Metaheuristics for a bi-objective green vendor managed inventory problem in a two-echelon supply chain network

Generally, finding an alternative solution for reducing fossil fuel consumption and greenhouse emissions of supply chain networks can shift Vendor Managed Inventory (VMI) to Green Vendor Managed Inventory (GVMI). Our literature search also confirms that the issue of environmental pollution and greenhouse emissions remains unfinished and requires further exploration. This motivates our attempt to o er 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 optimally solve the problem in large-scale samples. In this respect, the Non-dominated Sorting Genetic Algorithm-II (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 applied first. The outputs confirm that the allowed shortage and failure to reduce costs point to the greater amount of shipping and orders based on sensitivities. With regard to the comparison made among algorithms, the MORDA significantly outperforms MOKA and NSGA-II.