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

Document Type : Article


1 Deportment of Industrial Engineering, University of Science and Technology of Mazandaran, Beshahr, Iran

2 Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr

3 Department of Electrical Engineering, École de Technologie Supérieure, University of Québec, Montréal, Canada

4 1-School of Mechanical Engineering, Shandong University, Jinan, 250061, China 2-Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), Shandong University, Jinan 250061, China 3-National Demonstration Center for Experimental Mechanical Engineering Education, Shandong University, Jinan 250061, China


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 Non-dominated 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) are firstly applied in this research area. The results of metaheuristics are checked by the ε-constraint method in a set of small-scale samples as compared with the results of literature. Finally, the outputs confirm that the allowed shortage situation along with the lack of cost reduction shows a greater amount of shipping and orders. As such, the performance of MORDA is approved in comparison with MOKA and NSGA-II through different criteria.