Equilibrium Supply-Demand Allocation in a Single-Commodity Network

Authors

  • Alexander Y. Krylatov St. Petersburg State University; Institute of Applied Mathematical Research of the Karelian Research Centre of the Russian Academy of Sciences
  • Anastasiya P. Raevskaya Saint Petersburg State University
  • Jiangrong Li Yan'an University

DOI:

https://doi.org/10.21638/11701/spbu31.2022.10

Abstract

This paper is devoted to the recent findings in the analytical research of supply-demand allocation in a single-commodity network with distant (in space) suppliers and consumers. The allocation problem is formulated as an equilibrium flow assignment problem with affine functions of demand, supply, and logistic costs in a network represented by a digraph with suppliers and consumers located in nodes. We offer a brief overview of supply-demand relocation patterns obtained for elastic, shortage, and overproduction cases. Such kinds of results seem valuable since they allow one to develop different competitive distribution models to facilitate the decision-making of supply chain managers. In particular, supply chain managers can use available patterns to design decision-making strategies that mitigate risks concerning disruption or ripple effects.

Keywords:

nonlinear optimization, distribution network, relocation, homogeneity

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References

Barrett, C. B. and Li, J. R. (2002). Distinguishing between equilibrium and integration in spatial price analysis. Am. J. Agric. Econ., 84(2), 292–307

Barron, Y. and Hermel, D. (2017). Shortage decision policies for a fluid production model with map arrivals. International Journal of Production Research, 55(14), 3946–3969

Bramoulle, Y. and Kranton, R. (2007). Public goods in networks. J. Econ. Theory, 135, 478–494

Enke, S. (1951). Equilibrium among spatially separated markets: solution by electric analogue. Econometrica, 19(1), 40–47

Enke, S. (1942). Space and value. Q. J. Econ., 56(4), 627-637

Florian, M. and Los, M. (1982). A new look at static spatial price equilibrium models. Reg. Sci. Urban Econ., 12(4), 579–597

Grillo, H., Alemany, M. and Ortiz, A. (2016). A review of mathematical models for supporting the order promising process under lack of homogeneity in product and other sources of uncertainty. Computers and Industrial Engineering, 91, 239–261

Grillo, H., Alemany, M., Ortiz, A. and Mula, J. (2018). A fuzzy order promising model with non-uniform finished goods. International Journal of Fuzzy Systems, 20, 187–208

Ji, B., Ameri, F. and Cho, H. (2021). A non-conformance rate prediction method supported by machine learning and ontology in reducing underproduction cost and overproduction cost. International Journal of Production Research, 59(16), 5011–5031

Kiselev, A. O. and Yurchenko, N. I. (2021). Game equilibria and transition dynamics in a dyad with heterogeneous agents. Autom. Remote Control, 82(3), 549–564

Kovalenko, A. G. (2018). In search of equilibrium state at the spatial dispersed markets with imperfect competition of a uniform product. Ekon. Mat. Metody, 54(1), 52–68 (in Russian)

Kovalenko, A. G., Khachaturov, V. R. and Kalimoldaev, M. N. (2012). Models of a dispersed market of imperfect competition: problems of their development, application in the management of the regional economy. Probl. Inf., 4(16), 18–23 (in Russian)

Krylatov, A. Y. and Lonyagina, Y. E. (2022). Equilibrium flow assignment in a network of homogeneous goods. Autom. Remote Control, 83, 805–827

Krylatov, A., Lonyagina, Y. and Raevskaya, A. (2022). Competitive supply allocation in a distribution network under overproduction. Lecture Notes in Computer Science (to appear)

Krylatov, A., Lonyagina, Y. and Raevskaya, A. (2022). Competitive relocation of shortage supply in a distribution network. IFAC-PapersOnLine (to appear)

Marshall, A. (1920). Principles of Economics. Macmillan: London

McNew, K. (1996). Spatial market integration: definition, theory, and evidence. Agric. Resour. Econ. Rev., 25(1), 1–11

Nagurney, A. (1993). Network Economics: a Variational Inequality Approach. Kluwer Acad.: Amsterdam

Najid, N., Alaoui-Selsouli, M. and Mohafid, A. (2011). An integrated production and maintenance planning model with time windows and shortage cost. International Journal of Production Research, 49(8), 2265–2283

Novikov, D. A. (2014). Games and networks. Autom. Remote Control, 75(6), 1145–1154

Patriksson, M. (1994). The Traffic Assignment Problem: Models and Methods. Dover: New York

Samuel, C. and Mahanty, B. (2003). Shortage gaming and supply chain performance. International Journal of Manufacturing Technology and Management, 5(5/6), 536–548

Samuelson, P. A. (1952). Spatial price equilibrium and linear programming. Am. Econ. Rev., 42(3), 283–303

Stephens, E. C., Mabaya, E., von Cramon-Taubadel, S. and Barrett, C. B. (2012). Spatial price adjustment with and without trade. Oxford Bull. Econ. Stat., 74(3), 453–469

Takayama, T. and Judge, G. G. (1964). Equilibrium among spatially separated markets: a reformulation. Econometrica, 32(4), 510–524

Vasin, A. A. and Daylova, E. A. (2017). Two-node market under imperfect competition. Autom. Remote Control, 78(9), 1709–1729

Vasin, A., Grigoryeva, O. and Tsyganov, N. (2020). A model for optimization of transport infrastructure for some homogeneous goods markets. J. Global Optim., 76(3), 499–518

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Published

2023-01-26

How to Cite

Krylatov, A. Y., Raevskaya, A. P., & Li, J. (2023). Equilibrium Supply-Demand Allocation in a Single-Commodity Network. Contributions to Game Theory and Management, 15, 121–131. https://doi.org/10.21638/11701/spbu31.2022.10

Issue

Vol. 15 (2022)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.