A cross-regional emergency supply pre-positioning with partial collaboration cost-sharing strategy

Jingke Zhou; Yingzhen Chen; Jingke Zhou; Yingzhen Chen

doi:10.3934/jimo.2026166

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 10: 4796-4824. doi: 10.3934/jimo.2026166

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Research article

A cross-regional emergency supply pre-positioning with partial collaboration cost-sharing strategy

Jingke Zhou ¹,
Yingzhen Chen ^{2
,
,}

1.
School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang, Hubei, 441053, China
2.
School of Economics and Management, Hubei University of Arts and Science, Xiangyang, Hubei, 441053, China

Received: 27 March 2026 Revised: 03 September 2026 Accepted: 04 September 2026 Published: 09 September 2026
90B90, 90C17, 90C15

Collaborative pre-positioning of emergency supplies enhances the efficiency of emergency response. A partial collaboration cost-sharing strategy is proposed for cross-regional emergency supply pre-positioning. In the proposed strategy, demand-based costs and risk-based costs are incorporated while considering both the benefits of collaboration and the principle of territoriality. To encourage regional involvement, regional relevance is incorporated into the proposed cost-sharing strategy, reflecting the interdependence among regions. A distributionally robust chance-constrained optimization model is developed to address the uncertainties in emergency supply pre-positioning. Numerical results demonstrate that the proposed partial collaboration strategy achieves a more practically feasible trade-off between fairness and efficiency than the independent and centralized strategies. Sensitivity analyses are performed on the parameters of the proposed model. The findings yield practical managerial insights for implementing collaborative emergency supply pre-positioning. This study provides valuable implications for designing a cross-regional emergency supply pre-positioning system.
- cross-regional collaboration,
- cost sharing,
- emergency supply pre-positioning,
- distributionally robust chance-constrained optimization
Citation: Jingke Zhou, Yingzhen Chen. A cross-regional emergency supply pre-positioning with partial collaboration cost-sharing strategy[J]. Journal of Industrial and Management Optimization, 2026, 22(10): 4796-4824. doi: 10.3934/jimo.2026166

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Abstract

Collaborative pre-positioning of emergency supplies enhances the efficiency of emergency response. A partial collaboration cost-sharing strategy is proposed for cross-regional emergency supply pre-positioning. In the proposed strategy, demand-based costs and risk-based costs are incorporated while considering both the benefits of collaboration and the principle of territoriality. To encourage regional involvement, regional relevance is incorporated into the proposed cost-sharing strategy, reflecting the interdependence among regions. A distributionally robust chance-constrained optimization model is developed to address the uncertainties in emergency supply pre-positioning. Numerical results demonstrate that the proposed partial collaboration strategy achieves a more practically feasible trade-off between fairness and efficiency than the independent and centralized strategies. Sensitivity analyses are performed on the parameters of the proposed model. The findings yield practical managerial insights for implementing collaborative emergency supply pre-positioning. This study provides valuable implications for designing a cross-regional emergency supply pre-positioning system.

References

[1]	C. Hein, F. Behrens, R. Lasch, Insights on the costs of humanitarian logistics: A case study analysis, Logist. Res., 13 (2020), 1–17.https://doi.org/10.23773/2020_3 doi: 10.23773/2020_3
[2]	M. Falasca, C. W. Zobel, A two-stage procurement model for humanitarian relief supply chains, J. Humanit. Logist. Supply Chain Manag., 1 (2011), 151–169.https://doi.org/10.1108/20426741111188329 doi: 10.1108/20426741111188329
[3]	B. Balcik, B. M. Beamon, C. C. Krejci, K. M. Muramatsu, M. Ramirez, Coordination in humanitarian relief chains: Practices, challenges and opportunities, Int. J. Prod. Econ., 126 (2010), 22–34.https://doi.org/10.1016/j.ijpe.2009.09.008 doi: 10.1016/j.ijpe.2009.09.008
[4]	B. Balcik, S. Silvestri, M. È. Rancourt, G. Laporte, Collaborative prepositioning network design for regional disaster response, Prod. Oper. Manag., 28 (2019), 2431–2455.https://doi.org/10.1111/poms.13053 doi: 10.1111/poms.13053
[5]	J. Rodríguez-Pereira, B. Balcik, M. È. Rancourt, G. Laporte, A cost-sharing mechanism for multi-country partnerships in disaster preparedness, Prod. Oper. Manag., 30 (2021), 4541–4565.https://doi.org/10.1111/poms.13403 doi: 10.1111/poms.13403
[6]	Y. C. Li, Y. Liu, Distributionally robust optimization for collaborative emergency response network design, Transp. Res. Part E Logist. Transp. Rev., 176 (2023), 103221.https://doi.org/10.1016/j.tre.2023.103221 doi: 10.1016/j.tre.2023.103221
[7]	L. He, J. H. Chen, H. Chen, Q. Cui, Regional economic impact of flood disasters in Yangtze River Economic Zone: A TERM model with a decomposition analysis approach, Int. J. Disaster Risk Reduct., 120 (2025), 105346.https://doi.org/10.1016/j.ijdrr.2025.105346 doi: 10.1016/j.ijdrr.2025.105346
[8]	W. Ding, J. D. Wu, Interregional economic impacts of an extreme storm flood scenario considering transportation interruption: A case study of Shanghai, China, Sustain. Cities Soc., 88 (2023), 104296. https://doi.org/10.1016/j.scs.2022.104296
[9]	P. Zhang, Y. Liu, G. Yang, G. Zhang, A distributionally robust optimization model for designing humanitarian relief network with resource reallocation, Soft Comput., 24 (2020), 2749–2767.https://doi.org/10.1007/s00500-019-04362-z doi: 10.1007/s00500-019-04362-z
[10]	D. Wang, K. Yang, L. Yang, Risk-averse two-stage distributionally robust optimisation for logistics planning in disaster relief management, Int. J. Prod. Res., 61 (2023), 668–691.https://doi.org/10.1080/00207543.2021.2013559 doi: 10.1080/00207543.2021.2013559
[11]	Z. Jiang, R. Ji, Z. S. Dong, A distributionally robust chance-constrained model for humanitarian relief network design, OR Spectr., 45 (2023), 1153–1195.https://doi.org/10.1007/s00291-023-00726-y doi: 10.1007/s00291-023-00726-y
[12]	M. S. Chang, Y. L. Tseng, J. W. Chen, A scenario planning approach for the flood emergency logistics preparation problem under uncertainty, Transp. Res. Part E Logist. Transp. Rev., 43 (2007), 737–754.https://doi.org/10.1016/j.tre.2006.10.013 doi: 10.1016/j.tre.2006.10.013
[13]	C. G. Rawls, M. A. Turnquist, Pre-positioning of emergency supplies for disaster response, Transp. Res. Part B Methodol., 44 (2010), 521–534.https://doi.org/10.1016/j.trb.2009.08.003 doi: 10.1016/j.trb.2009.08.003
[14]	H. O. Mete, Z. B. Zabinsky, Stochastic optimization of medical supply location and distribution in disaster management, Int. J. Prod. Econ., 126 (2010), 76–84.https://doi.org/10.1016/j.ijpe.2009.10.004 doi: 10.1016/j.ijpe.2009.10.004
[15]	A. Döyen, N. Aras, G. Barbarosoğlu, A two-echelon stochastic facility location model for humanitarian relief logistics, Optim. Lett., 6 (2012), 1123–1145.https://doi.org/10.1007/s11590-011-0421-0 doi: 10.1007/s11590-011-0421-0
[16]	S. Duran, M. A. Gutierrez, P. Keskinocak, Pre-positioning of emergency items for CARE International, Interfaces, 41 (2011), 223–237.https://doi.org/10.1287/inte.1100.0526 doi: 10.1287/inte.1100.0526
[17]	M. Sabbaghtorkan, R. Batta, Q. He, Prepositioning of assets and supplies in disaster operations management: Review and research gap identification, Eur. J. Oper. Res., 284 (2020), 1–19.https://doi.org/10.1016/j.ejor.2019.06.029 doi: 10.1016/j.ejor.2019.06.029
[18]	Ö. Ergun, L. Gui, J. L. Heier Stamm, P. Keskinocak, J. Swann, Improving humanitarian operations through technology-enabled collaboration, Prod. Oper. Manag., 23 (2014), 1002–1014.https://doi.org/10.1111/poms.12107 doi: 10.1111/poms.12107
[19]	M. Aghajani, S. A. Torabi, J. Heydari, A novel option contract integrated with supplier selection and inventory prepositioning for humanitarian relief supply chains, Socio-Econ. Plan. Sci., 71 (2020), 100780.https://doi.org/10.1016/j.seps.2019.100780 doi: 10.1016/j.seps.2019.100780
[20]	F. Wang, Z. Xie, Z. Pei, D. Liu, Emergency relief chain for natural disaster response based on government-enterprise coordination, Int. J. Environ. Res. Public Health, 19 (2022), 11255.https://doi.org/10.3390/ijerph191811255 doi: 10.3390/ijerph191811255
[21]	H. Liu, Q. H. Zhao, Q. Lin, X. H. Yue, A novel disaster insurance model with capacity reservation for public-private collaboration, Risk Anal., 45 (2025), 4572–4588.https://doi.org/10.1111/risa.70132 doi: 10.1111/risa.70132
[22]	J. Jiang, J. Ma, X. Chen, Multi-regional collaborative mechanisms in emergency resource reserve and pre-dispatch design, Int. J. Prod. Econ., 270 (2024), 109161.https://doi.org/10.1016/j.ijpe.2024.109161 doi: 10.1016/j.ijpe.2024.109161
[23]	Y. Lei, G. Zhang, S. Lu, Revealing the generation mechanism of cross-regional emergency cooperation during accidents and disasters rescue, Saf. Sci., 163 (2023), 106140.https://doi.org/10.1016/j.ssci.2023.106140 doi: 10.1016/j.ssci.2023.106140
[24]	Q. Y. Wang, Z. M. Liu, P. Jiang, L. Luo, A stochastic programming model for emergency supplies pre-positioning, transshipment and procurement in a regional healthcare coalition, Socio-Econ. Plan. Sci., 82 (2022), 101279.https://doi.org/10.1016/j.seps.2022.101279 doi: 10.1016/j.seps.2022.101279
[25]	Y. Z. Chen, Q. H. Zhao, L. Wang, M. Dessouky, The regional cooperation-based warehouse location problem for relief supplies, Comput. Ind. Eng., 102 (2016), 259–267.https://doi.org/10.1016/j.cie.2016.10.021 doi: 10.1016/j.cie.2016.10.021
[26]	L. Liang, X. H. Wang, J. G. Gao, An option contract pricing model of relief material supply chain, Omega, 40 (2012), 594–600.https://doi.org/10.1016/j.omega.2011.11.004 doi: 10.1016/j.omega.2011.11.004
[27]	X. H. Wang, F. Li, L. Liang, Z. M. Huang, A. Ashley, Pre-purchasing with option contract and coordination in a relief supply chain, Int. J. Prod. Econ., 167 (2015), 170–176.https://doi.org/10.1016/j.ijpe.2015.05.031 doi: 10.1016/j.ijpe.2015.05.031
[28]	S. A. Torabi, I. Shokr, S. Tofighi, J. Heydari, Integrated relief pre-positioning and procurement planning in humanitarian supply chains, Transp. Res. Part E Logist. Transp. Rev., 113 (2018), 123–146.https://doi.org/10.1016/j.tre.2018.03.012 doi: 10.1016/j.tre.2018.03.012
[29]	A. Ghavamifar, S. A. Torabi, M. Moshtari, A hybrid relief procurement contract for humanitarian logistics, Transp. Res. Part E Logist. Transp. Rev., 167 (2022), 102916.https://doi.org/10.1016/j.tre.2022.102916 doi: 10.1016/j.tre.2022.102916
[30]	Y. Z. Chen, Q. H. Zhao, K. Huang, X. Z. Xi, A bi-objective optimization model for contract design of humanitarian relief goods procurement considering extreme disasters, Socio-Econ. Plan. Sci., 81 (2022), 101214.https://doi.org/10.1016/j.seps.2021.101214 doi: 10.1016/j.seps.2021.101214
[31]	P. H. Guo, J. J. Zhu, Capacity reservation for humanitarian relief: A logic-based Benders decomposition method with subgradient cut, Eur. J. Oper. Res., 311 (2023), 942–970.https://doi.org/10.1016/j.ejor.2023.06.006 doi: 10.1016/j.ejor.2023.06.006
[32]	D. Taghvaei, T. Ghods, M. Rabbani, A bi-objective two-stage stochastic optimization for designing a resilient humanitarian relief chain considering hybrid contracts, public donations, and item perishability, Comput. Ind. Eng., 205 (2025), 111147.https://doi.org/10.1016/j.cie.2025.111147 doi: 10.1016/j.cie.2025.111147
[33]	H. Kord, P. Samouei, Coordination of humanitarian logistic based on the quantity flexibility contract and buying in the spot market under demand uncertainty using NSGA-II and NRGA algorithms, Expert Syst. Appl., 214 (2023), 119187.https://doi.org/10.1016/j.eswa.2022.119187 doi: 10.1016/j.eswa.2022.119187
[34]	C. Yao, B. Fan, Y. P. Zhao, X. Y. Chen, Evolutionary dynamics of supervision-compliance game on optimal pre-positioning strategies in relief supply chain management, Socio-Econ. Plan. Sci., 87 (2023), 101598.https://doi.org/10.1016/j.seps.2023.101598 doi: 10.1016/j.seps.2023.101598
[35]	J. F. Shao, Y. Fan, X. H. Wang, Incentive contract in relief supply chains: The case of multiplayer competition and cooperation, Socio-Econ. Plan. Sci., 101 (2025), 102278.https://doi.org/10.1016/j.seps.2025.102278 doi: 10.1016/j.seps.2025.102278
[36]	K. Liu, Q. Li, Z. H. Zhang, Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints, Transp. Res. Part B Methodol., 119 (2019), 79–101.https://doi.org/10.1016/j.trb.2018.11.012 doi: 10.1016/j.trb.2018.11.012
[37]	W. Q. Wang, K. Yang, L. X. Yang, Z. Y. Gao, Distributionally robust chance-constrained programming for multi-period emergency resource allocation and vehicle routing in disaster response operations, Omega, 120 (2023), 102915.https://doi.org/10.1016/j.omega.2023.102915 doi: 10.1016/j.omega.2023.102915
[38]	K. Sarmadi, M. Amiri-Aref, A distributionally robust optimisation with joint chance constraints approach for location-routing problem in urban search and rescue operations, Comput. Oper. Res., 180 (2025), 107051.https://doi.org/10.1016/j.cor.2025.107051 doi: 10.1016/j.cor.2025.107051
[39]	W. Xie, On distributionally robust chance constrained programs with Wasserstein distance, Math. Program., 186 (2021), 115–155.https://doi.org/10.1007/s10107-019-01445-5 doi: 10.1007/s10107-019-01445-5
[40]	J. Blanchet, K. Murthy, Quantifying distributional model risk via optimal transport, Math. Oper. Res., 44 (2019), 565–600.https://doi.org/10.1287/moor.2018.0936 doi: 10.1287/moor.2018.0936
[41]	R. Gao, A. Kleywegt, Distributionally robust stochastic optimization with Wasserstein distance, Math. Oper. Res., 48 (2023), 603–655.https://doi.org/10.1287/moor.2022.1275 doi: 10.1287/moor.2022.1275
[42]	M. E. Tonbari, G. L. Nemhauser, A. Toriello, Distributionally robust disaster relief planning under the Wasserstein set, Comput. Oper. Res., 168 (2024), 106689.https://doi.org/10.1016/j.cor.2024.106689 doi: 10.1016/j.cor.2024.106689

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