Competitive green supply chain network design model considering inventory decisions under uncertainty: a real case of a filter company

A robust bi-level model of the single-product multi-period network design problem is proposed for a competitive green supply chain considering pricing and inventory decisions under uncertainty and disruption risks. The bi-level programming approach is used through this model to demonstrate the competition among two supply chains; the leader and the follower, respectively. After modelling the competition and applying pricing decisions by defining a price-dependent demand, disruption risks are analysed through the model. The proposed model simultaneously considers demand uncertainty and disruption risks and is capable of dealing with such uncertainties by implementing resilience strategies including, inventory decisions, and having a contract with reliable suppliers. Moreover, to consider the environmental issues, controlling CO2 emissions and managing the reverse flow were added to the model. Our approach to mitigate the problem uncertainties is to use the possibilistic programming method. The Karush-Kuhan-Tucker (K-K-T) optimality conditions are deployed to make a single-level equivalent form. Since the integrated model was bi-objective, the ϵ-constraint method is implemented to make a single objective integrated model. Finally, some managerial implications are discussed through an industrial case example.