The high logistics cost of cold chain logistics has become a key bottleneck hindering the development of the fresh produce e-commerce industry, where products have multi-temperature characteristics. Two transportation strategies commonly used in this industry are the mechanical and the insulated container multi-temperature joint distributions. For each transportation strategy, an inventory routing optimization model considering the characteristics of multi-temperature products, multi-period, and heterogeneous vehicles is proposed to find the optimal distribution plan to minimize logistics costs. Research results indicate that the threshold for choosing the optimal transportation strategy is related to the ratio of multi-temperature products. When the ratio of multi-temperature products is below 40%, the optimal transportation strategy is the mechanical multi-temperature joint distribution, which can reduce logistics costs by an average of 31.6%. Additionally, the key parameter exerting the predominant impact on logistics costs was identified, and its unit change can increase logistics costs by 3.2%. Furthermore, the laws of logistics cost changes during multi-temperature product distribution have been revealed, being influenced by transportation strategies, the ratio of multi-temperature products, and the total transportation volume. Based on this, valuable management insights have been put forward.
Citation: Wang Beibei, Zhong Jian. Research on inventory routing optimization considering multi-temperature joint distribution of mechanical and insulated container[J]. Journal of Industrial and Management Optimization, 2026, 22(6): 2784-2816. doi: 10.3934/jimo.2026102
The high logistics cost of cold chain logistics has become a key bottleneck hindering the development of the fresh produce e-commerce industry, where products have multi-temperature characteristics. Two transportation strategies commonly used in this industry are the mechanical and the insulated container multi-temperature joint distributions. For each transportation strategy, an inventory routing optimization model considering the characteristics of multi-temperature products, multi-period, and heterogeneous vehicles is proposed to find the optimal distribution plan to minimize logistics costs. Research results indicate that the threshold for choosing the optimal transportation strategy is related to the ratio of multi-temperature products. When the ratio of multi-temperature products is below 40%, the optimal transportation strategy is the mechanical multi-temperature joint distribution, which can reduce logistics costs by an average of 31.6%. Additionally, the key parameter exerting the predominant impact on logistics costs was identified, and its unit change can increase logistics costs by 3.2%. Furthermore, the laws of logistics cost changes during multi-temperature product distribution have been revealed, being influenced by transportation strategies, the ratio of multi-temperature products, and the total transportation volume. Based on this, valuable management insights have been put forward.
| [1] |
J. Zhong, X. Wang, L. Li, S. G. Quiles, Optimization for bi-objective express transportation network design under multiple topological structures, Int. J. Ind. Eng. Comp., 22 (2023), 239–264. https://doi.org/10.5267/j.ijiec.2023.2.003 doi: 10.5267/j.ijiec.2023.2.003
|
| [2] | Y. W. Deng, W. B. Wu, T. Q. Yu, Research on Current Development and Development Pattern of China's Agricultural Cold Chain Logistics, in 2012 International Conference on Management Science & Engineering 19th Annual Conference Proceedings, 19 (2012), 526–532. https://doi.org/10.1109/ICMSE.2012.6414230 |
| [3] |
H. Li, Research on the Composition and Management Strategy of Enterprise Logistics Cost in Supply Chains, Adv. Mater. Res., 8 (2012), 521–526. https://doi.org/10.4028/www.scientific.net/AMR.452-453.521 doi: 10.4028/www.scientific.net/AMR.452-453.521
|
| [4] | C. Pan, S. Yu, S. Li, Research on the Development Mode and Evaluation System of Green Cold Chain Logistics in China, in 2017 36th Chinese Control Conference (CCC), 36 (2017), 7541–7546. https://doi.org/10.23919/ChiCC.2017.8028547 |
| [5] | M. I. Gómez, C. B. Barrett, L. E. Buck, H. De Groote, S. Ferris, H. O. Gao, et al., Research Principles for Developing Country Food Value Chains, Science, 332 (2011), 1154–1155. https://doi.org/10.1126/science.1202543 |
| [6] |
L. Muyldermans, G. Pang, On the benefits of co-collection: Experiments with a multi-compartment vehicle routing algorithm, Eur. J. Oper. Res., 206 (2010), 93–103. https://doi.org/10.1016/j.ejor.2010.02.020 doi: 10.1016/j.ejor.2010.02.020
|
| [7] |
J. C. Kuo, M. C. Chen, Developing an advanced Multi-Temperature Joint Distribution System for the food cold chain, Food Contr., 21 (2010), 559–566. https://doi.org/10.1016/j.foodcont.2009.08.007 doi: 10.1016/j.foodcont.2009.08.007
|
| [8] | G. Huang, R. Lu, The Route Optimization of Multi-temperature Joint Distribution for Cold-Chain Products under the Condition of Random Driving Time, in Proceedings of the 2017 International Conference on Education, Economics and Management Research (ICEEMR 2017), 42 (2017), 163–166. https://doi.org/10.2991/iceemr-17.2017.42 |
| [9] |
Y. J. Cho, C. C. Li, W. Fu, H. Chu, Application of multi-temperature refrigerated container to improve the distribution of cold logistics, J. East Asia Soc. Transp. Stud., 6 (2005), 2794–2808. https://doi.org/10.11175/easts.6.2794 doi: 10.11175/easts.6.2794
|
| [10] |
C. I. Hsu, K. P. Liu, A model for facilities planning for multi-temperature joint distribution system, Food Contr., 22 (2011), 1873–1882. https://doi.org/10.1016/j.foodcont.2011.04.029 doi: 10.1016/j.foodcont.2011.04.029
|
| [11] |
Y. Chang, J. Yu, Y. Wang, X. Xie, An Improved Salp Swarm Algorithm for Solving a Multi-Temperature Joint Distribution Route Optimization Problem, Mathematics, 13 (2025), 667. https://doi.org/10.3390/math13040677 doi: 10.3390/math13040677
|
| [12] | X. Xu, F. Li, T. Wu, X. R. Huang, X. L. Guan, T. Y. Zheng, et al., Location-routing optimization problem of pharmaceutical cold chain logistics with oil-electric mixed fleets under uncertainties, Comput. Ind. Eng., 201 (2025), 110932. https://doi.org/10.1016/j.cie.2025.110932 |
| [13] |
L. Shen, Q. Yang, X. Xu, T. Wu, S. Zhang, H. Shao, A generalized three-stage optimization model for emergency medical services under uncertainties: Integrating rescue station locations, ambulance deployment, and vehicle dispatch, Transp. Res. Part E Logist. Transp. Rev., 205 (2026), 104499. https://doi.org/10.1016/j.tre.2025.104499 doi: 10.1016/j.tre.2025.104499
|
| [14] |
L. Shen, X. Xu, F. Shao, H. Shao, Y. X. Ge, A multi-objective optimization model for medical waste recycling network design under uncertainties, Transp. Res. Part E Logist. Transp. Rev., 184 (2024), 103492. https://doi.org/10.1016/j.tre.2024.103492 doi: 10.1016/j.tre.2024.103492
|
| [15] |
F. Guerriero, G. Macrina, V. Mosca, E. Scalzo, The vehicle routing problem and integrated challenges in the perishable product supply chain, Comput. Ind. Eng., 209 (2025), 111428. https://doi.org/10.1016/j.cie.2025.111428 doi: 10.1016/j.cie.2025.111428
|
| [16] |
Y. Zhang, X. D. Chen, An Optimization Model for the Vehicle Routing Problem in Multi-product Frozen Food Delivery, J. Appl. Res. Technol., 12 (2014), 239–250. https://doi.org/10.1016/S1665-6423(14)72340-5 doi: 10.1016/S1665-6423(14)72340-5
|
| [17] |
A. Hübner, M. Ostermeier, A Multi-Compartment Vehicle Routing Problem with Loading and Unloading Costs, Transport. Sci., 53 (2017), 282–300. https://doi.org/10.1287/trsc.2017.0775 doi: 10.1287/trsc.2017.0775
|
| [18] |
J. E. Mendoza, B. Castanier, C. Gueret, A. L. Medaglia, N. Velasco, A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands, Comput. Oper. Res., 37 (2010), 1886–1898. https://doi.org/10.1016/j.cor.2009.06.015 doi: 10.1016/j.cor.2009.06.015
|
| [19] |
M. M. S. Abdulkader, Y. Gajpal, T. Y. ElMekkawy, Hybridized ant colony algorithm for the Multi Compartment Vehicle Routing Problem, Appl. Soft Comput., 37 (2015), 196–203. https://doi.org/10.1016/j.asoc.2015.08.020 doi: 10.1016/j.asoc.2015.08.020
|
| [20] | C. Qi, Multi-objective Optimization-Based Algorithm for Selecting the Optimal Path of Rural Multi-temperature Zone Cold Chain Dynamic Logistics Intermodal Transportation, Int. J. Comput. Intell. Syst., 17 (2024), 1–14. https://doi.org/10.1007/s44196-024-00616-3 |
| [21] |
Y. Zou, J. Wu, X. Wang, K. Morales, G. Liu, A. Manzardo, An improved artificial neural network using multi-source data to estimate food temperature during multi-temperature delivery, J. Food Eng., 351 (2023), 111518. https://doi.org/10.1016/j.jfoodeng.2023.111518 doi: 10.1016/j.jfoodeng.2023.111518
|
| [22] | Y. Yang, S. P. Lin, J. S. Liaw, L. W. Hu, B. R. Fu, Dual-temperature control for two storage chambers in a cold-chain logistics vehicle: An experimental study, Appl. Therm. Eng., 272 (2025), 126422. https://doi.org/10.1016/j.applthermaleng.2025.126422 |
| [23] |
M. Frank, M. Ostermeier, A. Holzapfel, A. Hübner, H. Kuhn, Optimizing routing and delivery patterns with multi-compartment vehicles, Eur. J. Oper. Res., 293 (2021), 495–510. https://doi.org/10.1016/j.ejor.2020.12.033 doi: 10.1016/j.ejor.2020.12.033
|
| [24] |
C. I. Hsu, W. T. Chen, W. J. Wu, Optimal delivery cycles for joint distribution of multi-temperature food, Food Contr., 34 (2013), 106–114. https://doi.org/10.1016/j.foodcont.2013.04.003 doi: 10.1016/j.foodcont.2013.04.003
|
| [25] |
W. T. Chen, C. I. Hsu, Greenhouse gas emission estimation for temperature-controlled food distribution systems, J. Clean. Prod., 104 (2015), 139–147. https://doi.org/10.1016/j.jclepro.2015.05.038 doi: 10.1016/j.jclepro.2015.05.038
|
| [26] |
A. Zhang, Y. Zhang, Y. Liu, J. Hou, J. Hu, Optimization of Multi-Temperature Co-Transmission Paths under Time-Varying Road Networks, Pol. J. Environ. Stud., 33 (2024), 3963–3974. https://doi.org/10.15244/pjoes/177427 doi: 10.15244/pjoes/177427
|
| [27] |
L. Coelho, G. Laporte, An optimised target-level inventory replenishment policy for vendor-managed inventory systems, Int. J. Prod. Res., 53 (2015), 3651–3660. https://doi.org/10.1080/00207543.2014.986299 doi: 10.1080/00207543.2014.986299
|
| [28] | Z. Li, P. Jiao, Two-stage stochastic programming for the inventory routing problem with stochastic demands in fuel delivery, Int. J. Ind. Eng. Comp., 13 (2022), 507–522. https://doi.org/10.5267/j.ijiec.2022.7.004 |
| [29] |
C. Archetti, L. Bertazzi, A. Hertz, M. G. Speranza, A Hybrid Heuristic for an Inventory Routing Problem, Informs J. Comput., 24 (2012), 101–116. https://doi.org/10.1287/ijoc.1100.0439 doi: 10.1287/ijoc.1100.0439
|
| [30] |
M. C. Chen, C. C. Lu, Y. C. Liu, Optimal consolidation of fresh agricultural products in a multi-temperature joint distribution system, Int. J. Logist. Manag., 29 (2018), 887–901. https://doi.org/10.1108/IJLM-01-2017-0021 doi: 10.1108/IJLM-01-2017-0021
|
| [31] |
J. Chen, J. Shi, A multi-compartment vehicle routing problem with time windows for urban distribution-A comparison study on particle swarm optimization algorithms, Comput. Ind. Eng., 133 (2019), 95–106. https://doi.org/10.1016/j.cie.2019.05.008 doi: 10.1016/j.cie.2019.05.008
|
| [32] |
N. Zhang, Q. An, X. Wang, Loading Method and Routing Optimizations of Fresh Products on Multi-Temperature Joint Distribution With Limited Flexible-Size Compartments, IEEE Access, 11 (2023), 33261–33273. https://doi.org/10.1109/ACCESS.2023.3264211 doi: 10.1109/ACCESS.2023.3264211
|
| [33] |
S. Voigt, M. Frank, P. Fontaine, H. Kuhn, Hybrid adaptive large neighborhood search for vehicle routing problems with depot location decisions, Comput. Oper. Res., 146 (2022), 105856. https://doi.org/10.1016/j.cor.2022.105856 doi: 10.1016/j.cor.2022.105856
|
| [34] | D. F. Batero Manso, J. A. Orjuela Castro, El Problema de Ruteo e Inventarios en Cadenas de Suministro de Perecederos: Revisión de Literatura, Ingeniería, 23 (2018), 117–143. https://doi.org/10.14483/23448393.12691 |
| [35] |
S. Jahdi, S. Gulecyuz, S. O'Reilly, B. O'Sullivan, S. A. Tarim, An IRP model to improve the sustainability of cold food supply chains under stochastic demand, J. Clean. Prod., 462 (2024), 142615. https://doi.org/10.1016/j.jclepro.2024.142615 doi: 10.1016/j.jclepro.2024.142615
|
| [36] | J. Arturo Orjuela-Castro, D. Batero-Manso, J. Pablo Orejuela-Cabrera, Logistics IRP Model for the Supply Chain of Perishable Food, WEA, 5 (2018), 40–52. https://doi.org/10.1007/978-3-030-00353-1_4 |
| [37] |
Y. Ji, J. Du, X. Wu, Z. Wu, D. Qu, D. Yang, Robust optimization approach to two-echelon agricultural cold chain logistics considering carbon emission and stochastic demand, Environ. Dev. Sustain., 23 (2021), 13731–13754. https://doi.org/10.1007/s10668-021-01236-z doi: 10.1007/s10668-021-01236-z
|
| [38] |
T. Kim, C. H. Glock, On the use of RFID in the management of reusable containers in closed-loop supply chains under stochastic container return quantities, Transp. Res. Part E Logist. Transp. Rev., 64 (2014), 12–27. https://doi.org/10.1016/j.tre.2014.01.011 doi: 10.1016/j.tre.2014.01.011
|
| [39] |
L. Moussawi-Haidar, W. Dbouk, M. Y. Jaber, I. H. Osman, Coordinating a three-level supply chain with delay in payments and a discounted interest rate, Comput. Ind. Eng., 69 (2014), 29–42. https://doi.org/10.1016/j.cie.2013.12.007 doi: 10.1016/j.cie.2013.12.007
|
| [40] | X. Wang, J. Zhong. An integrated optimization for minimizing the operation cost of home delivery services in O2O retail, Int. J. Ind. Eng. Comp., 14 (2023), 341–360. https://doi.org/10.5267/j.ijiec.2022.12.005 |
| [41] |
C. E. Miller, A. W. Tucker, R. A. Zemlin, Integer Programming Formulation of Traveling Salesman Problems, J. ACM, 7 (1960), 326–329. https://doi.org/10.1145/321043.321046 doi: 10.1145/321043.321046
|
| [42] |
L. Coelho, G. Laporte, A branch-and-cut algorithm for the multi-product multi-vehicleinventory-routing problem, Int. J. Prod. Res., 51 (2013), 7156–7169. https://doi.org/10.1080/00207543.2012.757668 doi: 10.1080/00207543.2012.757668
|
| [43] |
C. Archetti, L. Bertazzi, G. Laporte, M. G. Speranza, A Branch-and-Cut Algorithm fora Vendor-Managed Inventory-Routing Problem, Transport. Sci., 41 (2007), 382–391. https://doi.org/10.1287/trsc.1060.0188 doi: 10.1287/trsc.1060.0188
|
| [44] |
X. Wan, R. Britto, Z. Zhou, In search of the negative relationship between product variety and inventory turnover, Int. J. Prod. Econ., 222 (2020), 107503. https://doi.org/10.1016/j.ijpe.2019.09.024 doi: 10.1016/j.ijpe.2019.09.024
|