A stochastic game theoretic framework for decentralized optimization of multi-stakeholder supply chains under uncertainty

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This paper investigates the influences of uncertainty in multi-stakeholder non-cooperative supply chains, and the corresponding optimal strategies based on game theory to hedge against uncertainty in design and operations of such decentralized supply chains. We propose a novel game-theory-based stochastic model that integrates two-stage stochastic programming with a single-leader-multiple-follower Stackelberg game scheme for optimizing decentralized supply chains under uncertainty. Both the leader's and the followers’ uncertainties are considered, which directly affect their design and operational decisions regarding infrastructure development, contracts selection, price setting, production profile, transportation planning, and inventory management. The resulting model is formulated as a two-stage stochastic mixed-integer bilevel nonlinear program, which can be further reformulated into a tractable single-level stochastic mixed-integer linear program by applying KKT conditions and Glover's linearization method. An illustrative example of flight booking under uncertain flight delays and a large-scale application to shale gas supply chains are presented to demonstrate the applicability of the proposed framework.