On the Stability of Coalitions in Supply Chain Networks via Generalized Complementarity Conditions
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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.
KeywordsSI: Evolutionary variational inequality Equilibrium conditions Lagrange multipliers
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.
- Daniele P, Maugeri A, Nagurney A (2017) Cybersecurity investments with nonlinear budget constraints: analysis of the marginal expected utilities. In: Daras N, Rassias T (eds) Operations research, engineering, and cyber security. Springer optimization and its applications, vol 113. Springer, ChamGoogle Scholar
- Maugeri A, Raciti F (2009) On existence theorems for monotone and nonmonotone variational inequalities. J Convex Anal 16(3-4):899–911Google Scholar
- Scrimali L (2018) Coalitional games in evolutionary supply chain networks. In: Daniele P, Scrimali L (eds) Optimization and decision science: new trends in emerging complex real life problems, SpringerGoogle Scholar