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 facilitywithminimal 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.
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References
A. V. Plyasunov and A. A. Panin, “The Pricing Problem. Part I: Exact and Approximate Algorithms,” Diskretn. Anal. Issled. Oper. 19 (5), 83–100 (2012) [J. Appl. Indust. Math. 7 (2), 241–251 (2013)].
A. V. Plyasunov and A. A. Panin, “The Pricing Problem. Part II: Computational Complexity,” Diskretn. Anal. Issled. Oper. 19 (6), 56–71 (2012) [J. Appl. Indust. Math. 7 (3), 420–430 (2013)].
A. V. Plyasunov and A. A. Panin, “On Three-Level Problem of Competitive Pricing,” in Numerical Computations: Theory and Algorithms (Proceedings of 2nd International Conference, Pizzo Calabro, Italy, June 19–25, 2016) (AIP Publ.,Melville, NY, 2016), pp. 050006-1–050006-5.
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,” European J. Oper. Res. 262 (2), 449–463 (2017).
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NPCompleteness (Freeman, San Francisco, 1979; Mir,Moscow, 1982).
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).
A.M. Geoffrion, “Generalized Benders Decomposition,” J. Optim. Theory Appl. 10 (4), 237–260 (1972).
D. McDaniel and M. Devine, “AModified Benders Partitioning Algorithm forMixed Integer Programming,” Manage. Sci. 24 (3), 312–319 (1977).
F. Vanderbeck and M. W. P. Savelsbergh, “A Generic View of Dantzig–Wolfe Decomposition for Integer Programming,” Oper. Res. Lett. 34 (3), 296–306 (2006).
J. V. Outrata, “On the Numerical Solution of a Class of Stackelberg Problems,” ZOR 34 (4), 255–277 (1990).
P. Hansen and N. Mladenović, “Variable Neighborhood Search,” European J. Oper. Res. 130 (3), 449–467 (2001).
E. W. Leggette, Jr., and D. J. Moore, “Optimization Problems and the Polynomial Hierarchy,” Theor. Comput. Sci. 15 (3), 279–289 (1981).
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Russian Text © A.V. Gubareva, A.A. Panin, A.V. Plyasunov, L.V. Som, 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 1, pp. 55–73.
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Gubareva, A.V., Panin, A.A., Plyasunov, A.V. et al. On a Three-Level Competitive Pricing Problem with Uniform and Mill Pricing Strategies. J. Appl. Ind. Math. 13, 54–64 (2019). https://doi.org/10.1134/S1990478919010071
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DOI: https://doi.org/10.1134/S1990478919010071