Abstract
Under study is a mathematical model for the processes of cyclic transportation in logistic systems in the case of a quantitative competition. The network under consideration is formed by some set of stations, each with the warehouses of several companies. The enterprises furnish and sell similar products the demand for which is deterministic. In simulating the management systems of each enterprise, we use a relaxation method of inventory control which permits deficit. For this model, the conditions are given for existence of an equilibrium solution.
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References
E. Yu. Lokshin, Economy of Logistics: A Tutorial (Gosplanizdat, Moscow, 1963) [in Russian].
N. D. Fasolyak, Management of Inventories (Economic Aspect of the Problem) (Ekonomika, Moscow, 1972) [in Russian].
E. A. Khrutskii, V. A. Sakovich, and S. P. Kolosov, Optimization of Economic Relations and Inventories: Issues and Methodology (Ekonomika, Moscow, 1977) [in Russian].
M. E. Koryagin, Study and Optimization of the Mathematical Models of Cyclic Processes in the Transport Logistics Systems: Candidate’s Dissertation in Technical Sciences (Kemerovo, 2003).
M. N. Grigor’ev, A. P. Dolgov, and S. A. Uvarov, Inventory Management in Logistics: Methods, Models, and Information Technologies: Textbook (Biznes-Pressa, St. Petersburg, 2006) [in Russian].
F. Klijn and M. Marco Slikker, “Distribution Center Consolidation Games,” Oper. Res. Lett. 33(3), 285–288 (2005).
Y. Dai, X. Chao, Sh.-Ch. Fang, and H. L. W. Nuttle, “Game Theoretic Analysis of a Distribution System with Customer Market Search,” Ann. Oper. Res. 135(1), 223–238 (2005).
Y. Yu and G. Q. Huang, “Nash Game Model for Optimizing Market Strategies, Configuration of Platform Products in a Vendor Managed Inventory (VMI) Supply Chain for a Product Family,” European J. Oper. Res. 206(2), 361–373 (2010).
R. Guan and X. Zhao, “Pricing and Inventory Management in a System with Multiple Competing Retailers under (r, Q) Policies,” Comput. Oper. Res. 38(8), 1294–1304 (2011).
X. Fang, “Capacity Games for Partially Complementary Products under Multivariate Random Demands,” Naval Res. Logistics, DOI: 10.1002/nav.146-159 (2012).
Zh. Liu, “Equilibrium Analysis of Capacity Allocation with Demand Competition,” Naval Res. Logistics, DOI: 10.1002/nav. 254–265 (2012)
S. Lozano, P. Moreno, B. Adenso-Diaz, and E. Algaba, “Cooperative Game Theory Approach to Allocating Benefits of Horizontal Cooperation,” European J. Oper. Res. 229(2), 444–452 (2013).
P. Egri and J. Vancza, “A Distributed Coordination Mechanism for Supply Networks with Asymmetric Information,” European J. Oper. Res. 226(3), 452–460 (2013).
A. Nagurney, “Formulation and Analysis of Horizontal Mergers among Oligopolistic Firms with Insights into the Merger Paradox: a Supply Chain Network Perspective,” Comput. Manag. Sci. 7(4), 377–406 (2010).
M. G. Gasratov and V. V. Zakharov, “Game Theoretic Models of the Supply Chain Optimization in the Case of Deterministic Demand,” Mat. Teor. Igr i Ee Prilozhen. 3(1), 23–59 (2011).
J. Tirole, The Theory of Industrial Organization (MIT Press, 1988]; Ekonom. Shkola, St. Petersburg, 2000).
G. Hadley, Nonlinear and Dynamical Programming (Addison-Wesley, Reading, MS, 1964; Mir, Moscow, 1967).
N. S. Kukushkin and V. V. Morozov, Theory of Nonantagonistic Games (Moskov. Gos. Univ., Moscow, 1984) [in Russian].
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Original Russian Text © N.A. Gasratova, M.G. Gasratov, 2015, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2015, Vol. XVIII, No. 1, pp. 14–27.
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Gasratova, N.A., Gasratov, M.G. A network model of inventory control in the case of a quantitative competition. J. Appl. Ind. Math. 9, 165–178 (2015). https://doi.org/10.1134/S1990478915020039
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DOI: https://doi.org/10.1134/S1990478915020039