Designing a Food Supply Chain Network under Uncertainty and Solving by Multi-objective Metaheuristics

Document Type : Research Paper


1 Industrial Engineering Department, Faculty of Engineering,Imam Hossein Comprehensive University, Tehran, Iran

2 Department of Industrial Engineering, Imam Hossein Comprehensive University, Tehran, Iran


Short life cycle products, especially food products, require a certain type of supply chain management due to their particular specifications such as perishability. On the other hand, the food distribution also requires special considerations and imparts more complexity compared with the distribution of other goods because in food distribution the quality of the food delivered to the customer should be considered as well as transportation costs. Therefore, in this paper, a new mathematical model is developed for integrating decisions regarding food supply and distribution under conditions of uncertainty (vehicles’ travel time) with aims to minimize purchase and transportation costs and maximize customer satisfaction. Customer satisfaction relies upon the quality of the food delivered to the customers. The multi-objective model proposed in this paper is NP-hard. Hence, a developed version of NSGA-II called Multi-Objective Time Travel to History (MOTTH) algorithm, inspired from the idea of traveling through history, is proposed to solve the problem. In order to validate the performance of the proposed algorithm, the results of MOTTH algorithm are compared with the results obtained from an exact augmented epsilon-constraint method. Furthermore, a comparison is provided between the NSGA-II and MOTTH algorithms, the results of which indicate the superiority of the MOTTH metaheuristic algorithm.


Brito J., Martinez F.J., Moreno J.A. and Verdegay J. L. (2012). Fuzzy optimization for distribution of frozen food with imprecise times. Fuzzy Optimization and Decision Making, Vol. 11(3), pp. 337-349.
Carson J.K. and East A.R. (2018). The cold chain in New Zealand–A review. International Journal of Refrigeration, Vol. 87, pp. 185-192.
Chankong V. and Haimes Y.Y. (1983). Multiobjective decision making theory and methodology, New York: Noth-Holland.
Deb K., Pratap A., Agarwal S. and Meyarivan T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, Vol. 6(2), pp. 182-197.
Derens E., Palagos B. and Guilpart J. (2006). The cold chain of chilled products under supervision in France. In 13th World Congress of Food Science & Technology 2006, pp. 823-823.
Ghare P.M. and Schrader G.F. (1963). An inventory model for exponentially deteriorating items. Journal of Industrial Engineering, Vol. 14(2), pp. 238-243.
Ghomi-Avili M., Khosrojerdi A. and Tavakkoli-Moghaddam R. (2019). A multi-objective model for the closed-loop supply chain network design with a price-dependent demand, shortage and disruption. Journal of Intelligent & Fuzzy Systems, Vol. 36(6), pp. 5261-5272.
Gustavsson J., Cederberg C., Sonesson U., Van Otterdijk R. and Meybeck A. (2011). Global food losses and food waste. Save Food Congress, Düsseldorf 16 May 2011.
Hsiao Y.H., Chen M.C. and Chin C.L. (2017). Distribution planning for perishable foods in cold chains with quality concerns: Formulation and solution procedure. Trends in food science & technology, Vol. 61, pp. 80-93.
Hsu C.I., Hung S.F. and Li H.C. (2007). Vehicle routing problem with time-windows for perishable food delivery. Journal of food engineering, Vol. 80(2), pp. 465-475.
Jiménez M., Arenas M., Bilbao A. and Rodrı M.V. (2007). Linear programming with fuzzy parameters: an interactive method resolution. European Journal of Operational Research, Vol. 177(3), pp. 1599-1609.
Joshi K., Warby J., Valverde J., Tiwari B., Cullen P.J. and Frias J.M. (2018). Impact of cold chain and product variability on quality attributes of modified atmosphere packed mushrooms (Agaricus bisporus) throughout distribution. Journal of Food Engineering, Vol. 232, pp. 44-55.
Koseki S. and Isobe S. (2005). Prediction of pathogen growth on iceberg lettuce under real temperature history during distribution from farm to table. International Journal of Food Microbiology, Vol. 104(3), pp. 239-248.
Koutsoumanis K., Pavlis A., Nychas G.J.E. and Xanthiakos K. (2010). Probabilistic model for Listeria monocytogenes growth during distribution, retail storage, and domestic storage of pasteurized milk. Appl. Environ. Microbiol., Vol. 76(7), pp. 2181-2191.
Lesmawati W., Rahmi A. and Mahmudy W.F. (2016). Optimization of frozen food distribution using genetic algorithms. Journal of Environmental Engineering and Sustainable Technology, Vol. 3(1), pp. 51-58.
Likar K. and Jevšnik M. (2006). Cold chain maintaining in food trade. Food control, Vol. 17(2), pp. 108-113.
Lundén J., Vanhanen V., Kotilainen K. and Hemminki K. (2014). Retail food stores' internet-based own-check databank records and health officers' on-site inspection results for cleanliness and food holding temperatures reveal inconsistencies. Food control, Vol. 35(1), pp. 79-84.
Mai N.T.T., Margeirsson S., Bogason S.G., Sigurgisladottir S. and Arason S. (2012). Temperature mapping of fresh fish supply chains–air and sea transport. Journal of food process engineering, Vol. 35(4), pp. 622-656.
Martinsdóttir E., Lauzon H.L., Margeirsson B., Sveinsdóttir K., Þorvaldsson L., Magnússon H. and Eden M. (2010). The effect of cooling methods at processing and use of gel packs on storage life of cod (Gadus morhua) loins. Effect of transport via air and sea on temperature control and retail-packaging on cod deterioration. Report/Skýrsla Matís.
Mavrotas G. (2009). Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied mathematics and computation, Vol. 213(2), pp. 455-465.
Mohebalizadehgashti F., Zolfagharinia H. and Amin S.H. (2020). Designing a green meat supply chain network: A multi-objective approach. International Journal of Production Economics, Vol. 219, pp. 312-327.
Ndraha N., Sung W.C. and Hsiao H.I. (2019). Evaluation of the cold chain management options to preserve the shelf life of frozen shrimps: A case study in the home delivery services in Taiwan. Journal of food engineering, Vol. 242, pp. 21-30.
Nedović V., Raspor P., Lević J., Šaponjac V.T. and Barbosa-Cánovas G.V. (2016). Emerging and traditional technologies for safe, healthy and quality food, pp. 257-268.
Osvald A. and Stirn L.Z. (2008). A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food. Journal of food engineering, Vol. 85(2), pp. 285-295.
Pelletier W., Brecht J K., Nunes, M.C. and Emond J.P. (2011). Quality of strawberries shipped by truck from California to Florida as influenced by postharvest temperature management practices. HortTechnology, Vol. 21(4), pp. 482-493.
Rediers H., Claes M., Peeters L. and Willems K.A. (2009). Evaluation of the cold chain of fresh-cut endive from farmer to plate. Postharvest Biology and Technology, Vol. 51(2), pp. 257-262.
Rong A., Akkerman R. and Grunow M. (2011). An optimization approach for managing fresh food quality throughout the supply chain. International Journal of Production Economics, Vol. 131(1), pp. 421-429.
Song B.D. and Ko Y.D. (2016). A vehicle routing problem of both refrigerated-and general-type vehicles for perishable food products delivery. Journal of food engineering, Vol. 169, pp. 61-71.
Srinivas N. and Deb K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary computation, Vol. 2(3), pp. 221-248.
Taheri S.M.R. and Beheshtinia M.A. (2019). A Genetic Algorithm Developed for a Supply Chain Scheduling Problem. Iranian Journal of Management Studies, Vol. 12(2), pp. 107-132.
Tarantilis C.D. and Kiranoudis C.T. (2001). A meta-heuristic algorithm for the efficient distribution of perishable foods. Journal of food Engineering, Vol. 50(1), pp. 1-9.
Ullrich C.A. (2013). Integrated machine scheduling and vehicle routing with time windows. European Journal of Operational Research, Vol. 227(1), pp. 152-165.
Zubeldia B.B., Jiménez M.N., Claros M.T.V., Andrés J.L.M. and Martin-Olmedo P. (2016). Effectiveness of the cold chain control procedure in the retail sector in Southern Spain. Food Control, Vol. 59, pp. 614-618.