As a relatively clean energy source, liquefied natural gas (LNG) is experiencing a growing demand. The uneven global distribution of LNG often compels residents in regions without local sources to import it, underscoring the need to optimize the global LNG transportation network. Therefore, this study formulates a nonlinear mixed-integer programming model for a multimodal transport and storage problem to optimize LNG carrier allocation, LNG storage planning, and LNG transport planning, aiming to minimize the total cost of multimodal transport, minus the rewards offered by ports. In order to facilitate the solving of the model, some linearization methods are used to transform the nonlinear model into a linear model. To assess the efficiency of the linear model, we conduct computational experiments on small-scale instances with five inland cities, medium-scale instances with 15 inland cities, and large-scale instances with 60 inland cities. The results show that all small- and medium-scale instances can be solved to optimality within 427.50 s. Feasible solutions with a maximum gap value of 0.03% for large-scale instances can be obtained within 1 h. In addition, sensitivity analyses are conducted to identify the impacts of the cost of transporting LNG by vehicles, the charter cost of LNG carriers, and the rewards for shipping LNG. In general, higher cost of transporting LNG by vehicles and higher charter cost of LNG carriers lead to a higher objective value. It is also found that when the rewards for shipping LNG increase to a certain extent, such that the additional rewards exceed the additional multimodal transport cost incurred, the amount of LNG unloaded at the subsidized port increases.
Citation: Hongyu Zhang, Yiwei Wu, Lu Zhen, Yong Jin, Shuaian Wang. Optimization problems in liquefied natural gas transport and storage for multimodal transport companies[J]. Electronic Research Archive, 2024, 32(8): 4828-4844. doi: 10.3934/era.2024221
As a relatively clean energy source, liquefied natural gas (LNG) is experiencing a growing demand. The uneven global distribution of LNG often compels residents in regions without local sources to import it, underscoring the need to optimize the global LNG transportation network. Therefore, this study formulates a nonlinear mixed-integer programming model for a multimodal transport and storage problem to optimize LNG carrier allocation, LNG storage planning, and LNG transport planning, aiming to minimize the total cost of multimodal transport, minus the rewards offered by ports. In order to facilitate the solving of the model, some linearization methods are used to transform the nonlinear model into a linear model. To assess the efficiency of the linear model, we conduct computational experiments on small-scale instances with five inland cities, medium-scale instances with 15 inland cities, and large-scale instances with 60 inland cities. The results show that all small- and medium-scale instances can be solved to optimality within 427.50 s. Feasible solutions with a maximum gap value of 0.03% for large-scale instances can be obtained within 1 h. In addition, sensitivity analyses are conducted to identify the impacts of the cost of transporting LNG by vehicles, the charter cost of LNG carriers, and the rewards for shipping LNG. In general, higher cost of transporting LNG by vehicles and higher charter cost of LNG carriers lead to a higher objective value. It is also found that when the rewards for shipping LNG increase to a certain extent, such that the additional rewards exceed the additional multimodal transport cost incurred, the amount of LNG unloaded at the subsidized port increases.
| [1] |
B. B. Kanbur, L. Xiang, S. Dubey, F. H. Choo, F. Duan, Cold utilization systems of LNG: A review, Renewable Sustainable Energy Rev., 79 (2017), 1171–1188. https://doi.org/10.1016/j.rser.2017.05.161 doi: 10.1016/j.rser.2017.05.161
|
| [2] |
J. Kim, Y. Seo, D. Chang, Economic evaluation of a new small-scale LNG supply chain using liquid nitrogen for natural-gas liquefaction, Appl. Energy, 182 (2016), 154–163. https://doi.org/10.1016/j.apenergy.2016.08.130 doi: 10.1016/j.apenergy.2016.08.130
|
| [3] | Elengy, How is LNG used? 2024. Available from: https://www.elengy.com/en/how-lng-used. |
| [4] |
L. Wei, P. Geng, A review on natural gas/diesel dual fuel combustion, emissions and performance, Fuel Process. Technol., 142 (2016), 264–278. https://doi.org/10.1016/j.fuproc.2015.09.018 doi: 10.1016/j.fuproc.2015.09.018
|
| [5] | International Energy Agency (IEA), The role of gas in today's energy transitions, 2019. Available from: https://www.iea.org/reports/the-role-of-gas-in-todays-energy-transitions. |
| [6] |
K. Dong, G. Hochman, Y. Zhang, R. Sun, H. Li, H. Liao, CO$_2$ emissions, economic and population growth, and renewable energy: Empirical evidence across regions, Energy Econ., 75 (2018), 180–192. https://doi.org/10.1016/j.eneco.2018.08.017 doi: 10.1016/j.eneco.2018.08.017
|
| [7] |
S. Imran, D. R. Emberson, A. Diez, D. S. Wen, R. J. Crookes, T. Korakianitis, Natural gas fueled compression ignition engine performance and emissions maps with diesel and RME pilot fuels, Appl. Energy, 124 (2014), 354–365. https://doi.org/10.1016/j.apenergy.2014.02.067 doi: 10.1016/j.apenergy.2014.02.067
|
| [8] | U.S. Energy Information Administration (U.S. EIA), Natural gas and the environment, 2024. Available from: https://www.eia.gov/energyexplained/natural-gas/natural-gas-and-the-environment.php. |
| [9] |
K. Wang, X. Qian, Y. He, T. Shi, X. Zhang, Failure analysis integrated with prediction model for LNG transport trailer and thermal hazards induced by an accidental VCE: A case study, Eng. Fail. Anal., 108 (2020), 104350. https://doi.org/10.1016/j.engfailanal.2019.104350 doi: 10.1016/j.engfailanal.2019.104350
|
| [10] |
H. Chen, G. Yang, J. Wu, A multi-zone thermodynamic model for predicting LNG ageing in large cryogenic tanks, Energy, 283 (2023), 128503. https://doi.org/10.1016/j.energy.2023.128503 doi: 10.1016/j.energy.2023.128503
|
| [11] |
S. Kumar, H. T. Kwon, K. H. Choi, W. Lim, J. H. Cho, K. Tak, et al., LNG: An eco-friendly cryogenic fuel for sustainable development, Appl. Energy, 88 (2011), 4264–4273. https://doi.org/10.1016/j.apenergy.2011.06.035 doi: 10.1016/j.apenergy.2011.06.035
|
| [12] | International Gas Union (IGU), 2023 world LNG report, 2023. Available from: https://igu.org/resources/lng2023-world-lng-report/. |
| [13] | Lloyd's List (LL), Shenzhen offers incentives for developing LNG shipping business, 2023. Available from: https://lloydslist.com/LL1144778/Shenzhen-offers-incentives-for-developing-LNG-shipping-business. |
| [14] |
R. Z. Rios-Mercado, C. Borraz-Sanchez, Optimization problems in natural gas transportation systems: A state-of-the-art review, Appl. Energy, 147 (2015), 536–555. https://doi.org/10.1016/j.apenergy.2015.03.017 doi: 10.1016/j.apenergy.2015.03.017
|
| [15] |
M. Schach, R. Madlener, Impacts of an ice-free northeast passage on LNG markets and geopolitics, Energy Policy, 122 (2018), 438–448. https://doi.org/10.1016/j.enpol.2018.07.009 doi: 10.1016/j.enpol.2018.07.009
|
| [16] |
L. Zhang, S. Zhang, C. Yu, Network optimisation for transporting liquefied natural gas from stations to end customers, Int. J. Prod. Res., 59 (2021), 1791–1813. https://doi.org/10.1080/00207543.2020.1725682 doi: 10.1080/00207543.2020.1725682
|
| [17] |
T. He, Z. R. Chong, J. Zheng, Y. Ju, P. Linga, LNG cold energy utilization: Prospects and challenges, Energy, 170 (2019), 557–568. https://doi.org/10.1016/j.energy.2018.12.170 doi: 10.1016/j.energy.2018.12.170
|
| [18] |
M. Mehrpooya, M. M. M. Sharifzadeh, M. A. Rosen, Optimum design and exergy analysis of a novel cryogenic air separation process with LNG (liquefied natural gas) cold energy utilization, Energy, 90 (2015), 2047–2069. https://doi.org/10.1016/j.energy.2015.07.101 doi: 10.1016/j.energy.2015.07.101
|
| [19] |
M. Mehrpooya, M. Kalhorzadeh, M. Chahartaghi, Investigation of novel integrated air separation processes, cold energy recovery of liquefied natural gas and carbon dioxide power cycle, J. Clean. Prod., 113 (2016), 411–425. https://doi.org/10.1016/j.jclepro.2015.12.058 doi: 10.1016/j.jclepro.2015.12.058
|
| [20] |
X. Chen, M. Wang, B. Wang, H. Hao, H. Shi, Z. Wu, et al., Energy consumption reduction and sustainable development for oil & gas transport and storage engineering, Energies, 16 (2023), 1775. https://doi.org/10.3390/en16041775 doi: 10.3390/en16041775
|
| [21] |
A. Sharafian, O. E. Herrera, W. Mérida, Performance analysis of liquefied natural gas storage tanks in refueling stations, J. Nat. Gas Sci. Eng., 36 (2016), 496–509. https://doi.org/10.1016/j.jngse.2016.10.062 doi: 10.1016/j.jngse.2016.10.062
|
| [22] |
M. Huffman, V. Hutchison, S. Ranganathan, G. Noll, C. Baxter, M. Hildebrand, et al., A comparative bibliometric study of the transport risk considerations of liquefied natural gas and liquefied petroleum gas, Can. J. Chem. Eng., 102 (2024), 2019–2038. https://doi.org/10.1002/cjce.25226 doi: 10.1002/cjce.25226
|
| [23] |
J. Wu, Y. Bai, H. Zhao, X. Hu, V. Cozzani, A quantitative LNG risk assessment model based on integrated Bayesian-Catastrophe-EPE method, Saf. Sci., 137 (2021), 105184. https://doi.org/10.1016/j.ssci.2021.105184 doi: 10.1016/j.ssci.2021.105184
|
| [24] |
J. Yu, H. Ding, Y. Yu, S. Wu, Q. Zeng, Y. Xu, Risk assessment of liquefied natural gas storage tank leakage using failure mode and effects analysis with Fermatean fuzzy sets and CoCoSo method, Appl. Soft Comput., 154 (2024), 111334. https://doi.org/10.1016/j.asoc.2024.111334 doi: 10.1016/j.asoc.2024.111334
|
| [25] |
M. Miana, R. D. Hoyo, V. Rodrigálvarez, J. R. Valdés, R. Llorens, Calculation models for prediction of liquefied natural gas (LNG) ageing during ship transportation, Appl. Energy, 87 (2010), 1687–1700. https://doi.org/10.1016/j.apenergy.2009.10.023 doi: 10.1016/j.apenergy.2009.10.023
|
| [26] |
J. Yuan, X. Shi, J. He, LNG market liberalization and LNG transportation: Evaluation based on fleet size and composition model, Appl. Energy, 358 (2024), 122657. https://doi.org/10.1016/j.apenergy.2024.122657 doi: 10.1016/j.apenergy.2024.122657
|
| [27] |
L. Xu, Y. Luo, J. Chen, S. Zhou, Capacity prioritization allocation and credit financing option in shipping freight forwarding market, Comput. Ind. Eng., 189 (2024), 109987. https://doi.org/10.1016/j.cie.2024.109987 doi: 10.1016/j.cie.2024.109987
|
| [28] | United Nations Economic Commission for Europe, Illustrated Glossary for Transport Statistics 4th Edition, OECD Publishing, 2009. |
| [29] |
M. SteadieSeifi, N. P. Dellaert, W. Nuijten, T. V. Woensel, R. Raoufi, Multimodal freight transportation planning: A literature review, Eur. J. Oper. Res., 233 (2014), 1–15. https://doi.org/10.1016/j.ejor.2013.06.055 doi: 10.1016/j.ejor.2013.06.055
|
| [30] |
A. Baykasoglu, K. Subulan, A. S. Tasan, N. Dudakli, A review of fleet planning problems in single and multimodal transportation systems, Transportmetrica A: Transp. Sci., 15 (2019), 631–697. https://doi.org/10.1080/23249935.2018.1523249 doi: 10.1080/23249935.2018.1523249
|
| [31] |
C. Archetti, L. Peirano, M. G. Speranza, Optimization in multimodal freight transportation problems: A Survey, Eur. J. Oper. Res., 299 (2022), 1–20. https://doi.org/10.1016/j.ejor.2021.07.031 doi: 10.1016/j.ejor.2021.07.031
|
| [32] |
W. Hou, Q. Shi, L. Guo, Impacts of COVID-19 pandemic on foreign trade intermodal transport accessibility: Evidence from the Yangtze River Delta region of mainland China, Transp. Res. Part A Policy Pract., 165 (2022), 419–438. https://doi.org/10.1016/j.tra.2022.09.019 doi: 10.1016/j.tra.2022.09.019
|
| [33] |
L. B. Real, I. Contreras, J. F. Cordeau, R. S. de Camargo, G. de Miranda, Multimodal hub network design with flexible routes, Transp. Res. Part E Logist. Transp. Rev., 146 (2021), 102188. https://doi.org/10.1016/j.tre.2020.102188 doi: 10.1016/j.tre.2020.102188
|
| [34] |
A. Abbassi, A. E. hilali Alaoui, J. Boukachour, Robust optimisation of the intermodal freight transport problem: Modeling and solving with an efficient hybrid approach, J. Comput. Sci., 30 (2019), 127–142. https://doi.org/10.1016/j.jocs.2018.12.001 doi: 10.1016/j.jocs.2018.12.001
|
| [35] |
R. Jokinen, F. Pettersson, H. Saxén, An MILP model for optimization of a small-scale LNG supply chain along a coastline, Appl. Energy, 138 (2015), 423–431. https://doi.org/10.1016/j.apenergy.2014.10.039 doi: 10.1016/j.apenergy.2014.10.039
|
| [36] |
D. J. Papageorgiou, G. L. Nemhauser, J. Sokol, M. S. Cheon, A. B. Keha, MIRPLib - A library of maritime inventory routing problem instances: Survey, core model, and benchmark results, Eur. J. Oper. Res., 235 (2014), 350–366. https://doi.org/10.1016/j.ejor.2013.12.013 doi: 10.1016/j.ejor.2013.12.013
|
| [37] |
M. Soysal, M. Çimen, S. Belbag, E. Togrul, A review on sustainable inventory routing, Comput. Ind. Eng., 132 (2019), 395–411. https://doi.org/10.1016/j.cie.2019.04.026 doi: 10.1016/j.cie.2019.04.026
|
| [38] |
H. Shaabani, A literature review of the perishable inventory routing problem, Asian J. Shipp. Logist., 38 (2022), 143–161. https://doi.org/10.1016/j.ajsl.2022.05.002 doi: 10.1016/j.ajsl.2022.05.002
|
| [39] |
C. Archetti, I. Ljubic, Comparison of formulations for the inventory routing problem, Eur. J. Oper. Res., 303 (2022), 997–1008. https://doi.org/10.1016/j.ejor.2021.12.051 doi: 10.1016/j.ejor.2021.12.051
|
| [40] |
H. Andersson, M. Christiansen, G. Desaulniers, A new decomposition algorithm for a liquefied natural gas inventory routing problem, Int. J. Prod. Res., 54 (2016), 564–578. https://doi.org/10.1080/00207543.2015.1037024 doi: 10.1080/00207543.2015.1037024
|
| [41] |
Y. Shao, K. C. Furman, V. Goel, S. Hoda, A hybrid heuristic strategy for liquefied natural gas inventory routing, Transp. Res. Part C Emerging Technol., 53 (2015), 151–171. https://doi.org/10.1016/j.trc.2015.02.001 doi: 10.1016/j.trc.2015.02.001
|
| [42] |
M. Li, K. Fagerholt, P. Schütz, Maritime inventory routing with transshipment: the case of Yamal LNG, Flexible Serv. Manuf. J., 35 (2023), 269–294. https://doi.org/10.1007/s10696-022-09476-5 doi: 10.1007/s10696-022-09476-5
|
| [43] |
Y. Wu, H. Zhang, S. Wang, L. Zhen, Mathematical optimization of carbon storage and transport problem for carbon capture, use, and storage chain, Mathematics, 11 (2023), 2765. https://doi.org/10.3390/math11122765 doi: 10.3390/math11122765
|
| [44] |
M. Wen, D. Pacino, C. A. Kontovas, H. N. Psaraftis, A multiple ship routing and speed optimization problem under time, cost and environmental objectives, Transp. Res. Part D Transp. Environ., 52 (2017), 303–321. https://doi.org/10.1016/j.trd.2017.03.009 doi: 10.1016/j.trd.2017.03.009
|
| [45] |
B. Liu, Z. C. Li, Y. Wang, A branch-and-price heuristic algorithm for the bunkering operation problem of a liquefied natural gas bunkering station in the inland waterways, Transp. Res. Part B Methodol., 167 (2023), 145–170. https://doi.org/10.1016/j.trb.2022.11.011 doi: 10.1016/j.trb.2022.11.011
|
| [46] | China Water Transport Website (CWTW), LNG carriers: Another dark horse in the shipping market, 2021. Available from: https://www.zgsyb.com/news.html?aid=601512. |
| [47] |
R. Gronhaug, M. Christiansen, G. Desaulniers, A branch-and-price method for a liquefied natural gas inventory routing problem, Transp. Sci., 44 (2010), 400–415. https://doi.org/10.1287/trsc.1100.0317 doi: 10.1287/trsc.1100.0317
|
| [48] |
D. H. Utku, B. Soyöz, A mathematical model on liquefied natural gas supply chain with uncertain demand, SN Appl. Sci., 2 (2020), 1–15. https://doi.org/10.1007/s42452-020-03297-7 doi: 10.1007/s42452-020-03297-7
|
| [49] |
A. Bittante, F. Pettersson, H. Saxén, Optimization of a small-scale LNG supply chain, Energy, 148 (2018), 79–89. https://doi.org/10.1016/j.energy.2018.01.120 doi: 10.1016/j.energy.2018.01.120
|
| [50] |
H. Zhang, Y. Liang, Q. Liao, J. Chen, W. Zhang, Y. Long, et al., Optimal design and operation for supply chain system of multi-state natural gas under uncertainties of demand and purchase price, Comput. Ind. Eng., 131 (2019), 115–130. https://doi.org/10.1016/j.cie.2019.03.041 doi: 10.1016/j.cie.2019.03.041
|
| [51] |
E. E. Halvorsen-Weare, K. Fagerholt, M. Rönnqvist, Vessel routing and scheduling under uncertainty in the liquefied natural gas business, Comput. Ind. Eng., 64 (2013), 290–301. https://doi.org/10.1016/j.cie.2012.10.011 doi: 10.1016/j.cie.2012.10.011
|
| [52] |
Y. Wu, H. Zhang, F. Li, S. Wang, L. Zhen, Optimal selection of multi-fuel engines for ships considering fuel price uncertainty, Mathematics, 11 (2023), 3621. https://doi.org/10.3390/math11173621 doi: 10.3390/math11173621
|
| [53] |
A. Bavar, A. Bavar, F. Gholian-Jouybari, M. Hajiaghaei-Keshteli, C. Mejía-Argueta, Developing new heuristics and hybrid meta-heuristics to address the bi-objective home health care problem, Cent. Eur. Oper. Res., (2023), 1–57. https://doi.org/10.1007/s10100-023-00862-4 doi: 10.1007/s10100-023-00862-4
|
| [54] |
D. B. M. M. Fontes, S. M. Homayouni, J. F. Gonçalves, A hybrid particle swarm optimization and simulated annealing algorithm for the job shop scheduling problem with transport resources, Eur. J. Oper. Res., 306 (2023), 1140–1157. https://doi.org/10.1016/j.ejor.2022.09.006 doi: 10.1016/j.ejor.2022.09.006
|
| [55] |
M. Chen, Y. Tan, SF-FWA: A self-adaptive fast fireworks algorithm for effective large-scale optimization, Swarm Evol. Comput., 80 (2023), 101314. https://doi.org/10.1016/j.swevo.2023.101314 doi: 10.1016/j.swevo.2023.101314
|
| [56] |
M. S. Turgut, O. E. Turgut, D. T. Eliiyi, Island-based crow search algorithm for solving optimal control problems, Appl. Soft Comput., 90 (2020), 106170. https://doi.org/10.1016/j.asoc.2020.106170 doi: 10.1016/j.asoc.2020.106170
|
| [57] |
M. A. Dulebenets, An adaptive polyploid memetic algorithm for scheduling trucks at a cross-docking terminal, Inf. Sci., 565 (2021), 390–421. https://doi.org/10.1016/j.ins.2021.02.039 doi: 10.1016/j.ins.2021.02.039
|
| [58] |
E. Singh, N. Pillay, A study of ant-based pheromone spaces for generation constructive hyper-heuristics, Swarm Evol. Comput., 72 (2022), 101095. https://doi.org/10.1016/j.swevo.2022.101095 doi: 10.1016/j.swevo.2022.101095
|
| [59] |
M. Safaeian, R. Khayamim, E. E. Ozguven, M. A. Dulebenets, Sustainable decisions in a ridesharing system with a tri-objective optimization approach, Transp. Res. Part D Transp. Environ., 125 (2023), 103958. https://doi.org/10.1016/j.trd.2023.103958 doi: 10.1016/j.trd.2023.103958
|
| [60] |
M. A. Dulebenets, A diffused memetic optimizer for reactive berth allocation and scheduling at marine container terminals in response to disruptions, Swarm Evol. Comput., 80 (2023), 101334. https://doi.org/10.1016/j.swevo.2023.101334 doi: 10.1016/j.swevo.2023.101334
|
| [61] |
B. Abd-El-Atty, A robust medical image steganography approach based on particle swarm optimization algorithm and quantum walks, Neural Comput. Appl., 35 (2023), 773–785. https://doi.org/10.1007/s00521-022-07830-0 doi: 10.1007/s00521-022-07830-0
|
| [62] |
S. Kaur, Y. Kumar, A. Koul, S. Kumar Kamboj, A systematic review on metaheuristic optimization techniques for feature selections in disease diagnosis: Open issues and challenges, Arch. Comput. Methods Eng., 30 (2023), 1863–1895. https://doi.org/10.1007/s11831-022-09853-1 doi: 10.1007/s11831-022-09853-1
|
| [63] |
Ş. Ay, E. Ekinci, Z. Garip, A comparative analysis of meta-heuristic optimization algorithms for feature selection on ML-based classification of heart-related diseases, J. Supercomput., 79 (2023), 11797–11826. https://doi.org/10.1007/s11227-023-05132-3 doi: 10.1007/s11227-023-05132-3
|
Figures(1) / Tables(2)
Hongyu Zhang, Yiwei Wu, Lu Zhen, Yong Jin, Shuaian Wang. Optimization problems in liquefied natural gas transport and storage for multimodal transport companies[J]. Electronic Research Archive, 2024, 32(8): 4828-4844. doi: 10.3934/era.2024221
DownLoad: