A Single-Vendor Multi-Retailer VMI Partnership Under Individual Carbon-Cap Constraints

Vendor Managed Inventory (VMI) is increasingly being adopted as a mean of enhancing the efficiency of supply chain (SC) operations. In this paper, we consider a scenario where a vendor is responsible for managing the inventory of several retailers following a VMI partnership and subject to restrictions on their maximum inventory levels. To better reflect reality, we first propose a mixed integer nonlinear programming model where the vendor and the retailers operate under different environmental legislations with distinct carbon caps. Additionally, to further reduce chain-wide costs, the developed model is extended to allow for carbon exchange among SC members. We derive structural properties for both models to devise efficient exact solution algorithms. The resulting cost savings can be shared with SC members to ensure they are not worse off under the newly proposed "carbon cap and exchange" policy. The benefits of this enhanced collaborative scheme are illustrated through a small example involving a single vendor and five retailers. Furthermore, a one-way sensitivity analysis is conducted to evaluate the impact of the number of retailers and the restrictiveness of the SC members' carbon caps on the performance of the two proposed models. The obtained results indicate that carbon exchange among SC members is more advantageous for a larger number of retailers. Moreover, the implementation of the new carbon policy yields higher cost reductions when there are strict constraints on the SC members' carbon emissions.