Journal Title

Computational Management Science

Publication Date



In this paper, we develop a competitive supply chain network model with multiple firms, each of which produces a differentiated product by brand and weights the emissions that it generates through its supply chain network activities in an individual way. The supply chain network activities of production, transport and distribution, and storage have associated with them distinct capacities and the firms seek to determine their optimal product flows and frequencies of operation so that their utilities are maximized where the utilities consist of profits and weighted emissions. Multiple production, storage, and transport mode options are allowed. The governing equilibrium concept is that of Cournot-Nash equilibrium. We provide both path and link flow variational inequality formulations of the equilibrium conditions and then propose an algorithm, which, at each iteration, yields closed form expressions for the underlying variables.Numerical examples illustrate the generality of the model and the information provided to managerial decision-makers and policy-makers. This paper adds to the growing literature on sustainable supply chains through the development of a computable general competitive supply chain network game theory model, which brings a greater realism to the evaluation of profit and emission trade-offs through the incorporation of frequencies.

Author Supplied Keywords

Game theory, Supply chains, Networks, Nash equilibrium, Emissions, Sustainability, Variational inequalities, Activity frequencies, Production, Distribution, Storage


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Publication Information

Computational Management Science, 2013, Volume 10, Issue 4, 397-422.

© Springer-Verlag Berlin Heidelberg 2013

Archived version is the accepted manuscript.





Document Type

Journal Article