Generally, finding an alternative solution for reducing fossil fuel consumption and green emissions of supply chain networks can shift the Vendor Managed Inventory (VMI) to the Green VMI (GVMI). Our literature search also confirms that the issue of environmental pollution and green emissions, is still scarce and required to be explored. This motivates our attempt to offer the issue of green backorder for the VMI in a two-echelon supply chain network among the first studies. To this end, a bi-objective non-linear optimization model with the goal of maximizing the profit of inventory and minimizing the carbon emissions of transportation, simultaneously, is developed. Another contribution of this work is to propose three capable metaheuristics to solve it optimality in large-scale samples. In this regard, the Nondominated Sorting Genetic Algorithm (NSGA-II) as a well-known method as well as Multi-Objective of Keshtel Algorithm (MOKA) and Multi-Objective of Red Deer Algorithm (MORDA) as two recent nature-inspired algorithms are firstly applied. The outputs confirm that the allowed shortage situation along with the lack of cost reduction shows a greater amount of shipping and orders based on sensitivities. With regards to the comparison among algorithms, the performance of MORDA is highly better than MOKA and NSGA-II.