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A Multi-objective Mathematical Optimization Approach to a Three-echelon Green Supply Chain Management Subject to Disruption at Plant Md. Ahnaf Sadat and Md. Doulotuzzaman Xames Department of Industrial and Production Engineering Bangladesh University of Engineering and Technology Dhaka-1000, Bangladesh [email protected] , [email protected] Abdullahil Azeem Department of Industrial and Production Engineering Bangladesh University of Engineering and Technology Dhaka-1000, Bangladesh [email protected] Abstract The objective of this research is to develop a reactive mitigation plan for a three-echelon Green Supply Chain Management where disruptions occur at manufacturing plants. The mathematical model developed here is a multi-objective optimization problem which at the same time minimizes both total supply chain cost and total CO 2 emission. This model considers back order, lost sales and outsourcing costs to mitigate the effects of disruptions. The multi-objective optimization problem is formulated as a single-objective one by using Weighted Sum approach and ε -constraint approach. For solution methodology, Branch and Cut algorithm is used. Then the solutions from two approaches are compared and discussed hereafter. Keywords Green Supply Chain, Disruption, Outsourcing Cost, Lost Sales Cost, Branch and Cut Algorithm, Weighted Sum Approach 1. Introduction A supply chain is a network that receives inputs or raw materials from suppliers, produces final products at its manufacturing facilities and delivers those products to customers through a distribution network. An ideal three- echelon supply chain network has multiple entities (such as manufacturing plants, distribution centers and retailers) in each echelon. A supply chain network that considers environmental impacts is termed as Green Supply Chain (GSC). As the concerns for our environment is increasing day by day, the GSC is emerging in business sectors. Most of the companies are focusing on this issue. The environmental impacts could be the carbon dioxide (CO 2 ) emission during the transportation and production, and the waste from scrapped products etc. Supply chain can face many uncontrollable problems, which cannot be predicted in advance. Interruptions of any forms are called disruptions in supply chain. The disruptions at plant can occur due to- material shortage, machine breakdown, labor strike, or any form of man-made or accidental disturbances. A considerable number of studies on disruptions management can be found in the supply chain literature. In the early 1990s, researchers tended to embed supply disruptions into classical inventory models (2015). Examples include Arreola-Risa & DeCroix (1998), Berk & Arreola-Risa (1994), Gupta (1996), Parlar & Berkin (1991), and Parlar (1997). In a similar fashion, following an economic production quantity (EPQ) system, Xia et al. (2004) developed a disruption recovery model and suggest a production/inventory plan so as to restore the original (pre-disruption) production plan. The most recent works include the works of Paul et al. (2014). They developed a reactive mitigation 44
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