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

  • Hiromasa Ijuin The University of Electro-Communications
  • Yuki Kinoshita The University of Electro-Communications
  • Tetsuo Yamada The University of Electro-Communications
  • Aya Ishigaki Tokyo University of Science
  • Masato Inoue Meiji University
Keywords: Reverse logistics, Environmentally Conscious Manufacturing, Multi-Criteria Decision Making, End-of-Life Product, Recycling, Disassemly


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 endof-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.


H. F. Wang and S.M. Gupta, Green Supply Chain Management: Product Life Cycle Approach, McGraw-Hill, New York, NY, USA, 2011.

M. Eskandarpour, P. Dejax, J. Miemczyk, O. Péton, “Sustainable supply chain network design: an optimization-oriented review,” Omega, vol.54, pp.11-32, 2015.

K. Govindan, H. Soleimani, D. Kannan, “Reverse logistics and closed-loop supply chain: a comprehensive review to explore the future,” European Journal of Operational Research, vol.240, no.3, pp.603-626, 2015.

D. F. Blumberg, Introduction to Management of Reverse Logistics and Closed Loop Supply Chain Processes, Boca Raton, FL, USA, CRC Press, 2005.

A. Messac, S. M. Gupta, and B. Akbulut, “Linear physical programming: a new approach to multiple objective optimization,” Transactions on Operational Research, vol.8, no.2, pp.39-59, 1996.

M. A. Ilgin, S. M. Gupta, “Physical programming: a review of the state of the art,” Studies in Informatics and Control, vol.21, no.4, pp.349-366, 2012.

O. Ondemir, S. M. Gupta, “A multi-criteria decision making model for advanced repair-toorder and disassembly-to-order system,” European Journal of Operational Research, vol.233, no.2, pp.408-419, 2014.

R.K. Pati,R. Jans, R.K. Tyagi, “Green logistics network design: a critical review,” Production and Operations Management Society 24th Annual Conference, 6 pages, Denver, CO, USA, May, 2013.

A.Alshamsi, A. Diabat, “A reverse logistics network design,” Journal of Manufacturing Systems, vol.37, no.3, pp.589-598, 2015.

S. S. Kara , S. Onut, “A two-stage stochastic and robust programming approach to strategic planning of a reverse supply network: the case of paper recycling,” Expert Systems with Applications, vol.37, no.9, pp.6129-6137, 2010.

O. Listeş, R. Dekker, “A stochastic approach to a case study for product recovery network design,” European Journal of Operational Research, vol.160, no.1, pp.268-287, 2005.

H. Ijuin, T, Yamada, Y. Kinoshita, A. Ishigaki, M. Inoue, “Design of reverse supply chain network with material recovery analysis,” Journal of The Society of Plant Engineers Japan, vol.28, no.4, pp.147-159 2017 (in Japanese).

H. Ijuin, T, Yamada, A. Ishigaki, M. Inoue, “Modeling and analysis of reverse supply chain network with end-of-life product status for costs and recycling rate,” Northeast Decision Science Institute 2016 Annual Meeting, pp.120-125, Alexandria, VA,USA, March, 2016.

H. Ijuin, T, Yamada, A. Ishigaki, M. Inoue, “Reverse supply chain flows with material recovery constraint,” The 12th Biennial International Conference on Ecobalance 2016, Kyoto, Japan, October 2016.

F.S. Hillier, G.J. Lieberman, Introduction to Operations Research 8th Edition, McGrawHill, New York, NY, USA, 2005.

Hitachi, Ltd., EcoAssist, (Accessed on Feb. 12, 2019), (in Japanese).

T. Akahori, Y. Matsuno, Y. Adachi, N. Yamamoto, Y. Hamatsuka, T. Nishi, “Application of REM (Recyclability Evaluation Method) to home electric appliances: evaluation of recycling rates and costs,” Journal of Japan Society of Waste Management Experts, vol.19, no.1, pp.44-50, 2008 (in Japanese).

K. Igarashi, T. Yamada, M. Inoue, “2-stage optimal design and analysis for disassembly system with environmental and economic parts selection using the recyclability evaluation method,” International Journal of Industrial Engineering and Management Systems, vol.13 no.1, pp.52-66, 2014.