On a Closed-Loop Supply Chain with Graded Returns

  • Najeeb Al-Matar Al-Baha University
  • Lotfi Tadj Alfaisal University Riyadh, Saudi Arabia
Keywords: Manufacturing; remanufacturing; quality; grading; optimal control; tracking.


We use optimal control theory to determine the optimal manufacturing, remanufacturing, and disposal rates in a closed-loop supply chain. The returned items are of different quality levels. The firm grades the returned items according to their quality. Each class of returned items is remanufactured and stocked separately. Also, all items are subject to deterioration and the deterioration rate depends on the class. Finally, each class of items is sold to a different segment of customers. An illustrative example is presented along with a sensitivity analysis on some of the system parameters.


Ansari, Z.N. and Daxini, S.D. (2022). A state-of-the-art review on metaheuristics application in remanufacturing, Archives of Computational Methods in Engineering, Vol. 29, 427-470, doi.org/10.1007/s11831-02109580-z.

Aziz, N.A., Adnan, N.A.A., Wahab, D.A., and Azman, A.H. (2021). Component design optimisation based on artificial intelligence in support of additive manufacturing repair and restoration: Current status and future outlook for remanufacturing, Journal of Cleaner Production, Vol. 296, 126401, doi:10.1016/j.jclepro.2021.126401.

Cai, X., Lai, M., Li, X., Li, Y., and Wu, X. (2014). Optimal acquisition and production policy in a hybrid manufacturing/remanufacturing system with core acquisition at different quality levels, European Journal of Operational Research, Vol. 233, No. 2, 374382, doi:10.1016/j.ejor.2013.07.017

Chakraborty, K., Mukherjee, K., Mondal, S., and Mitra, S. (2021). A systematic literature review and bibliometric analysis based on pricing related decisions in remanufacturing, Journal of Cleaner Production, Vol. 310, 127265, https://doi.org/10.1016/j.jclepro.2021.127265.

Chen, Z. and Huang, L. (2021). Digital twins for information-sharing in remanufacturing supply chain: A review, Energy, Vol. 220, 119712, doi.org/10.1016/j.energy.2020.119712. [6] Duong, Q.H., Zhou, L., Meng, M., Van Nguyen, T., Ieromonachou, P., and Nguyen, D.T. (2022). Understanding product returns: A systematic literature review using machine learning and bibliometric analysis, International Journal of Production Economics, Vol. 243, 108340, doi.org/10.1016/j.ijpe.2021.108340.

Farahani, S. (2018). Optimal Decision Making for Capacitated Reverse Logistics Networks with Quality Variations, Dissertation in Engineering, University of Wisconsin Milwaukee, WI.

Farahani, S., Otieno, W., and Omwando, T. (2019). The optimal disposition policy for remanufacturing systems with variable quality returns, Computers & Industrial Engineering, Col. 140, 106218. doi:10.1016/j.cie.2019.106218.

Feng, Y., Xia, X., Yin, X., Wang, L., and Zhang, Z. (2022). Pricing and coordination of remanufacturing supply chain with government participation considering consumers' preferences and quality of recycled products, Complexity, Volume 2022, Article ID 8378639, 25 pages, doi.org/10.1155/2022/8378639.

Ferguson, M., Guide, V.D., Koca, E., and Souza, G.C. (2009). The value of quality grading in remanufacturing, Production and Operations Management, Vol. 18, No. 3, 300-314. doi:10.1111/j.1937-5956.2009.01033.x.

Ferreira, C. and Gonçalves, G. (2021). A systematic review on life extension strategies in industry: The case of remanufacturing and refurbishment, Electronics, Vol. 10, 2669, doi.org/10.3390/electronics10212669.

Fofou, R.F., Jiang, Z., and Wang, Y. (2021). A review on the lifecycle strategies enhancing remanufacturing, Applied Science, Vol. 11, o. 12, 5937, doi.org/10.3390/app11135937.

Gaidhane, J., Ullah, I., Khalatkar, A. (2022). Tyre remanufacturing: A brief review, Materials Today: Proceedings, Vol. 60, Part 3, 2257-2261, doi.org/10.1016/j.matpr.2022.04.142.

Hu, Y., Xu, Y., and Jia, Y., (2021). Review of the optimization algorithms for remanufacturing disassembly line, 26th International Conference on Automation and Computing (ICAC), 2021, pp. 1-6, doi: 10.23919/ ICAC50006.2021.9594072. [15] Jia, Z. (2012). Essays on Auctions and Remanufacturing Strategies, Dissertation in Business Administration, The Smeal College of Business, The Pennsylvania State University, PA.

Jin, X. (2012). Modeling and Analysis of Remanufacturing Systems with Stochastic Returns and Quality Variation, Dissertation in Industrial and Operations Engineering, The University Of Michigan, MI.

Kang, C.M. and Hong, Y.S. (2012). Dynamic disassembly planning for remanufacturing of multiple types of products, International Journal of Production Research, Vol. 50, No. 22, 6236-6248. doi:10.1080/00207543.2011.616231.

Li, X., Li, Y., and Cai, X. (2015). On core sorting in RMTS and RMTO systems: A newsvendor framework, Decision Sciences, Vol. 47, No. 1, 60-93, doi:10.1111/deci.12152.

Okorie, O., Obi, M., Russell, J., Charnley, F., and Salonitis, K. (2021). A triple bottom line examination of product cannibalisation and remanufacturing: A review and research agenda, Sustainable Production and Consumption, Vol. 27, 958-974, doi.org/10.1016/j.spc.2021.02.013.

Peng, S., Ping, J., Li, T., Wang, F., Zhang, H., and Liu, C. (2022). Environmental benefits of remanufacturing mechanical products: A harmonized meta-analysis of comparative life cycle assessment studies, Journal of Environmental Management, Vol. 306, 114479, doi.org/10.1016/j.jenvman.2022.114479.

Rizova, I.M., Wong, T.C., and Ijomah, W. (2020). A systematic review of decision-making in remanufacturing. Computers & Industrial Engineering, 106681. doi:10.1016/j.cie.2020.106681.

Ropi, N.M., Hishamuddin, H., Abd Wahab, D., and Saibani, N. (2021). Optimisation models of remanufacturing uncertainties in closed-loop supply chains - A review, IEEE Access, Vol. 9, 160533-160551, doi: 10.1109/ACCESS.2021.3132096.

Salah, B., Ziout, A., Alkahtani, M., Alatefi, M., Abdelgawad, A., Badwelan, A., and Syarif, U. (2021). A qualitative and quantitative analysis of remanufacturing research, Processes, Vol. 9, 1766, doi.org/10.3390/pr9101766. [24] Sethi, S.P. (2019). Optimal Control Theory: Applications to Management Science and Economics, Third edition, Springer, Cham, Switzerland.

Shrivastava, A., Mukherjee, S., and Chakraborty, S.S. (2021). Addressing the challenges in remanufacturing by laser-based material deposition techniques, Optics & Laser Technology, Vol. 144, 107404, doi.org/10.1016/j.optlastec.2021.107404.

Souza, G.C., Ketzenberg, M.E., and Guide, V.D.R. (2009). Capacitated remanufacturing with service level constraints, Production and Operations Management, Vol. 11, No. 2, 231-248. doi:10.1111/j.19375956.2002.tb00493.x.

Sun, H., Chen, W., Liu, B., and Chen, X. (2018). Economic lot scheduling problem in a remanufacturing system with returns at different quality grades, Journal of Cleaner Production, Vol. 170, 559-569. doi:10.1016/j.jclepro.2017.09.184.

Tao, Z., Zhou, S.X., and Tang, C.S. (2012). Managing a remanufacturing system with random yield: Properties, observations, and heuristics, Production and Operations Management, Vol. 21, No. 5, 797-813. doi:10.1111/j.1937-5956.2011.01313.x.

Teixeira, E.L.S., Tjahjono, B., Beltran, M., and Julião, J. (2022). Demystifying the digital transition of remanufacturing: A systematic review of literature, Computers in Industry, Vol. 134, 103567, https://doi.org/10.1016/j.compind.2021.103567.

Xiong, Y., Li, G., Zhou, Y., Fernandes, K., Harrison, R., and Xiong, Z. (2014). Dynamic pricing models for used products in remanufacturing with lost-sales and uncertain quality, International Journal of Production Economics, Vol. 147, 678-688. doi:10.1016/j.ijpe.2013.04.025.

Yusoh, M.S.S, Abd Wahab, D., Habeeb A.H., Azman A.H. (2021). Intelligent systems for additive manufacturing-based repair in remanufacturing: A systematic review of its potential, Peer Journal of Computer Science, Vol. 7, Issue e808, doi.org/10.7717/peerj-cs.808.

Zhang, X., Liu, R., Yan, W., Wang, Y., and Subramanian, N. (2022). Systematic literature review on remanufacturing trade based on bibliometric analysis. Processes, Vol. 10, 596. doi.org/10.3390/pr10030596.

Zhang, X., Tang, Y., Zhang, H., Jiang, Z., and Cai, W. (2021). Remanufacturability evaluation of end-of-life products considering technology, economy and environment: A review, Science of The Total Environment, Vol. 764, 142922, doi.org/10.1016/j.scitotenv.2020.142922.

Zhang, X., Zou, B., Feng, Z., Wang, Y., Yan, W. (2022). A Review on remanufacturing reverse logistics network design and model optimization, Processes, Vol. 10, 84, doi.org/10.3390/pr10010084.

Zhou, S.X., Tao, Z., and Chao, X. (2011). Optimal control of inventory systems with multiple types of remanufacturable products, Manufacturing & Service Operations Management, Vol. 13, No. 1, 20-34. doi:10.1287/msom.1100.0298.

Zhu, X., Zhang, T., and Cao, Y. (2022). Managing production and inventory in a remanufacturing supply chain with two classes of cores under consignment stock agreement, International Transactions in Operational Research, doi.org/10.1111/itor.13175.

How to Cite
Al-Matar, N., & Tadj, L. (2023). On a Closed-Loop Supply Chain with Graded Returns. Statistics, Optimization & Information Computing, 11(2), 531-540. https://doi.org/10.19139/soic-2310-5070-1758
Research Articles