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A Benders’ decomposition algorithm for optimizing distribution of perishable products considering postharvest biological behavior in agri-food supply chain: a case study of tomato. (English) Zbl 1364.90201

Summary: This paper presents a periodical planning mathematical model for distribution of fresh agri-food (a case study of tomato) after qualitative segregating. The main objective of the model is to maximize the profit of a distributor that has relative control on logistics decisions associated with distribution of fresh products in a agri-food supply chain. In a real world, there are some differences between suitable qualities of each customer and thus, fair pricing is determined by their level of satisfaction. Simultaneously, this model takes into account freshness and ripeness as for the food grade. For estimation of the ripeness, a formulation is used that is related to postharvest biological behavior of the fresh crops. In turn, quality loss functions for quantification of degrading are designed to accommodate fair pricing. In addition, potential warehouses are considered in this model to achieve suitable maturity and service level. This paper presents a mixed integer programming model according to the problem descriptions. Since the model is hard to be solved for large scale problems, a primal decomposition solution procedure is proposed based on Benders’ decomposition method. Meanwhile, performance of the proposed solution method will be evaluated through some test problems. Finally, the model is validated through decision making for a domestic distributor of fresh tomato in Iran.

MSC:

90B90 Case-oriented studies in operations research
90B06 Transportation, logistics and supply chain management
90C11 Mixed integer programming
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[1] Ahumada O, Villalobos JR (2009) Application of planning models in the agri-food supply chain: a review. Eur J Oper Res 196(1):1-20 · Zbl 1159.90441 · doi:10.1016/j.ejor.2008.02.014
[2] Ahumada O, Villalobos JR (2011a) A tactical model for planning the production and distribution of fresh produce. Ann Oper Res 190(1):339-358 · Zbl 1233.90137 · doi:10.1007/s10479-009-0614-4
[3] Ahumada O, Villalobos JR (2011b) Operational model for planning the harvest and distribution of perishable agricultural products. Int J Prod Econ 133(2):677-687 · doi:10.1016/j.ijpe.2011.05.015
[4] Akkerman R, Farahani P, Grunow M (2010) Quality, safety and sustainability in food distribution: a review of quantitative operations management approaches and challenges. Or Spectr 32(4):863-904 · doi:10.1007/s00291-010-0223-2
[5] Amorim P, Günther HO, Almada-Lobo B (2012) Multi-objective integrated production and distribution planning of perishable products. Int J Prod Econ 138(1):89-101 · doi:10.1016/j.ijpe.2012.03.005
[6] Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4(1):238-252 · Zbl 0109.38302 · doi:10.1007/BF01386316
[7] Blackburn J, Scudder G (2009) Supply chain strategies for perishable products: the case of fresh produce. Prod Oper Manag 18(2):129-137 · doi:10.1111/j.1937-5956.2009.01016.x
[8] Camargo RS, Miranda G Jr, Luna HP (2008) Benders decomposition for the uncapacitated multiple allocation hub location problem. Comput Oper Res 35(4):1047-1064 · Zbl 1180.90038 · doi:10.1016/j.cor.2006.07.002
[9] Calvin L, Cook RL, Dimitri C, Glaser L, Handy C, Jekanowski M, Thornsbury S (2001) US fresh fruit and vegetable marketing: emerging trade practices, trends, and issues. US Department of Agriculture, Economic Research Service
[10] Chen IJ, Paulraj A (2004) Understanding supply chain management: critical research and a theoretical framework. Int J Prod Res 42(1):131-163 · Zbl 1052.90504 · doi:10.1080/00207540310001602865
[11] Coasta AM (2005) A survey on benders decomposition applied to fixed-charge network design problems. Comput Oper Res 32(6):1429-1450 · Zbl 1071.90009 · doi:10.1016/j.cor.2003.11.012
[12] Dogan K, Goetschalckx M (1999) A primal decomposition method for the integrated design of multi-period production-distribution systems. Iie Trans 31(11):1027-1036
[13] Ferrer JC, Mac Cawley A, Maturana S, Toloza S, Vera J (2008) An optimization approach for scheduling wine grape harvest operations. Int J Prod Econ 112(2):985-999 · doi:10.1016/j.ijpe.2007.05.020
[14] Gary C, Tchamitchian M (2001) Modelling and management of fruit production: the case of tomatoes, food process modelling. CRC Press, Boca Raton · doi:10.1201/9781439823064.ch10
[15] Geoffrion AM, Powers RF (1995) Twenty years of strategic distribution system design: an evolutionary perspective. Interfaces 25(5):105-127 · doi:10.1287/inte.25.5.105
[16] Hertog ML, Lammertyn J, Desmet M, Scheerlinck N, Nicolaï BM (2004) The impact of biological variation on postharvest behavior of tomato fruit. Postharvest Biol Technol 34(3):271-284 · doi:10.1016/j.postharvbio.2004.05.014
[17] Ivanov D, Sokolov B, Kaeschel J (2011) Integrated supply chain planning based on a combined application of operations research and optimal control. Cent Eur J Oper Res 19(3):299-317 · doi:10.1007/s10100-010-0185-0
[18] Lowe TJ, Preckel PV (2004) Decision technologies for agribusiness problems: a brief review of selected literature and a call for research. Manuf Serv Oper Manag 6(3):201-208
[19] Lütke Entrup M, Günther HO, Van Beek P, Grunow M, Seiler T (2005) Mixed-Integer linear programming approaches to shelf-life-integrated planning and scheduling in yoghurt production. Int J Prod Res 43(23):5071-5100 · doi:10.1080/00207540500161068
[20] Manzini R, Accorsi R (2013) The new conceptual framework for food supply chain assessment. J Food Eng 115(2):251-263 · doi:10.1016/j.jfoodeng.2012.10.026
[21] McLaughlin EW, Green GM, Park K (1999) Changing distribution patterns in the US fresh produce industry: Mid/Late-70s to Mid/Late-90s. Department of Agricultural, Resource, and Managerial Economics, College of Agriculture and Life Sciences, Cornell University · Zbl 1292.90034
[22] Osvald A, Stirn LZ (2008) A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food. J Food Eng 85(2):285-295 · doi:10.1016/j.jfoodeng.2007.07.008
[23] Rong A, Akkerman R, Grunow M (2011) An optimization approach for managing fresh food quality throughout the supply chain. Int J Prod Econ 131(1):421-429 · doi:10.1016/j.ijpe.2009.11.026
[24] Saltveit ME (2005) Fruit ripening and fruit quality. Crop Prod Sci Hortic 13:145
[25] Tan B, Çömden N (2012) Agricultural planning of annual plants under demand, maturation, harvest, and yield risk. Eur J Oper Res 220(2):539-549 · Zbl 1253.90158 · doi:10.1016/j.ejor.2012.02.005
[26] Tijskens LMM, Evelo RG (1994) Modelling colour of tomatoes during postharvest storage. Postharvest Biol Technol 4(1):85-98 · doi:10.1016/0925-5214(94)90010-8
[27] Tijskens LMM, Polderdijk JJ (1996) A generic model for keeping quality of vegetable produce during storage and distribution. Agric Syst 51(4):431-452 · doi:10.1016/0308-521X(95)00058-D
[28] [USDA] US Department of Agriculture (1997) United States standards for grades of fresh tomatoes
[29] Widodo KH, Nagasawa H, Morizawa K, Ota M (2006) A periodical flowering-harvesting model for delivering agricultural fresh products. Eur J Oper Res 170(1):24-43 · Zbl 1079.90575 · doi:10.1016/j.ejor.2004.05.024
[30] Yüksektepe F (2014) A novel approach to cutting decision trees. Cent Eur J Oper Res 22(3):553-565 · Zbl 1339.90330 · doi:10.1007/s10100-013-0312-9
[31] Yu M, Nagurney A (2013) Competitive food supply chain networks with application to fresh produce. Eur J Oper Res 224(2):273-282 · Zbl 1292.90034 · doi:10.1016/j.ejor.2012.07.033
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