Designing Reverse Supply Chain Network with Costs and Recycling Rate by Using Linear Physical Programming

In recent years, economic growth and an increasing population have led to increased consumption of numerous amounts of assembly products and material resources all over the world. As the result, material shortages have become a serious global problem. To circulate materials from end-of-life (EOL) assembly products, manufacturers have to design reverse supply chain networks for EOL products. The reverse supply chain includes transportation of the EOL products from collection centers to recovery and/or disposal facilities. There are costs involved in recycling, transporting the EOL products and opening facilities. In addition, the EOL product statuses differ by user situation, and the recycling rate and cost of each product and part are dependent on the statuses. To design a reverse supply chain network, a decision maker (DM) decides the transportation route, the number of products on each route, and the production volumes at each facility to minimize the total cost while maximizing the recycling rate of the whole network. However, the relationship between the recycling rate and the total cost becomes a tradeoff. Therefore, the DM has to solve these issues simultaneously. On the other hand, Linear Physical Programming (LPP) is one of the effective methods for solving multi-objective problems. It allows the DM to express desirable ranges for each criterion. One of the most significant advantages of using LPP is that the DM does not need to specify the mathematical weights for each criterion. This study designs a bi-objective reverse supply chain network to collect and recycle the EOL assembly products using LPP. First, based on our previous study, the reverse supply chain network is modeled to transport the EOL products from collection centers to recycling facilities depending on the EOL product status, which includes the possible recycling cost and rate. Next, the reverse supply chain network is formulated using LPP to minimize the total cost while maintaining the recycling rate of the whole network. Third, a case study is conducted and the results obtained by the LPP and the integer programming from our previous study are compared. Finally, the sensitivity analysis for facility cost and the effect of changing the preference ranges of objective functions are investigated.