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**Distribution network design for fixed lifetime perishable products: a model and solution approach.**
*(English)*
Zbl 1266.90008

Summary: Nowadays, many distribution networks deal with the distribution and storage of perishable products. However, distribution network design models are largely based on assumptions that do not consider time limitations for the storage of products within the network. This study develops a model for the design of a distribution network that considers the short lifetime of perishable products. The model simultaneously determines the network configuration and inventory control decisions of the network. Moreover, as the lifetime is strictly dependent on the storage conditions, the model develops a trade-off between enhancing storage conditions (higher inventory cost) to obtain a longer lifetime and selecting those storage conditions that lead to shorter lifetimes (less inventory cost). To solve the model, an efficient Lagrangian relaxation heuristic algorithm is developed. The model and algorithm are validated by sensitivity analysis on some key parameters. Results show that the algorithm finds optimal or near optimal solutions even for large-size cases.

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\textit{Z. Firoozi} et al., J. Appl. Math. 2013, Article ID 891409, 13 p. (2013; Zbl 1266.90008)

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### References:

[1] | M. Ferguson and M. E. Ketzenberg, “Information sharing to improve retail product freshness of perishables,” Production and Operations Management, vol. 15, no. 1, pp. 57-73, 2006. |

[2] | Who, Global Database on Blood Safety, Summary Report 2011, World Health Organization, 2011, http://www.who.int/bloodsafety/global_database/GDBS_Summary_Report_2011.pdf. |

[3] | P. Amorim, H. Meyr, C. Almeder, and B. Almada-Lobo, “Managing perishability in production-distribution planning: a discussion and review,” Flexible Services and Manufacturing Journal, pp. 1-25, 2011. |

[4] | C. Kouki, E. Sahin, Z. Jemaï, and Y. Dallery, “Assessing the impact of perishability and the use of time temperature technologies on inventory management,” International Journal of Production Economics, 2010. · doi:10.1016/j.ijpe.2010.09.032 |

[5] | S. Minner and S. Transchel, “Periodic review inventory-control for perishable products under service-level constraints,” OR Spectrum, vol. 32, no. 4, pp. 979-996, 2010. · Zbl 1230.90020 · doi:10.1007/s00291-010-0196-1 |

[6] | J. Jia and Q. Hu, “Dynamic ordering and pricing for a perishable goods supply chain,” Computers & Industrial Engineering, vol. 60, no. 2, pp. 302-309, 2011. · doi:10.1016/j.cie.2010.11.013 |

[7] | P. A. Miranda and R. A. Garrido, “Valid inequalities for Lagrangian relaxation in an inventory location problem with stochastic capacity,” Transportation Research Part E: Logistics and Transportation Review, vol. 44, no. 1, pp. 47-65, 2008. · doi:10.1016/j.tre.2006.04.002 |

[8] | P. A. Miranda and R. A. Garrido, “Inventory service-level optimization within distribution network design problem,” International Journal of Production Economics, vol. 122, no. 1, pp. 276-285, 2009. · doi:10.1016/j.ijpe.2009.06.010 |

[9] | F. Altiparmak, M. Gen, L. Lin, and T. Paksoy, “A genetic algorithm approach for multi-objective optimization of supply chain networks,” Computers and Industrial Engineering, vol. 51, no. 1, pp. 196-215, 2006. · doi:10.1016/j.cie.2006.07.011 |

[10] | M. Faccio, A. Persona, F. Sgarbossa, and G. Zanin, “Multi-stage supply network design in case of reverse flows: a closed-loop approach,” International Journal of Operational Research, vol. 12, no. 2, pp. 157-191, 2011. · Zbl 1260.90037 · doi:10.1504/IJOR.2011.042504 |

[11] | A. Amiri, “Designing a distribution network in a supply chain system: formulation and efficient solution procedure,” European Journal of Operational Research, vol. 171, no. 2, pp. 567-576, 2006. · Zbl 1090.90024 · doi:10.1016/j.ejor.2004.09.018 |

[12] | S. Melkote and M. S. Daskin, “Capacitated facility location/network design problems,” European Journal of Operational Research, vol. 129, no. 3, pp. 481-495, 2001. · Zbl 1125.90380 · doi:10.1016/S0377-2217(99)00464-6 |

[13] | M. Punakivi and V. Hinkka, “Selection criteria of transportation mode: a case study in four finnish industry sectors,” Transport Reviews, vol. 26, no. 2, pp. 207-219, 2006. · doi:10.1080/01441640500191638 |

[14] | L. Ozsen, C. R. Coullard, and M. S. Daskin, “Capacitated warehouse location model with risk pooling,” Naval Research Logistics, vol. 55, no. 4, pp. 295-312, 2008. · Zbl 1153.90484 · doi:10.1002/nav.20282 |

[15] | Z. Firoozi, S. Tang, S. Ariafar, and M. K. Ariffin, “An optimization approach for A joint location inventory model considering quantity discount policy,” Arabian Journal for Science and Engineering, vol. 38, no. 4, pp. 983-991, 2013. · doi:10.1007/s13369-012-0360-9 |

[16] | Z. J. Max Shen and L. Qi, “Incorporating inventory and routing costs in strategic location models,” European Journal of Operational Research, vol. 179, no. 2, pp. 372-389, 2007. · Zbl 1111.90012 · doi:10.1016/j.ejor.2006.03.032 |

[17] | P. A. Miranda and R. A. Garrido, “Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand,” Transportation Research Part E: Logistics and Transportation Review, vol. 40, no. 3, pp. 183-207, 2004. · doi:10.1016/j.tre.2003.08.006 |

[18] | O. Berman, D. Krass, and M. M. Tajbakhsh, “A coordinated location-inventory model,” European Journal of Operational Research, vol. 217, no. 3, pp. 500-508, 2012. · Zbl 1244.90012 · doi:10.1016/j.ejor.2011.09.039 |

[19] | Y. C. Tsao, D. Mangotra, J. C. Lu, and M. Dong, “A continuous approximation approach for the integrated facility-inventory allocation problem,” European Journal of Operational Research, vol. 222, no. 2, pp. 216-228, 2012. · Zbl 1253.90013 |

[20] | C. I. Hsu, S. F. Hung, and H. C. Li, “Vehicle routing problem with time-windows for perishable food delivery,” Journal of Food Engineering, vol. 80, no. 2, pp. 465-475, 2007. · doi:10.1016/j.jfoodeng.2006.05.029 |

[21] | R. A. C. M. Broekmeulen and K. H. van Donselaar, “A heuristic to manage perishable inventory with batch ordering, positive lead-times, and time-varying demand,” Computers and Operations Research, vol. 36, no. 11, pp. 3013-3018, 2009. · Zbl 1162.90303 · doi:10.1016/j.cor.2009.01.017 |

[22] | F. Olsson and P. Tydesjö, “Inventory problems with perishable items: fixed lifetimes and backlogging,” European Journal of Operational Research, vol. 202, no. 1, pp. 131-137, 2010. · Zbl 1173.90313 · doi:10.1016/j.ejor.2009.05.010 |

[23] | F. Dabbene, P. Gay, and N. Sacco, “Optimisation of fresh-food supply chains in uncertain environments, part II: a case study,” Biosystems Engineering, vol. 99, no. 3, pp. 360-371, 2008. · doi:10.1016/j.biosystemseng.2007.11.012 |

[24] | Z. J. M. Shen, “Integrated supply chain design models: a survey and future research directions,” Journal of Industrial and Management Optimization, vol. 3, no. 1, pp. 1-27, 2007. · Zbl 1166.90346 · doi:10.3934/jimo.2007.3.1 |

[25] | M. S. Daskin, C. R. Coullard, and Z.-J. M. Shen, “An inventory-location model: formulation, solution algorithm and computational results,” Annals of Operations Research, vol. 110, no. 1-4, pp. 83-106, 2002. · Zbl 1013.90001 · doi:10.1023/A:1020763400324 |

[26] | Z. J. M. Shen, C. Coullard, and M. S. Daskin, “A joint location-inventory model,” Transportation Science, vol. 37, no. 1, pp. 40-55, 2003. · doi:10.1287/trsc.37.1.40.12823 |

[27] | Z. J. M. Shen, “A multi-commodity supply chain design problem,” IIE Transactions (Institute of Industrial Engineers), vol. 37, no. 8, pp. 753-762, 2005. · doi:10.1080/07408170590961120 |

[28] | J. Shu, C. P. Teo, and Z. J. M. Shen, “Stochastic transportation-inventory network design problem,” Operations Research, vol. 53, no. 1, pp. 48-60, 2005. · Zbl 1165.90367 · doi:10.1287/opre.1040.0140 |

[29] | K. Sourirajan, L. Ozsen, and R. Uzsoy, “A single-product network design model with lead time and safety stock considerations,” IIE Transactions (Institute of Industrial Engineers), vol. 39, no. 5, pp. 411-424, 2007. · Zbl 1159.90389 · doi:10.1080/07408170600941631 |

[30] | K. Sourirajan, L. Ozsen, and R. Uzsoy, “A genetic algorithm for a single product network design model with lead time and safety stock considerations,” European Journal of Operational Research, vol. 197, no. 2, pp. 599-608, 2009. · Zbl 1159.90389 · doi:10.1016/j.ejor.2008.07.038 |

[31] | L. Qi and Z. J. M. Shen, “A supply chain design model with unreliable supply,” Naval Research Logistics, vol. 54, no. 8, pp. 829-844, 2007. · Zbl 1135.90361 · doi:10.1002/nav.20255 |

[32] | E. Gebennini, R. Gamberini, and R. Manzini, “An integrated production-distribution model for the dynamic location and allocation problem with safety stock optimization,” International Journal of Production Economics, vol. 122, no. 1, pp. 286-304, 2009. · doi:10.1016/j.ijpe.2009.06.027 |

[33] | A. Jha, K. Somani, M. K. Tiwari, F. T. S. Chan, and K. J. Fernandes, “Minimizing transportation cost of a joint inventory location model using modified adaptive differential evolution algorithm,” International Journal of Advanced Manufacturing Technology, vol. 60, pp. 1329-4341, 2012. |

[34] | M. T. Melo, S. Nickel, and F. Saldanha-da-Gama, “A tabu search heuristic for redesigning a multi-echelon supply chain network over a planning horizon,” International Journal of Production Economics, vol. 136, no. 1, pp. 218-230, 2012. · doi:10.1016/j.ijpe.2011.11.022 |

[35] | H. Shavandi and B. Bozorgi, “Developing a location-inventory model under fuzzy environment,” International Journal of Advanced Manufacturing Technology, pp. 1-10, 2012. |

[36] | A. Atamtürk, G. Berenguer, and Z.-J. Shen, “A conic integer programming approach to stochastic joint location-inventory problems,” Operations Research, vol. 60, no. 2, pp. 366-381, 2012. · Zbl 1248.90057 · doi:10.1287/opre.1110.1037 |

[37] | P. A. Miranda and R. A. Garrido, “A simultaneous inventory control and facility location model with stochastic capacity constraints,” Networks and Spatial Economics, vol. 6, no. 1, pp. 39-53, 2006. · Zbl 1106.90010 · doi:10.1007/s11067-006-7684-5 |

[38] | S. K. Goyal and B. C. Giri, “Recent trends in modeling of deteriorating inventory,” European Journal of Operational Research, vol. 134, no. 1, pp. 1-16, 2001. · Zbl 0978.90004 · doi:10.1016/S0377-2217(00)00248-4 |

[39] | K. Kanchanasuntorn and A. Techanitisawad, “An approximate periodic model for fixed-life perishable products in a two-echelon inventory-distribution system,” International Journal of Production Economics, vol. 100, no. 1, pp. 101-115, 2006. · doi:10.1016/j.ijpe.2004.10.010 |

[40] | S. E. Omosigho, “Determination of outdate and shortage quantities in the inventory problem with fixed lifetime,” International Journal of Computer Mathematics, vol. 79, no. 11, pp. 1169-1177, 2002. · Zbl 1050.90006 · doi:10.1080/00207160213944 |

[41] | M. Held and R. M. Karp, “The traveling-salesman problem and minimum spanning trees,” Operations Research, vol. 18, no. 6, pp. 1138-1162, 1970. · Zbl 0226.90047 · doi:10.1287/opre.18.6.1138 |

[42] | A. M. Geoffrion and R. McBride, “Lagrangean relaxation applied to capacitated facility location problems,” AIIE Transactions, vol. 10, no. 1, pp. 40-47, 1978. |

[43] | B. Shetty, “Approximate solutions to large scale capacitated facility location problems,” Applied Mathematics and Computation, vol. 39, no. 2, pp. 159-175, 1990. · Zbl 0707.65042 · doi:10.1016/0096-3003(90)90029-3 |

[44] | I. Al-Harkan and M. Hariga, “A simulation optimization solution to the inventory continuous review problem with lot size dependent lead time,” Arabian Journal for Science and Engineering, vol. 32, no. 2 B, pp. 327-338, 2007. |

[45] | S. Park, T. E. Lee, and C. S. Sung, “A three-level supply chain network design model with risk-pooling and lead times,” Transportation Research Part E: Logistics and Transportation Review, vol. 46, no. 5, pp. 563-581, 2010. · doi:10.1016/j.tre.2009.12.004 |

[46] | M. L. Fisher, “Applications oriented guide to Lagrangian relaxation,” Interfaces, vol. 15, no. 2, pp. 10-21, 1985. |

[47] | L. V. Snyder, M. S. Daskin, and C. P. Teo, “The stochastic location model with risk pooling,” European Journal of Operational Research, vol. 179, no. 3, pp. 1221-1238, 2007. · Zbl 1127.90039 · doi:10.1016/j.ejor.2005.03.076 |

[48] | H. Y. Mak and Z. J. M. Shen, “A two-echelon inventory-location problem with service considerations,” Naval Research Logistics, vol. 56, no. 8, pp. 730-744, 2009. · Zbl 1177.90019 · doi:10.1002/nav.20376 |

[49] | M. Daskin, Network and Discrete Location: Models, Algorithms and Applications, Palgrave Macmillan, New York, NY, USA, 1997. · Zbl 0870.90076 |

[50] | R. Haijema, J. van der Wal, and N. M. van Dijk, “Blood platelet production: optimization by dynamic programming and simulation,” Computers and Operations Research, vol. 34, no. 3, pp. 760-779, 2007. · Zbl 1125.90057 · doi:10.1016/j.cor.2005.03.023 |

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