Robust optimization to design a four-echelon perishable supply chain under stochastic deterioration rate: A case study.

Document Type : Research Paper


1 Department of Industrial Management, Kish Campus, University of Tehran, Kish, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

3 Department of Industrial Management, Faculty of Management, University of Tehran, Tehran, Iran


The perishable dairy industry has to deal with multiple challenges such as demand forecasting, price fluctuations, lead time, and inflated orders along with difficulties of climatic and traffic conditions, storage areas and shipment in unfavorable circumstances. This research introduces a robust bi-level mathematical model to optimize a multi-echelon Perishable Supply Chain (PSC. To this end, integrated multi-objective Mixed Integer Linear Programming (MILP) models are developed to formulate the problem. stochastic deterioration rate is taken into account as the main factor that determines model performance due to perishability of products. In order to contribute to the literature, mainly by addressing uncertainty and perishability, a solution technique based on robust programming and -constrait approach is developed to accommodate suggested bi-level model. This technique can deal with problem uncertainty while also ensuring the robustness of the overall system. Sensitivity analysis is implemented along with three well-known quality indicators to assess the performance of the proposed solution method and quality of obtained solutions. Finally, real case study is provided using the CPLEX solver to showcase the applicability of the proposed methodology and discuss the complexity of the model. Results demonstrate the efficiency of the proposed methodology in finding optimal solutions.


Main Subjects

Accorsi, R., Ferrari, E., & Manzini, R. (2019). Modeling inclusive food supply chains toward sustainable ecosystem planning. In Sustainable Food Supply Chains: Planning, Design, and Control through Interdisciplinary Methodologies (pp. 1–21). Elsevier.
Aggarwal, R. (2018). A chance constraint based low carbon footprint supply chain configuration for an FMCG product. Management of Environmental Quality: An International Journal, 29(6), 1002–1025.
Aghaei, J., Amjady, N., & Shayanfar, H. A. (2011). Multi-objective electricity market clearing considering dynamic security by lexicographic optimization and augmented epsilon constraint method. Applied Soft Computing Journal, 11(4), 3846–3858.
Aghezzaf, E. H., Sitompul, C., & Najid, N. M. (2010). Models for robust tactical planning in multi-stage production systems with uncertain demands. Computers and Operations Research, 37(5), 880–889.
Azami, A., Jabarzadeh, A., & Makoi, A. (2017). Presenting a robust optimization model for integrated production planning considering postponement policy. Specialized Journal of Industrial Engineering (Special to the 12th International Conference on Industrial Engineering)., 389–404.
Bakhsh, N. J., & Tawhidi, H. (2020). Competitive design of perishable goods logistics chain network based on optimizing demand and increasing customer satisfaction.
Bortolini, M., Galizia, F. G., Mora, C., Botti, L., & Rosano, M. (2018). Bi-objective design of fresh food supply chain networks with reusable and disposable packaging containers. Journal of Cleaner Production, 184, 375–388.
Bottani, E., Murino, T., Schiavo, M., & Akkerman, R. (2019). Resilient food supply chain design: Modelling framework and metaheuristic solution approach. Computers and Industrial Engineering, 135, 177–198.
Chernonog, T. (2020). Inventory and marketing policy in a supply chain of a perishable product. International Journal of Production Economics, 219, 259–274.
Dagne, T. B., Jayaprakash, J., & Geremew, S. (2020). Design of supply chain network model for perishable products with stochastic demand: An optimized model. Journal of Optimization in Industrial Engineering, 13(1), 29–37.
Darestani, S. A., & Hemmati, M. (2019). Robust optimization of a bi-objective closed-loop supply chain network for perishable goods considering queue system. Computers and Industrial Engineering, 136, 277–292.
Deng, X., Yang, X., Zhang, Y., Li, Y., & Lu, Z. (2019). Risk propagation mechanisms and risk management strategies for a sustainable perishable products supply chain. Computers and Industrial Engineering, 135, 1175–1187.
Diabat, A., Jabbarzadeh, A., & Khosrojerdi, A. (2019). A perishable product supply chain network design problem with reliability and disruption considerations. International Journal of Production Economics, 212, 125–138.
Eskandari-Khanghahi, M., Tavakkoli-Moghaddam, R., Taleizadeh, A. A., & Amin, S. H. (2018). Designing and optimizing a sustainable supply chain network for a blood platelet bank under uncertainty. Engineering Applications of Artificial Intelligence, 71, 236–250.
Ghezavati, V. R., Hooshyar, S., & Tavakkoli-Moghaddam, R. (2017). A Benders’ decomposition algorithm for optimizing distribution of perishable products considering postharvest biological behavior in agri-food supply chain: a case study of tomato. Central European Journal of Operations Research, 25(1), 29–54.
Govindan, K., Jafarian, A., Khodaverdi, R., & Devika, K. (2014). Two-echelon multiple-vehicle location-routing problem with time windows for optimization of sustainable supply chain network of perishable food. International Journal of Production Economics, 152, 9–28.
Grillo, H., Alemany, M. M. E., Ortiz, A., & Fuertes-Miquel, V. S. (2017). Mathematical modelling of the order-promising process for fruit supply chains considering the perishability and subtypes of products. Applied Mathematical Modelling, 49, 255–278.
Hsu, H. W. (2019). A Compromise Programming Model for Perishable Food Logistics under Environmental Sustainability and Customer Satisfaction. 2019 IEEE 6th International Conference on Industrial Engineering and Applications, ICIEA 2019, 294–298.
Jonkman, J., Barbosa-Póvoa, A. P., & Bloemhof, J. M. (2019). Integrating harvesting decisions in the design of agro-food supply chains. European Journal of Operational Research, 276(1), 247–258.
Jouzdani, J., & Govindan, K. (2021). On the sustainable perishable food supply chain network design: A dairy products case to achieve sustainable development goals. Journal of Cleaner Production, 278.
Kalbadi, S. M., & Barkinejad., M. S. (2020). Development of closed supply chain network considering environmental factors and inventory location decisions under uncertainty conditions. Scientific Journal of Supply Chain Management., 67, 5–2022.
Khan, F. J., & Yacoubi., H. (2016). Presenting a robust mathematical model and innovative solution algorithm for the integrated production problem of inventory routing of perishable products with lateral transfer.
Khan, M. A. A., Shaikh, A. A., Panda, G. C., Konstantaras, I., & Cárdenas-Barrón, L. E. (2020). The effect of advance payment with discount facility on supply decisions of deteriorating products whose demand is both price and stock dependent. International Transactions in Operational Research, 27(3), 1343–1367.
Komasi, H., & Hashem., S. M. J. M. Al. (2020). Designing a sustainable supply chain network using lean principles. of supply chain management, year 22, number 69.
Ma, X., Bai, Q., Islam, S. M., Wang, S., & Liu, X. (2019). Coordinating a three-echelon fresh agricultural products supply chain considering freshness-keeping effort with asymmetric information. Applied Mathematical Modelling, 67, 337–356.
Mahmoudi, A., Seyedhosseini, S. M., Pishvaee A Mahmoudi, M. S., & Student, G. (n.d.). A location-inventory model for perishable products in global supply chain.
Mavrotas, G. (2009). Introduction: Development aid - Theory, policies, and performance. In Review of Development Economics (Vol. 13, Issue 3 SPEC. ISS., pp. 373–381).
Mohebalizadehgashti, F., Zolfagharinia, H., & Amin, S. H. (2020). Designing a green meat supply chain network: A multi-objective approach. International Journal of Production Economics, 219, 312–327.
Mulvey, J. M., & RuszczyƄski, A. (1995). A New Scenario Decomposition Method for Large-Scale Stochastic Optimization. In Operations Research (Vol. 43, Issue 3).
Musavi, M. M., & Bozorgi-Amiri, A. (2017). A multi-objective sustainable hub location-scheduling problem for perishable food supply chain. Computers and Industrial Engineering, 113, 766–778.
Onggo, B. S., Panadero, J., Corlu, C. G., & Juan, A. A. (2019). Agri-food supply chains with stochastic demands: A multi-period inventory routing problem with perishable products. Simulation Modelling Practice and Theory, 97.
Rahbari, A., Nasiri, M. M., Werner, F., Musavi, M. M., & Jolai, F. (2019). The vehicle routing and scheduling problem with cross-docking for perishable products under uncertainty: Two robust bi-objective models. Applied Mathematical Modelling, 70, 605–625.
Rashidi, S., Saghaei, A., Sadjadi, S. J., & Sadi-Nezhad, S. (2016). Optimizing supply chain network design with location-inventory decisions for perishable items: A Pareto-based MOEA approach. Scientia Iranica, 23(6), 3035–3045.
Sahebjamnia, N., Goodarzian, F., & Hajiaghaei-Keshteli, M. (2020). Optimization of multi-period three-echelon citrus supply chain problem. Journal of Optimization in Industrial Engineering, 13(1), 39–53.
Savadkoohi, E., Mousazadeh, M., & Torabi, S. A. (2018). A possibilistic location-inventory model for multi-period perishable pharmaceutical supply chain network design. Chemical Engineering Research and Design, 138, 490–505.
Sazvar, Z., & Sepehri, M. (2020). An integrated replenishment-recruitment policy in a sustainable retailing system for deteriorating products. Socio-Economic Planning Sciences, 69.
Sazvar, Z., Sepehri, M., & Baboli, A. (2016). A Multi-objective Multi-Supplier Sustainable Supply Chain with Deteriorating Products, Case of Cut Flowers. IFAC-PapersOnLine, 49(12), 1638–1643.
Scholten, K., & Fynes, B. (2017). Risk and Uncertainty Management for Sustainable Supply Chains. Springer Series in Supply Chain Management, 4, 413–436.
Shafiee, F., Kazemi, A., Jafarnejad, A., Sazvar, Z., & Amoozad Mahdiraji, H. (2020). Proposing a Robust Optimization Model for Sustainable Supply Chain of Perishable Dairy Products (Vol. 11, Issue 22). Production and Operations Management.
Shafiee, F., Kazemi, A., Jafarnejad Chaghooshi, A., Sazvar, Z., & Amoozad Mahdiraji, H. (2021). A robust multi-objective optimization model for inventory and production management with environmental and social consideration: A real case of dairy industry. Journal of Cleaner Production, 294.
Shrivastava, H., Dutta, P., Krishnamoorthy, M., & Suryawanshi, P. (2018). A Supply Chain Design of Perishable Products Under Uncertainty. In Transactions on Engineering Technologies (pp. 71–86). Springer Singapore.
Tavakkoli Moghaddam, S., Javadi, M., & Hadji Molana, S. M. (2019). A reverse logistics chain mathematical model for a sustainable production system of perishable goods based on demand optimization. Journal of Industrial Engineering International, 15(4), 709–721.
Tirkolaee, E. B., & Aydin, N. S. (2022). Integrated design of sustainable supply chain and transportation network using a fuzzy bi-level decision support system for perishable products. Expert Systems with Applications, 195.
Yadav, V. S., Singh, A. R., Gunasekaran, A., Raut, R. D., & Narkhede, B. E. (2022). A systematic literature review of the agro-food supply chain: Challenges, network design, and performance measurement perspectives. In Sustainable Production and Consumption (Vol. 29, pp. 685–704). Elsevier B.V.
Yavari, M., & Geraeli, M. (2019). Heuristic method for robust optimization model for green closed-loop supply chain network design of perishable goods. Journal of Cleaner Production, 226, 282–305.
Yavari, M., & Zaker, H. (2020). Designing a resilient-green closed loop supply chain network for perishable products by considering disruption in both supply chain and power networks. Computers and Chemical Engineering, 134.
Yazdani, M., Torkayesh, A. E., Chatterjee, P., Fallahpour, A., Montero-Simo, M. J., Araque-Padilla, R. A., & Wong, K. Y. (2022). A fuzzy group decision-making model to measure resiliency in a food supply chain: A case study in Spain. Socio-Economic Planning Sciences.
Zandkarimkhani, S., Mina, H., Biuki, M., & Govindan, K. (2020). A chance constrained fuzzy goal programming approach for perishable pharmaceutical supply chain network design. Annals of Operations Research, 295(1), 425–452.
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.