In this research, an agro-supply chain in the context of both economic and environmental issues has been investigated. To this end, a bi-objective model is formulated as a mixed-integer linear programming that aims to minimize the total costs and CO2 emissions. It generates the integration between purchasing, transporting, and storing decisions, considering specific characteristics of agro-products such as seasonality, perishability, and uncertainty. This study provides a different set of temperature conditions for preserving products from spoilage. In addition, a robust optimization approach is used to tackle the uncertainty in this paper. Then, \(\varepsilon\)-constraint method is used to convert the bi-objective model to a single one. To solve the problem, Lagrangian relaxation algorithm is applied as an efficient approach giving lower bounds for the original problem and used for estimating upper bounds. At the end, a real case study is presented to give valuable insight via assessing the impacts of uncertainty in system costs.
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Accorsi, R., Gallo, A., & Manzini, R. (2017). A climate driven decision-support model for the distribution of perishable products. Journal of Cleaner Production, 165, 917–929. https://doi.org/10.1016/j.jclepro.2017.07.170.
Allaoui, H., Guo, Y., Choudhary, A., & Bloemhof, J. (2018). Sustainable agro-food supply chain design using two-stage hybrid multi-objective decision-making approach. Computers & Operations Research, 89, 369–384. https://doi.org/10.1016/j.cor.2016.10.012.
Amin, S. H., & Zhang, G. (2013). A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return. Applied Mathematical Modelling, 37(6), 4165–4176. https://doi.org/10.1016/j.apm.2012.09.039.
Atabaki, M. S., & Aryanpur, V. (2018). Multi-objective optimization for sustainable development of the power sector: An economic, environmental, and social analysis of Iran. Energy, 161, 493–507. https://doi.org/10.1016/j.energy.2018.07.149.
Banasik, A., Kanellopoulos, A., Claassen, G., Bloemhof-Ruwaard, J. M., & van der Vorst, J. G. (2017). Closing loops in agricultural supply chains using multi-objective optimization: A case study of an industrial mushroom supply chain. International Journal of Production Economics, 183, 409–420. https://doi.org/10.1016/j.ijpe.2016.08.012.
Behzadi, G., O’Sullivan, M. J., Olsen, T. L., Scrimgeour, F., & Zhang, A. (2017). Robust and resilient strategies for managing supply disruptions in an agribusiness supply chain. International Journal of Production Economics, 191, 207–220. https://doi.org/10.1016/j.ijpe.2017.06.018.
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35–53. https://doi.org/10.1287/opre.1030.0065.
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. https://doi.org/10.1016/j.jclepro.2018.02.231.
Boschiero, M., Zanotelli, D., Ciarapica, F. E., Fadanelli, L., & Tagliavini, M. (2019). Greenhouse gas emissions and energy consumption during the post-harvest life of apples as affected by storage type, packaging and transport. Journal of Cleaner Production, 220, 45–56. https://doi.org/10.1016/j.jclepro.2019.01.300.
Bourlakis, M. A., & Weightman, P. W. (2004). Food supply chain management. Wiley Online Library. https://doi.org/10.1002/9780470995556.
Cheraghalipour, A., Paydar, M. M., & Hajiaghaei-Keshteli, M. (2018). A bi-objective optimization for citrus closed-loop supply chain using Pareto-based algorithms. Applied Soft Computing, 69, 33–59. https://doi.org/10.1016/j.asoc.2018.04.022.
Coello, C. A. C., Lamont, G. B., & Van Veldhuizen, D. A. (2007). Evolutionary algorithms for solving multi-objective problems (Vol. 5). Berlin : Springer. https://doi.org/10.1007/978-0-387-36797-2.
Costa, A. M., dos Santos, L. M. R., Alem, D. J., & Santos, R. H. (2014). Sustainable vegetable crop supply problem with perishable stocks. Annals of Operations Research, 219(1), 265–283. https://doi.org/10.1007/s10479-010-0830-y.
Dehghani, E., Jabalameli, M. S., Jabbarzadeh, A., & Pishvaee, M. S. (2018). Resilient solar photovoltaic supply chain network design under business-as-usual and hazard uncertainties. Computers & Chemical Engineering, 111, 288–310. https://doi.org/10.1016/j.compchemeng.2018.01.013.
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. https://doi.org/10.1016/j.ijpe.2018.09.018.
Dora, M., Wesana, J., Gellynck, X., Seth, N., Dey, B., & De Steur, H. (2019). Importance of sustainable operations in food loss: evidence from the Belgian food processing industry. Annals of Operations Research. https://doi.org/10.1007/s10479-019-03134-0.
Fahimnia, B., Jabbarzadeh, A., Ghavamifar, A., & Bell, M. (2017). Supply chain design for efficient and effective blood supply in disasters. International Journal of Production Economics, 183, 700–709. https://doi.org/10.1016/j.ijpe.2015.11.007.
Fisher, M. L. (2004). The Lagrangian relaxation method for solving integer programming problems. Management Science, 50(12_supplement), 1861–1871. https://doi.org/10.1287/mnsc.1040.0263.
Ganesh Kumar, C., Murugaiyan, P., & Madanmohan, G. (2017). Agri-food supply chain management: literature review. Intelligent Information Management, 9, 68–96. https://doi.org/10.2139/ssrn.309324.
Ghezavati, V., 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. https://doi.org/10.1007/s10100-015-0418-3.
Guignard, M. (2003). Lagrangean relaxation. Top, 11(2), 151–200. https://doi.org/10.1007/BF02579036.
Heidari-Fathian, H., & Pasandideh, S. H. R. (2018). Green-blood supply chain network design: Robust optimization, bounded objective function & Lagrangian relaxation. Computers & Industrial Engineering, 122, 95–105. https://doi.org/10.1016/j.cie.2018.05.051.
Held, M., & Karp, R. M. (1970). The traveling-salesman problem and minimum spanning trees. Operations Research, 18(6), 1138–1162. https://doi.org/10.1287/opre.18.6.1138.
Hwang, C.-L., & Masud, A. S. M. (2012). Multiple objective decision making—methods and applications: A state-of-the-art survey (Vol. 164). Berlin : Springer. https://doi.org/10.1007/978-3-642-45511-7.
Jabbarzadeh, A., Haughton, M., & Pourmehdi, F. (2019). A robust optimization model for efficient and green supply chain planning with postponement strategy. International Journal of Production Economics, 214, 266–283. https://doi.org/10.1016/j.ijpe.2018.06.013.
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. https://doi.org/10.1016/j.ejor.2018.12.024.
Kusumastuti, R. D., Van Donk, D. P., & Teunter, R. (2016). Crop-related harvesting and processing planning: A review. International Journal of Production Economics, 174, 76–92. https://doi.org/10.1016/j.ijpe.2016.01.010.
Li, Y., Chu, F., Côté, J.-F., Coelho, L. C., & Chu, C. (2020). The multi-plant perishable food production routing with packaging consideration. International Journal of Production Economics, 221, 107472. https://doi.org/10.1016/j.ijpe.2019.08.007.
Liu, H., Zhang, J., Zhou, C., & Ru, Y. (2018). Optimal purchase and inventory retrieval policies for perishable seasonal agricultural products. Omega, 79, 133–145. https://doi.org/10.1016/j.omega.2017.08.006.
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. https://doi.org/10.1016/j.ijpe.2019.07.007.
Morganti, E., & Gonzalez-Feliu, J. (2015). City logistics for perishable products. The case of the Parma’s Food Hub. Case Studies on Transport Policy, 3(2), 120–128. https://doi.org/10.1016/j.cstp.2014.08.003.
Naderi, B., Govindan, K., & Soleimani, H. (2020). A Benders decomposition approach for a real case supply chain network design with capacity acquisition and transporter planning: Wheat distribution network. Annals of Operations Research, 291(1), 685–705. https://doi.org/10.1007/s10479-019-03137-x.
Orjuela-Castro, J. A., Sanabria-Coronado, L. A., & Peralta-Lozano, A. M. (2017). Coupling facility location models in the supply chain of perishable fruits. Research in Transportation Business & Management, 24, 73–80. https://doi.org/10.1016/j.rtbm.2017.08.002.
Paam, P. (2019). Energy-aware Loss-based Warehousing and Inventory Optimization Models for Agri-fresh Food Supply Chains. University of Newcastle, http://hdl.handle.net/1959.13/1408842.
Paam, P., Berretta, R., & Heydar, M. (2018). An integrated loss-based optimization model for apple supply chain. In Operations Research Proceedings 2017 (pp. 663–669): Springer, https://doi.org/https://doi.org/10.1007/978-3-319-89920-6_88.
Paam, P., Berretta, R., Heydar, M., & García-Flores, R. (2019). The impact of inventory management on economic and environmental sustainability in the apple industry. Computers and Electronics in Agriculture, 163, 104848. https://doi.org/10.1016/j.compag.2019.06.003.
Paam, P., Berretta, R., Heydar, M., Middleton, R., García-Flores, R., & Juliano, P. (2016). Planning models to optimize the agri-fresh food supply chain for loss minimization: a review. Reference Module in Food Science. https://doi.org/10.1016/B978-0-08-100596-5.21069-X.
Paul, J. A., & Wang, X. J. (2015). Robust optimization for United States Department of Agriculture food aid bid allocations. Transportation Research Part E: Logistics and Transportation Review, 82, 129–146. https://doi.org/10.1016/j.tre.2015.08.001.
Rafie-Majd, Z., Pasandideh, S. H. R., & Naderi, B. (2018). Modelling and solving the integrated inventory-location-routing problem in a multi-period and multi-perishable product supply chain with uncertainty: Lagrangian relaxation algorithm. Computers & Chemical Engineering, 109, 9–22. https://doi.org/10.1016/j.compchemeng.2017.10.013.
Rahmani, D. (2019). Designing a robust and dynamic network for the emergency blood supply chain with the risk of disruptions. Annals of Operations Research, 283(1), 613–641. https://doi.org/10.1007/s10479-018-2960-6.
Roghanian, E., & Cheraghalipour, A. (2019). Addressing a set of meta-heuristics to solve a multi-objective model for closed-loop citrus supply chain considering CO2 emissions. Journal of Cleaner Production, 239, 118081. https://doi.org/10.1016/j.jclepro.2019.118081.
Sazvar, Z., Rahmani, M., & Govindan, K. (2018). A sustainable supply chain for organic, conventional agro-food products: The role of demand substitution, climate change and public health. Journal of Cleaner Production, 194, 564–583. https://doi.org/10.1016/j.jclepro.2018.04.118.
Soto-Silva, W. E., González-Araya, M. C., Oliva-Fernández, M. A., & Plà-Aragonés, L. M. (2017). Optimizing fresh food logistics for processing: Application for a large Chilean apple supply chain. Computers and Electronics in Agriculture, 136, 42–57. https://doi.org/10.1016/j.compag.2017.02.020.
Tsang, Y., Choy, K., Wu, C., Ho, G., Lam, H., & Tang, V. (2018). An intelligent model for assuring food quality in managing a multi-temperature food distribution centre. Food Control, 90, 81–97. https://doi.org/10.1016/j.foodcont.2018.02.030.
Widodo, K. H., Nagasawa, H., Morizawa, K., & Ota, M. (2006). A periodical flowering–harvesting model for delivering agricultural fresh products. European Journal of Operational Research, 170(1), 24–43. https://doi.org/10.1016/j.ejor.2004.05.024.
Xu, Z., Yao, L., & Chen, X. (2020). A robust optimization for agricultural crops area planning and industrial production level in the presence of effluent trading. Journal of Cleaner Production, 254, 119987. https://doi.org/10.1016/j.jclepro.2020.119987.
Yakavenka, V., Mallidis, I., Vlachos, D., Iakovou, E., & Eleni, Z. (2019). Development of a multi-objective model for the design of sustainable supply chains: the case of perishable food products. Annals of Operations Research. https://doi.org/10.1007/s10479-019-03434-5.
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. https://doi.org/10.1016/j.jclepro.2019.03.279.
Yu, M., & Nagurney, A. (2013). Competitive food supply chain networks with application to fresh produce. European Journal of Operational Research, 224(2), 273–282. https://doi.org/10.1016/j.ejor.2012.07.033.
Yu, Y., Xiao, T., & Feng, Z. (2020). Price and cold-chain service decisions versus integration in a fresh agri-product supply chain with competing retailers. Annals of Operations Research, 287(1), 465–493. https://doi.org/10.1007/s10479-019-03368-y.
Zhang, Z.-H., Li, B.-F., Qian, X., & Cai, L.-N. (2014). An integrated supply chain network design problem for bidirectional flows. Expert Systems with Applications, 41(9), 4298–4308. https://doi.org/10.1016/j.eswa.2013.12.053.
Zokaee, S., Jabbarzadeh, A., Fahimnia, B., & Sadjadi, S. J. (2017). Robust supply chain network design: An optimization model with real world application. Annals of Operations Research, 257(1–2), 15–44. https://doi.org/10.1007/s10479-014-1756-6.
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Keshavarz-Ghorbani, F., Pasandideh, S.H.R. A Lagrangian relaxation algorithm for optimizing a bi-objective agro-supply chain model considering CO2 emissions. Ann Oper Res (2021). https://doi.org/10.1007/s10479-021-03936-1
- Supply chain
- Lagrangian relaxation algorithm
- Robust optimization
- Environmental impacts