics, 2019, 13:1, 54-64
Volume 26, No 1, 2019, P. 55-73
UDC 519.8
A. V. Gubareva, A. A. Panin, A. V. Plyasunov, and L. V. Som
On a three-level competitive pricing problem with uniform and mill pricing strategies
Abstract:
Under study is a three-level pricing problem formulated as a Stackelberg game in which the two companies, the Leader and the Follower, compete with each other for customers demand by setting prices for homogeneous products on their facilities. The first decision is made by the Leader. Then, having full information about the Leader’s choice, the Follower makes his own decision. After that each customer chooses the facility with minimal service costs to be serviced from. The Leader and the Follower use different pricing strategies: uniform and mill pricing respectively. We study the behavior of company revenues depending on the number of facilities. For this, an exact decomposition type algorithm is proposed. Moreover, we developed a hybrid approximation algorithm that is based on the variable neighborhood descent and coordinate descent.
Tab. 2, bibliogr. 12.
Keywords: Stackelberg game, competitive pricing problem, three-level problem, uniform and mill pricing, exact and approximate algorithm, variable neighborhood descent, coordinate descent, decomposition.
DOI: 10.33048/daio.2019.26.625
Anna V. Gubareva 1
Artem A. Panin 1,2
Aleksandr V. Plyasunov 1,2
Lyudmila V. Som 1
1. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
2. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: a.gubareva@g.nsu.ru, aapanin1988@gmail.com, apljas@math.nsc.ru, milisom@mail.ru
Received July 23, 2018
Revised November 26, 2018
Accepted November 28, 2018
References
[1] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979. Translated under the title Vychislitel’nye mashiny i trudnoreshaemye zadachi, Mir, Moscow, 1982 [Russian].[2] A. V. Plyasunov and A. A. Panin, The pricing problem. Part I: Exact and approximate algorithms, Diskretn. Anal. Issled. Oper., 19, No. 5, 83–100, 2012 [Russian]. Translated in J. Appl. Ind. Math., 7, No. 2, 241–251, 2013.
[3] A. V. Plyasunov and A. A. Panin, The pricing problem. Part II: Computational complexity, Diskretn. Anal. Issled. Oper., 19, No. 6, 56–71, 2012 [Russian]. Translated in J. Appl. Ind. Math., 7, No. 3, 420–430, 2013.
[4] G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Springer, Heidelberg, 1999.
[5] C. Florensa, P. Garcia-Herreros, P. Misra, E. Arslan, S. Mehta, and I. E. Grossmann, Capacity planning with competitive decision-makers: Trilevel MILP formulation, degeneracy, and solution approaches, Eur. J. Oper. Res., 262, No. 2, 449–463, 2017.
[6] A. M. Geoffrion, Generalized Benders decomposition, J. Optim. Theory Appl., 10, No. 4, 237–260, 1972.
[7] P. Hansen and N. Mladenovic, Variable neighborhood search, Eur. J. Oper. Res., 130, No. 3, 449–467, 2001.
[8] E. W. Leggette, Jr. and D. J. Moore, Optimization problems and the polynomial hierarchy, Theor. Comput. Sci., 15, No. 3, 279–289, 1981.
[9] D. McDaniel and M. Devine, A modified Benders partitioning algorithm for mixed integer programming, Manage. Sci., 24, No. 3, 312–319, 1977.
[10] J. V. Outrata, On the numerical solution of a class of Stackelberg problems, ZOR, 34, No. 4, 255–277, 1990.
[11] A. V. Plyasunov and A. A. Panin, On three-level problem of competitive pricing, in Numerical Computations: Theory and Algorithms (Proc. 2nd Int. Conf., Pizzo Calabro, Italy, June 19–25, 2016), pp. 050006-1–050006-5, AIP Publ., Melville, NY, 2016 (AIP Conf. Proc., Vol. 1776).
[12] F. Vanderbeck and M. W. P. Savelsbergh, A generic view of Dantzig–Wolfe decomposition for integer programming, Oper. Res. Lett., 34, No. 3, 296–306, 2006.
