A bi-level programming approach to the decision problems in a vendor-buyer eco-friendly supply chain

- A multi-product vendor-buyer supply chain considering environmental improvement is proposed.
- A bi-level programming approach is applied to determine the optimal decision problems.
- An effective solution approach has been proposed and evaluated.
- Managerial insights have been investigated with numerical examples.

This paper focuses on a multi-product vendor-buyer supply chain considering environmental factors in the product manufacturing process. We assume that the unit price charged by the buyer, the unit advertising expenditure and the vendor's unit environmental improvement influence the demand of the product being sold. The relationship between the vendor and the buyer is modeled by a non-cooperative game based on Stackelberg strategy framework under two power scenarios including vendor-leader model and buyer-leader model. A bi-level programming approach is applied to determine the optimal selling prices, advertising expenditures, wholesale prices, vendor's environmental improvements and ordering policies of the vendor and the buyer. Then, a modified differential evolution algorithm is proposed for solving the models. Numerical experiments carried out in this paper, including sensitivity analysis for some key parameters, evaluate the effectiveness of the models and compare the results between the different models considered. Several research findings have been obtained and explained.