Document Type : Research Paper
Authors
1 Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran
2 Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran, Iran
3 Department of Industrial Engineering, Shahed University, Tehran, Iran
4 School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
Abstract
In today’s competitive markets, determining the optimum distribution centers, delivery routes, and inventory levels is crucial for cold chain logistics of perishable products to reduce costs as well as backorder rate. Meanwhile, a new bi-phase mixed integer non-linear programming model-based robust possibilistic approach is developed by goals of minimizing total costs and reducing the backorder rate for key customers to solve the hub location-routing model for a cold chain of perishable products. To address the issue, the augmented ε-constraint method is considered to construct a single objective model, and the obtained Pareto optimal points are analyzed. Additionally, the robust possibilistic approach is executed to cope with imprecise demand in the presented bi-phase hub location-routing model. To represent the verification and applicability of the proposed approach, a case study on cold chain logistics of perishable products is regarded. Finally, a comparative analysis is considered to compare the obtained results from the proposed approach with real case information. This validation process is defined by schematically reporting the trend comparison results over the entire planning horizon. Moreover, the obtained results represents that the proposed approach can enhance the objective function by reducing the 22% of total costs, improved the backorder level by 24%, the number of deteriorating items decreased by 16.48%, and the inventory levels enhanced by 12.86% regarding the current practice.
Keywords
- Hub location-routing problem
- Robust possibilistic programming model
- Mixed integer non-linear programming model
- Fuzzy sets theory
- Augmented ε-constraint method
Main Subjects
[1] A. Alinezhad Esboei, M. Karimi Gavareshki, Using a fuzzy expert system as a decision support system to decrease
time consumption in the UAST development process: A case study, Iranian Journal of Fuzzy Systems, 18(3) (2021),
27-38. https://doi.org/10.22111/ijfs.2021.6079
time consumption in the UAST development process: A case study, Iranian Journal of Fuzzy Systems, 18(3) (2021),
27-38. https://doi.org/10.22111/ijfs.2021.6079
[2] F. Alkaabneh, A. Diabat, H. O. Gao, Benders decomposition for the inventory vehicle routing problem with perishable
products and environmental costs, Computers and Operations Research, 113 (2020), 104751. https://doi.org/
10.1016/j.cor.2019.07.009
products and environmental costs, Computers and Operations Research, 113 (2020), 104751. https://doi.org/
10.1016/j.cor.2019.07.009
[3] F. Alkaabneh, A. Diabat, H. O. Gao, Ch-and-cut and a hybrid heuristic algorithm for an inventory routing problem
with perishable products, European Journal of Operational Research, 283(2) (2020), 511-529. https://doi.org/
10.1016/j.ejor.2019.11.015
with perishable products, European Journal of Operational Research, 283(2) (2020), 511-529. https://doi.org/
10.1016/j.ejor.2019.11.015
[4] A. Azadeh, et al., A genetic algorithm-Taguchi based approach to inventory routing problem of a single perishable
product with transshipment, Computers and Industrial Engineering, 104 (2017), 124-133. https://doi.org/10.
1016/j.cie.2016.12.019
product with transshipment, Computers and Industrial Engineering, 104 (2017), 124-133. https://doi.org/10.
1016/j.cie.2016.12.019
[5] P. S. Barma, et al., A multi-objective ring star vehicle routing problem for perishable items, Journal of Ambient In
telligence and Humanized Computing, 13(5) (2022), 2355-2380. https://doi.org/10.1007/s12652-021-03059-2
telligence and Humanized Computing, 13(5) (2022), 2355-2380. https://doi.org/10.1007/s12652-021-03059-2
[6] M. Biuki, A. Kazemi, A. Alinezhad, An integrated location-routing-inventory model for sustainable design of a
perishable products supply chain network, Journal of Cleaner Production, 260 (2020), 120842. https://doi.org/
10.1016/j.jclepro.2020.120842
perishable products supply chain network, Journal of Cleaner Production, 260 (2020), 120842. https://doi.org/
10.1016/j.jclepro.2020.120842
[7] F. T. Chan, et al., Multi-objective particle swarm optimisation based integrated production inventory routing planning
for efficient perishable food logistics operations, International Journal of Production Research, 58(17) (2020), 5155
5174. https://doi.org/10.1080/00207543.2019.1701209
for efficient perishable food logistics operations, International Journal of Production Research, 58(17) (2020), 5155
5174. https://doi.org/10.1080/00207543.2019.1701209
[8] X. Chen, Y. Jiu, D. Hu, Two-echelon location–routing problem of perishable products based on the integrated mode
of in-store pick-up and delivery, Transportation Research Record, 2678(8) (2024), 622-636. https://doi.org/10.
1177/03611981231218008
of in-store pick-up and delivery, Transportation Research Record, 2678(8) (2024), 622-636. https://doi.org/10.
1177/03611981231218008
[9] T. Chernonog, Inventory and marketing policy in a supply chain of a perishable product, International Journal of
Production Economics, 219 (2020), 259-274. https://doi.org/10.1016/j.ijpe.2019.06.019
Production Economics, 219 (2020), 259-274. https://doi.org/10.1016/j.ijpe.2019.06.019
[10] Z. Dai, et al., A location-inventory supply chain network model using two heuristic algorithms for perishable products
with fuzzy constraints, Computers and Industrial Engineering, 119 (2018), 338-352. https://doi.org/10.1016/j.
cie.2018.04.007
with fuzzy constraints, Computers and Industrial Engineering, 119 (2018), 338-352. https://doi.org/10.1016/j.
cie.2018.04.007
[11] S. Daroudi, et al., The minimum latency in location routing fuzzy inventory problem for perishable multi-product
materials, Applied Soft Computing, 110 (2021), 107543. https://doi.org/10.1016/j.asoc.2021.107543
materials, Applied Soft Computing, 110 (2021), 107543. https://doi.org/10.1016/j.asoc.2021.107543
[12] A. De Maio, R. Musmanno, F. Vocaturo, Unbiased decision making in location-routing problems with uncertain
customer demands, Soft Computing, (2022), 1-11. https://doi.org/10.1007/s00500-022-06785-7
customer demands, Soft Computing, (2022), 1-11. https://doi.org/10.1007/s00500-022-06785-7
[13] R. Eslamipoor, A new heuristic approach for a multi-depot three-level location-routing-inventory problem, Interna
tional Journal of Management Concepts and Philosophy, 17(3) (2024), 322-339. https://doi.org/10.1504/IJMCP.
2024.139345
tional Journal of Management Concepts and Philosophy, 17(3) (2024), 322-339. https://doi.org/10.1504/IJMCP.
2024.139345
[14] P. Fattahi, M. Tanhatalab, Stochastic inventory-routing problem with lateral transshipment for perishable product,
Journal of Modelling in Management, 17(2) (2021), 539-568. https://doi.org/10.1108/JM2-09-2019-0230
Journal of Modelling in Management, 17(2) (2021), 539-568. https://doi.org/10.1108/JM2-09-2019-0230
[15] Y. Feng, A. Che, N. Tian, Robust inventory routing problem under uncertain demand and risk-averse criterion,
Omega, 127 (2024), 103082. https://doi.org/10.1016/j.omega.2024.103082
Omega, 127 (2024), 103082. https://doi.org/10.1016/j.omega.2024.103082
[16] A. Ghasemkhani, et al., Integrated production-inventory-routing problem for multi-perishable products under un
certainty by meta-heuristic algorithms, International Journal of Production Research, 60(9) (2022), 2766-2786.
https://doi.org/10.1080/00207543.2021.1902013
certainty by meta-heuristic algorithms, International Journal of Production Research, 60(9) (2022), 2766-2786.
https://doi.org/10.1080/00207543.2021.1902013
[17] H. Gitinavard, S. H. Ghodsypour, M. Akbarpour Shirazi, A bi-objective multi-echelon supply chain model with
Pareto optimal points evaluation for perishable products under uncertainty, Scientia Iranica, 26(5) (2019), 2952
2970. https://doi.org/10.24200/sci.2018.5047.1060
Pareto optimal points evaluation for perishable products under uncertainty, Scientia Iranica, 26(5) (2019), 2952
2970. https://doi.org/10.24200/sci.2018.5047.1060
[18] H. Gitinavard, V. Mohagheghi, et al., A new bi-stage interactive possibilistic programming model for perishable
logistics distribution systems under uncertainty, Expert Systems with Applications, 238 (2024), 122121. https:
//doi.org/10.1016/j.eswa.2023.122121
logistics distribution systems under uncertainty, Expert Systems with Applications, 238 (2024), 122121. https:
//doi.org/10.1016/j.eswa.2023.122121
[19] M. Golestani, et al., A multi-objective green hub location problem with multi item-multi temperature joint distribu
tion for perishable products in cold supply chain, Sustainable Production and Consumption, 27 (2021), 1183-1194.
https://doi.org/10.1016/j.spc.2021.02.026
tion for perishable products in cold supply chain, Sustainable Production and Consumption, 27 (2021), 1183-1194.
https://doi.org/10.1016/j.spc.2021.02.026
[20] Z. He, Y. Liu, K. Liu, Robust optimization approaches for the perishable product inventory routing problem with
demand uncertainty, Journal of Industrial and Management Optimization, 20(8) (2024), 2740-2769. https://doi.
org/10.3934/jimo.2024024
demand uncertainty, Journal of Industrial and Management Optimization, 20(8) (2024), 2740-2769. https://doi.
org/10.3934/jimo.2024024
[21] A. Hiassat, A. Diabat, I. Rahwan, A genetic algorithm approach for location-inventory-routing problem with per
ishable products, Journal of Manufacturing Systems, 42 (2017), 93-103. https://doi.org/10.1016/j.jmsy.2016.
10.004
ishable products, Journal of Manufacturing Systems, 42 (2017), 93-103. https://doi.org/10.1016/j.jmsy.2016.
10.004
[22] Y. Ji, et al., A mixed integer robust programming model for two-echelon inventory routing problem of perishable
products, Physica A: Statistical Mechanics and its Applications, 548 (2020), 124481. https://doi.org/10.1016/
j.physa.2020.124481
products, Physica A: Statistical Mechanics and its Applications, 548 (2020), 124481. https://doi.org/10.1016/
j.physa.2020.124481
[23] F. Khalili Goudarzi, H. Maleki, S. Niroomand, An interactive fuzzy programming approach for a new multi-objective
multi-product oil pipeline scheduling problem, Iranian Journal of Fuzzy Systems, 18(4) (2021), 95-112. https:
//doi.org/10.22111/ijfs.2021.6179
multi-product oil pipeline scheduling problem, Iranian Journal of Fuzzy Systems, 18(4) (2021), 95-112. https:
//doi.org/10.22111/ijfs.2021.6179
[24] M. Komijani, M. S. Sajadieh, An integrated planning approach for perishable goods with stochastic lifespan: Pro
duction, inventory, and routing, Cleaner Logistics and Supply Chain, 12 (2024), 100163. https://doi.org/10.
1016/j.clscn.2024.100163
duction, inventory, and routing, Cleaner Logistics and Supply Chain, 12 (2024), 100163. https://doi.org/10.
1016/j.clscn.2024.100163
[25] P. Li, H. Lan, F. Saldanha-Da-Gama, A bi-objective capacitated location-routing problem for multiple perishable
commodities, IEEE Access, 7 (2019), 136729-136742. https://doi.org/10.1109/ACCESS.2019.2941363
commodities, IEEE Access, 7 (2019), 136729-136742. https://doi.org/10.1109/ACCESS.2019.2941363
[26] K. Li, J. Zheng, D. Wu, A new discrete particle swarm optimization for location inventory routing problem in cold
logistics, Revista Facultad de Ingenier´ıa, 31 (2016), 89-99. https://doi.org/10.21311/002.31.5.10
logistics, Revista Facultad de Ingenier´ıa, 31 (2016), 89-99. https://doi.org/10.21311/002.31.5.10
[27] M. L. R. Lingkon, A. Dash, Vehicle routing optimization for perishable goods to develop a sustainable supply chain
in the Bangladeshi emerging markets: An integrated location inventory model, Springer Science and Business Media
LLC, (2024). https://doi.org/10.21203/rs.3.rs-5066291/v1
in the Bangladeshi emerging markets: An integrated location inventory model, Springer Science and Business Media
LLC, (2024). https://doi.org/10.21203/rs.3.rs-5066291/v1
[28] A. Liu, et al., Sustainable supply chain management for perishable products in emerging markets: An integrated
location-inventory-routing model, Transportation Research Part E: Logistics and Transportation Review, 150 (2021),
102319. https://doi.org/10.1016/j.tre.2021.102319
location-inventory-routing model, Transportation Research Part E: Logistics and Transportation Review, 150 (2021),
102319. https://doi.org/10.1016/j.tre.2021.102319
[29] P. Liu, et al., A solution algorithm for integrated production-inventory-routing of perishable goods with transship
ment and uncertain demand, Complex and Intelligent Systems, 7(3) (2021), 1349-1365. https://link.springer.
com/article/10.1007/s40747-020-00264-y
ment and uncertain demand, Complex and Intelligent Systems, 7(3) (2021), 1349-1365. https://link.springer.
com/article/10.1007/s40747-020-00264-y
[30] A. Majidi, P. Farghadani-Chaharsooghi, S. M. J. Mirzapour Al-e-Hashem, Sustainable pricing-production
workforce-routing problem for perishable products by considering demand uncertainty; A case study from the dairy
industry, Transportation Journal, 61(1) (2022), 60-102. https://doi.org/10.5325/transportationj.61.1.0060
workforce-routing problem for perishable products by considering demand uncertainty; A case study from the dairy
industry, Transportation Journal, 61(1) (2022), 60-102. https://doi.org/10.5325/transportationj.61.1.0060
[31] M. Mesquita-Cunha, J. R. Figueira, A. P. Barbosa-P´ovoa, New ϵ− constraint methods for multi-objective integer
linear programming: A Pareto front representation approach, European Journal of Operational Research, 306(1)
(2023), 286-307. https://doi.org/10.1016/j.ejor.2022.07.044
linear programming: A Pareto front representation approach, European Journal of Operational Research, 306(1)
(2023), 286-307. https://doi.org/10.1016/j.ejor.2022.07.044
[32] S. Mirzaei, A. Seifi, Considering lost sale in inventory routing problems for perishable goods, Computers and
Industrial Engineering, 87 (2015), 213-227. https://doi.org/10.1016/j.cie.2015.05.010
Industrial Engineering, 87 (2015), 213-227. https://doi.org/10.1016/j.cie.2015.05.010
[33] M. Musavi, A. Bozorgi-Amiri, A multi-objective sustainable hub location-scheduling problem for perishable food
supply chain, Computers and Industrial Engineering, 113 (2017), 766-778. https://doi.org/10.1016/j.cie.
2017.07.039
supply chain, Computers and Industrial Engineering, 113 (2017), 766-778. https://doi.org/10.1016/j.cie.
2017.07.039
[34] M. S. Pishvaee, J. Razmi, S. A. Torabi, Robust possibilistic programming for socially responsible supply chain
network design: A new approach, Fuzzy Sets and Systems, 206 (2012), 1-20. https://doi.org/10.1016/j.fss.
2012.04.010
network design: A new approach, Fuzzy Sets and Systems, 206 (2012), 1-20. https://doi.org/10.1016/j.fss.
2012.04.010
[35] M. Pouraliakbari-Mamaghani, et al., A robust possibilistic programming approach for blood supply chain network
design in disaster relief considering congestion, Operational Research, 22(3) (2022), 1987-2032. https://doi.org/
10.1007/s12351-021-00648-z
design in disaster relief considering congestion, Operational Research, 22(3) (2022), 1987-2032. https://doi.org/
10.1007/s12351-021-00648-z
[36] Z. Rafie-Majd, S. H. R. Pasandideh, B. Naderi, Modelling and solving the integrated inventory-location-routing prob
lem in a multi-period and multi-perishable product supply chain with uncertainty: Lagrangian relaxation algorithm,
Computers and Chemical Engineering, 109 (2018), 9-22. https://doi.org/10.1016/j.compchemeng.2017.10.013
lem in a multi-period and multi-perishable product supply chain with uncertainty: Lagrangian relaxation algorithm,
Computers and Chemical Engineering, 109 (2018), 9-22. https://doi.org/10.1016/j.compchemeng.2017.10.013
[37] M. Rahbari, et al., Modeling and solving a five-echelon location-inventory-routing problem for red meat supply
chain: Case study in Iran, Kybernetes, 50(1) (2020), 66-99. https://doi.org/10.1108/K-10-2019-0652
chain: Case study in Iran, Kybernetes, 50(1) (2020), 66-99. https://doi.org/10.1108/K-10-2019-0652
[38] S. Rashvand Falari, K. Fathi Hafshjani, M. A. Afshar Kazemi, Smart multi-commodity location-routing model
for perishable goods with an emphasis on big data under uncertainty and congestion, Interdisciplinary Journal of
Management Studies (Formerly known as Iranian Journal of Management Studies), 17(2) (2024), 653-668. https:
//doi.org/10.22059/ijms.2023.359254.675865
for perishable goods with an emphasis on big data under uncertainty and congestion, Interdisciplinary Journal of
Management Studies (Formerly known as Iranian Journal of Management Studies), 17(2) (2024), 653-668. https:
//doi.org/10.22059/ijms.2023.359254.675865
[39] S. Rohmer, G. Claassen, G. Laporte, A two-echelon inventory routing problem for perishable products, Computers
and Operations Research, 107 (2019), 156-172. https://doi.org/10.1016/j.cor.2019.03.015
and Operations Research, 107 (2019), 156-172. https://doi.org/10.1016/j.cor.2019.03.015
[40] N. I. Saragih, N. Bahagia, I. Syabri, A heuristic method for location-inventory-routing problem in a three-echelon
supply chain system, Computers and Industrial Engineering, 127 (2019), 875-886. https://doi.org/10.1016/j.
cie.2018.11.026
supply chain system, Computers and Industrial Engineering, 127 (2019), 875-886. https://doi.org/10.1016/j.
cie.2018.11.026
[41] L. Song, Z. Wu, An integrated approach for optimizing location-inventory and location-inventory-routing problem
for perishable products, International Journal of Transportation Science and Technology, 12(1) (2022), 148-172.
https://doi.org/10.1016/j.ijtst.2022.02.002
for perishable products, International Journal of Transportation Science and Technology, 12(1) (2022), 148-172.
https://doi.org/10.1016/j.ijtst.2022.02.002
[42] M. Soysal, et al., Modeling an inventory routing problem for perishable products with environmental considerations
and demand uncertainty, International Journal of Production Economics, 164 (2015), 118-133. https://doi.org/
10.1016/j.ijpe.2015.03.008
and demand uncertainty, International Journal of Production Economics, 164 (2015), 118-133. https://doi.org/
10.1016/j.ijpe.2015.03.008
[43] E. B. Tirkolaee, et al., An efficient biography-based optimization algorithm to solve the location routing problem
with intermediate depots for multiple perishable products, in deep learning and parallel computing environment for
bioengineering systems, Elsevier, (2019), 189-205. https://doi.org/10.1016/B978-0-12-816718-2.00019-1
with intermediate depots for multiple perishable products, in deep learning and parallel computing environment for
bioengineering systems, Elsevier, (2019), 189-205. https://doi.org/10.1016/B978-0-12-816718-2.00019-1
[44] B. Vahdani, S. Niaki, S. Aslanzade, Production-inventory-routing coordination with capacity and time window
constraints for perishable products: Heuristic and meta-heuristic algorithms, Journal of Cleaner Production, 161
(2017), 598-618. https://doi.org/10.1016/j.jclepro.2017.05.113
constraints for perishable products: Heuristic and meta-heuristic algorithms, Journal of Cleaner Production, 161
(2017), 598-618. https://doi.org/10.1016/j.jclepro.2017.05.113
[45] S. Wang, F. Tao, Y. Shi, Optimization of location–routing problem for cold chain logistics considering carbon
footprint, International Journal of Environmental Research and Public Health, 15(1) (2018), 86. https://doi.
org/10.3390/ijerph15010086
footprint, International Journal of Environmental Research and Public Health, 15(1) (2018), 86. https://doi.
org/10.3390/ijerph15010086
[46] X. K. Wang, Y. T. Wang, et al., An asymmetric trapezoidal cloud-based linguistic group decision-making method
under unbalanced linguistic distribution assessments, Computers and Industrial Engineering, 160 (2021), 107457.
https://doi.org/10.1016/j.cie.2021.107457
under unbalanced linguistic distribution assessments, Computers and Industrial Engineering, 160 (2021), 107457.
https://doi.org/10.1016/j.cie.2021.107457
[47] A. Yaghoubi, F. Akrami, Proposing a new model for location-routing problem of perishable raw material suppliers
with using meta-heuristic algorithms, Heliyon, 5(12) (2019), e03020. https://doi.org/10.1016/j.heliyon.2019.
e03020
with using meta-heuristic algorithms, Heliyon, 5(12) (2019), e03020. https://doi.org/10.1016/j.heliyon.2019.
e03020
[48] S. Zandkarimkhani, et al., A chance constrained fuzzy goal programming approach for perishable pharmaceutical
supply chain network design, Annals of Operations Research, 295(1) (2020), 425-452. https://doi.org/10.1007/
s10479-020-03677-7
supply chain network design, Annals of Operations Research, 295(1) (2020), 425-452. https://doi.org/10.1007/
s10479-020-03677-7
[49] Y. Zhang, et al., Closed-loop inventory routing problem for perishable food with returnable transport items selec
tion, International Journal of Production Research, 62(1-2) (2024), 501-521. https://doi.org/10.1080/00207543.
2023.2275639
tion, International Journal of Production Research, 62(1-2) (2024), 501-521. https://doi.org/10.1080/00207543.
2023.2275639
[50] L. Zhang, et al., Research on location-inventory-routing optimization of emergency logistics based on multiple
reliability under uncertainty, Computers and Industrial Engineering, 200 (2025), 110826. https://doi.org/10.
1016/j.cie.2024.110826
reliability under uncertainty, Computers and Industrial Engineering, 200 (2025), 110826. https://doi.org/10.
1016/j.cie.2024.110826
)