Competitive Supply Chain Network Design under Resource Constraints and Market Equilibrium
This paper studies the effect of resource constraints on a competitive supply chain network design. The authors propose a Stackelberg Nash game model under market equilibrium and resource constraints, and also a cap and trade mechanism to incentivize the suppliers to comply with the regulation. The supply chain network model is directly applicable to the biofuel industry to address food, fuel and environment trilemma. The authors explore the government regulation of farmland use by directly imposing a constraint on farmers. To provide them with incentives to comply with the land use regulation, the authors implement the land use constraint through a cap and trade mechanism which is shown to attain equivalent land use pattern. The authors further prove the existence of optimal solutions to the two equivalent discretely constrained mathematical program with equilibrium constraints (DCMPEC) models and propose two adaptive "relax and tighten" schemes: integrality and Lagrangian duality based relaxation, to handle the binary variables in a mixed integer formulation of the models. The proposed methodology is tested in a case study for the biofuel industry for the State of Illinois. The computational results demonstrate superiority of the authors' customized algorithms to publicly available solvers for solving problems with realistic sizes. Finally, economic insights are also drawn from the case study.