A comprehensive model for concurrent optimization of product family and its supply chain network design considering reverse logistic

Document Type : Research Paper


Department of Industrial Engineering, Amirkabir University of Technology (Tehran Polytechnic)


The study of product family and its design as well as issues related to supply chain is as fascinating discussion, and its modeling and optimization consider as a challenge for industries and businesses. In this paper, using a consolidated approach, a comprehensive model in the Mixed Integer Linear Program (MILP) dominant is proposed to concurrent optimization of product family and its supply chain network design by considering reverse logistics. In the proposed model, different levels of bill of material, including components, sub-assemblies, sub-sub-assemblies and finished products is considered while there is possibility of substitution at all levels. The supply chain network, includes 5 levels consist of suppliers, factories, distribution centers, customers and recycling centers. To solve low complexity instances in the view of products design and supply chain network structure, CPLEX solver has been applied. To solve high complexity instances, a heuristic method based on linear programming rounding has been developed, which caused a considerable reduction in solving time with an acceptable gap.


Main Subjects

Baud-Lavigne, B., Agard, B., & Penz, B. (2016). Simultaneous product family and supply chain design: An optimization approach. International Journal of production economics, 174, 111-118.
Baud-Lavigne, B., Bassetto, S., & Agard, B. (2016). A method for a robust optimization of joint product and supply chain design. Journal of Intelligent Manufacturing, 27(4), 741-749.
Bonev, M., Hvam, L., Clarkson, J., & Maier, A. (2015). Formal computer-aided product family architecture design for mass customization. Computers in Industry, 74, 58-70.
Byrka, J., Ghodsi, M., & Srinivasan, A. (2010). LP-rounding algorithms for facility-location problems. arXiv preprint arXiv:1007.3611.
Charikar, M., Khuller, S., Mount, D. M., & Narasimhan, G. (2001). Algorithms for facility location problems with outliers. Paper presented at the Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms.
Chen, H.-Y. (2010). The impact of item substitutions on production–distribution networks for supply chains. Transportation Research Part E: Logistics and Transportation Review, 46(6), 803-819.
Chiu, M. C., & Okudan, G. (2014). An investigation on the impact of product modularity level on supply chain performance metrics: an industrial case study. Journal of Intelligent Manufacturing, 25(1), 129-145.
Cornuéjols, G. (2007). Revival of the Gomory cuts in the 1990’s. Annals of Operations Research, 149(1), 63-66.
de Weck, O. L., Suh, E. S., & Chang, D. (2003). Product family and platform portfolio optimization. Paper presented at the ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.
Du, G., Jiao, R. J., & Chen, M. (2014). Joint optimization of product family configuration and scaling design by Stackelberg game. European Journal of Operational Research, 232(2), 330-341.
Fixson, S. K. (2005). Product architecture assessment: a tool to link product, process, and supply chain design decisions. Journal of operations management, 23(3-4), 345-369.
Gabow, H. N., Goemans, M. X., Tardos, É., & Williamson, D. P. (2009). Approximating the smallest k‐edge connected spanning subgraph by LP‐rounding. Networks, 53(4), 345-357.
Gokhan, N. M., Needy, K. L., & Norman, B. A. (2010). Development of a simultaneous design for supply chain process for the optimization of the product design and supply chain configuration problem. Engineering Management Journal, 22(4), 20-30.
H‘mida, F., & Martin, P. (2007). Costs estimation in design phase. Proceeding of CPI ‘07.
Hsuan Mikkola, J., & Skjøtt-Larsen, T. (2004). Supply-chain integration: implications for mass customization, modularization and postponement strategies. Production Planning & Control, 15(4), 352-361.
Hu, S., Zhu, X., Wang, H., & Koren, Y. (2008). Product variety and manufacturing complexity in assembly systems and supply chains. CIRP Annals-Manufacturing Technology, 57(1), 45-48.
Khajavirad, A., Michalek, J. J., & Simpson, T. W. (2009). An efficient decomposed multiobjective genetic algorithm for solving the joint product platform selection and product family design problem with generalized commonality. Structural and Multidisciplinary Optimization, 39(2), 187-201.
Labbi, O., Ouzizi, L., & Douimi, M. (2015). Simultaneous design of a product and its supply chain integrating reverse logistic operations: An optimization model. Paper presented at the Xème Conférence Internationale: Conception et Production Intégrées.
Lamothe, J., Hadj-Hamou, K., & Aldanondo, M. (2006). An optimization model for selecting a product family and designing its supply chain. European Journal of Operational Research, 169(3), 1030-1047.
Laurentie, J., Berthelemy, F., Grégoire, L., & Terrier, C. (2006). Logistic processes and methods. Supply chain Management, AFNOR.
Magazine, M. J., & Chern, M.-S. (1984). A note on approximation schemes for multidimensional knapsack problems. Mathematics of Operations Research, 9(2), 244-247.
Mansoornejad, B., Chambost, V., & Stuart, P. (2010). Integrating product portfolio design and supply chain design for the forest biorefinery. Computers & chemical engineering, 34(9), 1497-1506.
Melo, M. T., Nickel, S., & Da Gama, F. S. (2006). Dynamic multi-commodity capacitated facility location: a mathematical modeling framework for strategic supply chain planning. Computers & Operations Research, 33(1), 181-208.
Melo, T., Nickel, S., & Saldanha-da-Gama, F. (2009). An LP-rounding heuristic to solve a multi-period facility relocation problem.
Meyer, M. H., & Lehnerd, A. P. (1997). The power of product platforms: Simon and Schuster.
Meyer, M. H., & Utterback, J. M. (1993). The product family and the dynamics of core capability. Sloan management review, 34(3), 29.
Mostafavi, M. (2014). The Design of supply chain configuration for a new product in the case of multi supplier selection. Tarbiat Modares University.  
Nepal, B., Monplaisir, L., & Famuyiwa, O. (2012). Matching product architecture with supply chain design. European Journal of Operational Research, 216(2), 312-325.
Petersen, K. J., Handfield, R. B., & Ragatz, G. L. (2005). Supplier integration into new product development: coordinating product, process and supply chain design. Journal of operations management, 23(3-4), 371-388.
Porter, M. E. (2008). The five competitive forces that shape strategy. Harvard business review, 86(1), 25-40.
Rezapour, S., Hassani, A., & Farahani, R. Z. (2015). Concurrent design of product family and supply chain network considering quality and price. Transportation Research Part E: Logistics and Transportation Review, 81, 18-35.
Robertson, D., & Ulrich, K. (1998). Planning for product platforms. Sloan management review, 39(4), 19.
Ruijter, E., Scheffelaar, R., & Orru, R. V. (2011). Multicomponent reaction design in the quest for molecular complexity and diversity. Angewandte Chemie International Edition, 50(28), 6234-6246.
Seitz, M. A., & Peattie, K. (2004). Meeting the closed-loop challenge: the case of remanufacturing. California management review, 46(2), 74-89.
Simpson, T. W., Bobuk, A., Slingerland, L. A., Brennan, S., Logan, D., & Reichard, K. (2012). From user requirements to commonality specifications: an integrated approach to product family design. Research in Engineering Design, 23(2), 141-153.
Stefansdottir, B., & Grunow, M. (2018). Selecting new product designs and processing technologies under uncertainty: Two-stage stochastic model and application to a food supply chain. International Journal of Production Economics, 201, 89-101.
Üster, H., Easwaran, G., Akçali, E., & Çetinkaya, S. (2007). Benders decomposition with alternative multiple cuts for a multi‐product closed‐loop supply chain network design model. Naval Research Logistics (NRL), 54(8), 890-907.
Wang, D., Du, G., Jiao, R. J., Wu, R., Yu, J., & Yang, D. (2016). A Stackelberg game theoretic model for optimizing product family architecting with supply chain consideration. International Journal of production economics, 172, 1-18.
Yang, D., Jiao, J. R., Ji, Y., Du, G., Helo, P., & Valente, A. (2015). Joint optimization for coordinated configuration of product families and supply chains by a leader-follower Stackelberg game. European Journal of Operational Research, 246(1), 263-280.
Young, A. (2005). Increasing returns and economic progress Readings In The Economics Of The Division Of Labor: The Classical Tradition (pp. 234-248): World Scientific.
Yu, Y., & Huang, G. Q. (2010). Nash game model for optimizing market strategies, configuration of platform products in a Vendor Managed Inventory (VMI) supply chain for a product family. European Journal of Operational Research, 206(2), 361-373.
Zhu, W., & He, Y. (2017). Green product design in supply chains under competition. European Journal of Operational Research, 258(1), 165-180.
Volume 11, Issue 4 - Serial Number 4
November 2018
Pages 116-131
  • Receive Date: 22 April 2018
  • Revise Date: 29 June 2018
  • Accept Date: 28 October 2018
  • First Publish Date: 29 November 2018