PMID- 32767212 OWN - NLM STAT- MEDLINE DCOM- 20201125 LR - 20210723 IS - 1614-7499 (Electronic) IS - 0944-1344 (Linking) VI - 27 IP - 35 DP - 2020 Dec TI - Mathematical modeling for green supply chain considering product recovery capacity and uncertainty for demand. PG - 44378-44395 LID - 10.1007/s11356-020-10331-z [doi] AB - Competition in today's market is the most important concern of companies and producers in free markets. Buyers are also looking for higher quality and lower prices. Manufacturers should, therefore, reduce production costs and increase budgets for research and product development. On the other hand, the limitation of mineral resources in each country and in the world in general is a very important factor for increasing the price of raw materials which increases the cost of production of a product. In this study, a green aspect of decision-making, concurrent modeling for inventory-routing, and application of maximum entropy (ME) method for overcoming uncertainties of demands are applied to optimize the usage of raw materials and returning of defective products to the production cycle in a closed-looped supply chain under multi-period planning horizon. Also, dynamic modeling is used to balance the inventory level in all stages of the network that leads to optimum usage of the raw materials. For this purpose, the first objective function reduces production, transportation-routing, and inventory costs, and the second objective reduces greenhouse gas emissions through all levels of the network. Finally, this model is solved by using the exact solution method with the help of Gams software as well as the non-dominated sorting genetic algorithm II (NSGAII) and multi-objective particle swarm optimization (MOPSO) algorithm. Sensitivity analysis has been performed on failure rates, greenhouse gas emissions during recycling and production, and the optimistic-pessimistic coefficient of the ME solution method. Solution methods have been compared using several criteria, and the NSGAII method has finally obtained the best result. The results show that the manager should pay more costs in order to prevent backorder demands. Also, collecting the more defective products leads to increasing production amount since the collective products can return to the production line. Finally, it is required for the managers to control products' failure rate to optimize capacity usage in the model. FAU - Mehrbakhsh, Sanaz AU - Mehrbakhsh S AD - School of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran. FAU - Ghezavati, Vahidreza AU - Ghezavati V AD - School of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran. v_ghezavati@azad.ac.ir. LA - eng PT - Journal Article DEP - 20200807 PL - Germany TA - Environ Sci Pollut Res Int JT - Environmental science and pollution research international JID - 9441769 RN - 0 (Greenhouse Gases) SB - IM MH - Algorithms MH - *Greenhouse Gases MH - *Models, Theoretical MH - Transportation MH - Uncertainty OTO - NOTNLM OT - Closed-loop supply chain OT - Green supply chain OT - Greenhouse gas emissions OT - Maximum entropy method OT - Meta-heuristics OT - Optimistic-pessimistic approach EDAT- 2020/08/09 06:00 MHDA- 2020/11/26 06:00 CRDT- 2020/08/09 06:00 PHST- 2020/02/27 00:00 [received] PHST- 2020/07/30 00:00 [accepted] PHST- 2020/08/09 06:00 [pubmed] PHST- 2020/11/26 06:00 [medline] PHST- 2020/08/09 06:00 [entrez] AID - 10.1007/s11356-020-10331-z [pii] AID - 10.1007/s11356-020-10331-z [doi] PST - ppublish SO - Environ Sci Pollut Res Int. 2020 Dec;27(35):44378-44395. doi: 10.1007/s11356-020-10331-z. Epub 2020 Aug 7.