Equilibrium supply-demand allocation in a single-commodity network

Alexander Y. Krylatov ; Anastasiya P. Raevskaya ; Jiangrong Li

Contributions to game theory and management, Tome 15 (2022), pp. 121-131.

Résumé

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.

Détail

Keywords: nonlinear optimization, distribution network, relocation, homogeneity.

Bibliographie

[1] Barrett, C. B. and Li, J. R., “Distinguishing between equilibrium and integration in spatial price analysis”, Am. J. Agric. Econ., 84:2 (2002), 292–307 | DOI

[2] Barron, Y. and Hermel, D., “Shortage decision policies for a fluid production model with map arrivals”, International Journal of Production Research, 55:14 (2017), 3946–3969 | DOI

[3] Bramoulle, Y. and Kranton, R., “Public goods in networks”, J. Econ. Theory, 135 (2007), 478–494 | DOI | MR | Zbl

[4] Enke, S., “Equilibrium among spatially separated markets: solution by electric analogue”, Econometrica, 19:1 (1951), 40–47 | DOI | Zbl

[5] Enke, S., “Space and value”, Q. J. Econ., 56:4 (1942), 627–637 | DOI

[6] Florian, M. and Los, M., “A new look at static spatial price equilibrium models”, Reg. Sci. Urban Econ., 12:4 (1982), 579–597 | DOI

[7] Grillo, H., Alemany, M. and Ortiz, A., “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 (2016), 239–261 | DOI

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

[9] Ji, B., Ameri, F. and Cho, H., “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 (2021), 5011–5031 | DOI

[10] Kiselev, A. O. and Yurchenko, N. I., “Game equilibria and transition dynamics in a dyad with heterogeneous agents”, Autom. Remote Control, 82:3 (2021), 549–564 | DOI | MR | Zbl

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

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

[13] Krylatov, A. Y. and Lonyagina, Y. E., “Equilibrium flow assignment in a network of homogeneous goods”, Autom. Remote Control, 83 (2022), 805–827 | DOI | Zbl

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

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

[16] Marshall, A., Principles of Economics, Macmillan, 1920

[17] McNew, K., “Spatial market integration: definition, theory, and evidence”, Agric. Resour. Econ. Rev., 25:1 (1996), 1–11 | DOI | MR

[18] Nagurney, A., Network Economics: a Variational Inequality Approach, Kluwer Acad., Amsterdam, 1993 | MR | Zbl

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

[20] Novikov, D. A., “Games and networks”, Autom. Remote Control, 75:6 (2014), 1145–1154 | DOI | MR

[21] Patriksson, M., The Traffic Assignment Problem: Models and Methods, Dover, New York, 1994

[22] Samuel, C. and Mahanty, B., “Shortage gaming and supply chain performance”, International Journal of Manufacturing Technology and Management, 5:5/6 (2003), 536–548 | DOI

[23] Samuelson, P. A., “Spatial price equilibrium and linear programming”, Am. Econ. Rev., 42:3 (1952), 283–303

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

[25] Takayama, T. and Judge, G. G., “Equilibrium among spatially separated markets: a reformulation”, Econometrica, 32:4 (1964), 510–524 | DOI | MR

[26] Vasin, A. A. and Daylova, E. A., “Two-node market under imperfect competition”, Autom. Remote Control, 78:9 (2017), 1709–1729 | DOI | MR

[27] Vasin, A., Grigoryeva, O. and Tsyganov, N., “A model for optimization of transport infrastructure for some homogeneous goods markets”, J. Global Optim., 76:3 (2020), 499–518 | DOI | MR | Zbl