A two-level pricing-inventory-routing problem in green Closed-loop supply chain: Bi-level programming and heuristic method

Document Type : Research Paper


1 Department of computer and industrial engineering, Birjand University of Technology,Birjand, Southern Khorasan, Iran

2 Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran

3 Department of Computer Science, Birjand University of Technology, Birjand, Southern Khorasan, Iran


In this paper, a bi-level mathematical formulation for a pricing-inventory-routing problem in the context of sustainable closed-loop supply chains is developed. The two levels are entitled as the upper level model and the lower level model. The upper level model (the leader model) tries to minimize greenhouse gas (GHG) emissions while the lower level model (the follower model) focuses on profit maximization. To solve the problem, an enumeration heuristic method based on knapsack problem and genetic algorithm (GA) is devised. The results show that the heuristic method is capable of obtaining high-quality solutions in reasonable CPU-times.


Main Subjects

Amirtaheri, O., Zandieh, M., Dorri, B., & Motameni, A. (2017). A bi-level programming approach for production-distribution supply chain problem. Computers & Industrial Engineering, 110, 527-537.
Aviso, K. B., Tan, R. R., Culaba, A. B., & Cruz, J. B. (2010). Bi-level fuzzy optimization approach for water exchange in eco-industrial parks. Process Safety and Environmental Protection, 88(1), 31-40.
Avlonitis, G. J., & Indounas, K. A. (2005). Pricing objectives and pricing methods in the services sector. Journal of services marketing, 19(1), 47-57.
Babagolzadeh, M., Shrestha, A., Abbasi, B., Zhang, Y., Woodhead, A., & Zhang, A. (2020). Sustainable cold supply chain management under demand uncertainty and carbon tax regulation. Transportation Research Part D: Transport and Environment, 80, 102245.
Biuki, M., Kazemi, A., & Alinezhad, A. (2020). An integrated location-routing-inventory model for sustainable design of a perishable products supply chain network. Journal of cleaner production, 120842.
Christensen, C. (2013). The innovator's dilemma: when new technologies cause great firms to fail: Harvard Business Review Press.
Dolgui, A., & Proth, J.-M. (2010). Pricing strategies and models. Annual Reviews in Control, 34(1), 101-110.
Ebrahimi M. and Tavakkoli-Moghadam R. (2020). Benders decomposition algorithm for a green closed-loop supply chain under a build-to-order environment, Journal of Industrial and Systems Engineering, 13, 102-111.
Farias, K., Hadj-Hamou, K., & Yugma, C. (2019). Mathematical formulations for a two-echelon inventory routing problem. IFAC-PapersOnLine, 52(13), 1996-2001.
Forghani, A., Dehghanian, F., Salari, M., & Ghiami, Y. (2020). A bi-level model and solution methods for partial interdiction problem on capacitated hierarchical facilities. Computers & Operations Research, 114, 104831.
Forouzanfar, F., Tavakkoli-Moghaddam, R., Bashiri, M., Baboli, A., & Molana, S. H. (2017). New mathematical modeling for a location–routing–inventory problem in a multi-period closed loop  supply chain in a car industry. Journal of Industrial Engineering International, 1-17.
Gao, J., Han, H., Hou, L., & Wang, H. (2016). Pricing and effort decisions in a closed loop  supply chain under different channel power structures. Journal of Cleaner Production, 112, 2043-2057.
Gholizadeh, H., Fazlollahtabar, H., & Khalilzadeh, M. (2020). A robust fuzzy stochastic programming for sustainable procurement and logistics under hybrid uncertainty using big data. Journal of cleaner production, 120640.
Golpîra, H., Najafi, E., Zandieh, M., & Sadi-Nezhad, S. (2017). Robust bi-level optimization for green opportunistic supply chain network design problem against uncertainty and environmental risk. Computers & Industrial Engineering, 107, 301-312.
Govindan, K., Soleimani, H., & Kannan, D. (2015). Reverse logistics and closed loop  supply chain: A comprehensive review to explore the future. European journal of operational research, 240(3), 603-626.
Guimarães, T. A., Coelho, L. C., Schenekemberg, C. M., & Scarpin, C. T. (2019). The two-echelon multi-depot inventory-routing problem. Computers & Operations Research, 101, 220-233.
Hsueh, C.-F. (2015). A bilevel programming model for corporate social responsibility collaboration in sustainable supply chain management. Transportation Research Part E: Logistics and Transportation Review, 73, 84-95.
Hadi, T., Sheikhmohammady, M., Chaharsooghi, S. K., & Hafezalkotob, A. (2021). Competition between regular and closed loop  supply chains under financial intervention of government; a game theory approach. Journal of Industrial and Systems Engineering, 13(2), 179-199.
Imran, M., Salman Habib, M., Hussain, A., Ahmed, N., & M Al-Ahmari, A. (2020). Inventory Routing Problem in Supply Chain of Perishable Products under Cost Uncertainty. Mathematics, 8(3), 382.
Jain, R. K., Martyniuk, A. O., Harris, M. M., Niemann, R. E., & Woldmann, K. (2003). Evaluating the commercial potential of emerging technologies. International journal of technology transfer and commercialisation, 2(1), 32-50.
Jangali, M. T., Makui, A., & Dehghani, E. (2020). Designing a closed loop supply chain network for engine oil in an uncertain environment: A case study in Behran Oil Company. Journal of Industrial and Systems Engineering, 13(2), 49-64.
Kaya, O., & Urek, B. (2016). A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain. Computers & Operations Research, 65, 93-103.
Khalafi, S., Hafezalkotob, A., Mohamaditabar, D., & Sayadi, M. K. (2020). A novel model for a network of a closed loop  supply chain with recycling of returned perishable goods: A case study of dairy industry. Journal of Industrial and Systems Engineering, 12(4), 136-153.
Khatami, M., Mahootchi, M., & Farahani, R. Z. (2015). Benders’ decomposition for concurrent redesign of forward and closed loop  supply chain network with demand and return uncertainties. Transportation Research Part E: Logistics and Transportation Review, 79, 1-21.
Kotler, P., & Armstrong, G. (2013). Principles of Marketing (16th Global Edition): Harlow: Pearson.
Krishnan, R., Agarwal, R., Bajada, C., & Arshinder, K. (2020). Redesigning a food supply chain for environmental sustainability–An analysis of resource use and recovery. Journal of cleaner production, 242, 118374.
Kumar, A., Mangla, S. K., Kumar, P., & Karamperidis, S. (2020). Challenges in perishable food supply chains for sustainability management: A developing economy perspective. Business Strategy and the Environment.
Liu, W., Wan, Z., Wan, Z., & Gong, B. (2020). Sustainable recycle network of heterogeneous pharmaceuticals with governmental subsidies and service-levels of third-party logistics by bi-level programming approach. Journal of cleaner production, 249, 119324.
Mohammadnejad, M., Abadi, I. N. K., Sadeghian, R., & Ahmadizar, F. (2016). An Efficient Imperialistic Competitive Algorithm for the Closed loop  Supply Chains Considering Pricing tor Product, and Fleet of Heterogeneous Vehicles. Transylvanian Review.
Moghadas Poor, B., Jabalameli, M. S., & Bozorgi-Amiri, A. (2020). A closed loop  supply chain network design with considering third party logistics: A case study. Journal of Industrial and Systems Engineering, 13(1), 92-110.
Munson, C. L., & Rosenblatt, M. J. (2001). Coordinating a three-level supply chain with quantity discounts. IIE Transactions, 33(5), 371-384.
Roghanian, E., Sadjadi, S. J., & Aryanezhad, M.-B. (2007). A probabilistic bi-level linear multi-objective programming problem to supply chain programming. Applied Mathematics and computation, 188(1), 786-800.
Rowshannahad, M., Absi, N., Dauzère-Pérès, S., & Cassini, B. (2018). Multi-item bi-level supply chain programming with multiple remanufacturing of reusable by-products. International Journal of Production Economics, 198, 25-37.
Sherafati, M., Bashiri, M., Tavakkoli-Moghaddam, R., & Pishvaee, M. S. (2020). Achieving sustainable development of supply chain by incorporating various carbon regulatory mechanisms. Transportation Research Part D: Transport and Environment, 81, 102253.
Soleimani, H., & Kannan, G. (2015). A hybrid particle swarm optimization and genetic algorithm for closed loop  supply chain network design in large-scale networks. Applied Mathematical Modelling, 39(14), 3990-4012.
Taleizadeh, A. A., & Noori-daryan, M. (2016). Pricing, manufacturing and inventory policies for raw material in a three-level supply chain. International Journal of Systems Science, 47(4), 919-931.
Wen, U.-P., & Hsu, S.-T. (1991). Linear bi-level programming problems—a review. Journal of the operational research society, 42(2), 125-133.
Xu, J., Deng, Y., Shi, Y., & Huang, Y. (2020). A bi-level optimization approach for sustainable development and carbon emissions reduction towards construction materials industry: a case study from China. Sustainable cities and society, 53, 101828.
Yue, D., & You, F. (2017). Stackelberg-game-based modeling and optimization for supply chain design and operations: A mixed integer bilevel programming framework. Computers & Chemical Engineering, 102, 81-95.
Zeballos, L. J., Méndez, C. A., Barbosa-Povoa, A. P., & Novais, A. Q. (2014). Multi-period design and programming of closed loop  supply chains with uncertain supply and demand. Computers & Chemical Engineering, 66, 151-164.
Zhalechian, M., Tavakkoli-Moghaddam, R., Zahiri, B., & Mohammadi, M. (2016). Sustainable design of a closed loop  location-routing-inventory supply chain network under mixed uncertainty. Transportation Research Part E: Logistics and Transportation Review, 89, 182-214.
Volume 13, Issue 4
November 2021
Pages 62-80
  • Receive Date: 04 March 2021
  • Revise Date: 02 May 2021
  • Accept Date: 07 June 2021
  • First Publish Date: 07 June 2021