N. Torabi - Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
R. Tavakkoli-Moghaddam - School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran | Arts et Métiers ParisTech, LCFC, Metz, France
E. Najafi - Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
. Hosseinzadeh-Lotfi - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

This paper presented a new two-stage green supply chain network, in which includes two innovations. Firstly, it presents a new multi-objective model for a two-stage green supply chain problem that considers the amount of shortage in the network, reworking, and carbon-trading cost produced in the green supply chain. Secondly, because of the complexity of this model, it uses a new multi-objective interior search algorithm (MOISA) to solve the presented model. The obtained results of the proposed algorithm were compared with the results of other multi-objective meta-heuristics, namely MOPSO, SPEA2, and NSGA-II. The outcomes demonstrate that the proposed MOISA gives better Pareto solutions and indicates the superiority of the proposed algorithm in most cases. This paper presented a new two-stage green supply chain network, in which includes two innovations. Firstly, it presents a new multi-objective model for a two-stage green supply chain problem that considers the amount of shortage in the network, reworking, and carbon-trading cost produced in the green supply chain. Secondly, because of the complexity of this model, it uses a new multi-objective interior search algorithm (MOISA) to solve the presented model. The obtained results of the proposed algorithm were compared with the results of other multi-objective meta-heuristics, namely MOPSO, SPEA2, and NSGA-II. The outcomes demonstrate that the proposed MOISA gives better Pareto solutions and indicates the superiority of the proposed algorithm in most cases.

Green Supply Chain Network, Multi-Objective Optimization, Carbon Price, Interior search algorithm, meta-heuristic algorithm