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On the Stability of Coalitions in Supply Chain Networks via Generalized Complementarity Conditions

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Abstract

In this paper, we consider a supply chain network model that consists of three layers of decision-makers, namely, suppliers, manufacturers and retailers, with prices and shipments that evolve in time. We focus on the vertical integration of the levels of the supply chain and consider the retailer as the dominant player of the coalition. We give a novel reformulation of the evolutionary variational inequality related to the equilibrium conditions underlying the model. This approach, based on complementarity conditions, allows us to analyze the Lagrange multipliers associated with production capacities to understand better market’s trend. We study the behavior of marginal profits and provide some results for the efficiency and the stability of the coalitions. We apply our theoretical achievements to a duopolistic model.

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Acknowledgements

The research was partially supported by the research project “Modelli Matematici nell’Insegnamento-Apprendimento della Matematica” DMI, University of Catania. This support is gratefully acknowledged.

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  1. Dipartimento di Matematica e Informatica, University of Catania, Viale A. Doria 6, 95125, Catania, Italy

    Laura Scrimali

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  1. Laura Scrimali
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Correspondence to Laura Scrimali.

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Scrimali, L. On the Stability of Coalitions in Supply Chain Networks via Generalized Complementarity Conditions. Netw Spat Econ 22, 379–394 (2022). https://doi.org/10.1007/s11067-019-09461-w

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