Skip to main content
SpringerLink
Log in

A Mean-Variance Disaster Relief Supply Chain Network Model for Risk Reduction with Stochastic Link Costs, Time Targets, and Demand Uncertainty

  • Conference paper
  • First Online:
Dynamics of Disasters—Key Concepts, Models, Algorithms, and Insights (DOD 2015 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 185))

Included in the following conference series:

  • 1090 Accesses

Abstract

In this paper, we develop a mean-variance disaster relief supply chain network model with stochastic link costs and time targets for delivery of the relief supplies at the demand points, under demand uncertainty. The humanitarian organization seeks to minimize its expected total operational costs and the total risk in operations with an individual weight assigned to its valuation of the risk, as well as the minimization of expected costs of shortages and surpluses and tardiness penalties associated with the target time goals at the demand points. The risk is captured through the variance of the total operational costs, which is relevant to the reporting of the proper use of funds to stakeholders, including donors. The time goal targets associated with the demand points enable prioritization as to the timely delivery of relief supplies. The framework handles both the pre-positioning of relief supplies, whether local or nonlocal, as well as the procurement (local or nonlocal), transport, and distribution of supplies post-disaster. The time element is captured through link time completion functions as the relief supplies progress along paths in the supply chain network. Each path consists of a series of directed links, from the origin node, which represents the humanitarian organization, to the destination nodes, which are the demand points for the relief supplies. We propose an algorithm, which yields closed form expressions for the variables at each iteration, and demonstrate the efficacy of the framework through a series of illustrative numerical examples, in which trade-offs between local versus nonlocal procurement, post- and pre-disaster, are investigated. The numerical examples include a case study on hurricanes hitting Mexico.

Presented at the 2nd International Conference on Dynamics of Disasters, Kalamata, Greece, June 29–July 2, 2015; revised December 2015. To appear in Dynamics of Disasters, I.S. Kotsireas, A. Nagurney, and P.M. Pardalos, Eds., Springer International Publishing Switzerland.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Balcik, B., Beamon, B.M.: Facility location in humanitarian relief. Int. J. Log. Res. Appl. 11 (2), 101–121 (2005)

    Article  Google Scholar 

  • Barbarosoglu, G., Arda, Y.: A two-stage stochastic programming framework for transportation planning in disaster response. J. Oper. Res. Soc. 55 (1), 43–53 (2004)

    Article  MATH  Google Scholar 

  • BBC News: Nepal quake: towns near epicentre ‘devastated’ - Red Cross, 1 May 2015

    Google Scholar 

  • Beamon, B., Kotleba, S.: Inventory management support systems for emergency humanitarian relief operations in South Sudan. Int. J. Logist. Manag. 17 (2), 187–212 (2006)

    Article  Google Scholar 

  • Boyles, S.D., Waller, S.T.: A mean-variance model for the minimum cost flow problem with stochastic arc costs. Networks 56 (3), 215–227 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Bozorgi-Amiri, A., Jabalameli, M.S., Mirzapour Al-e-Hashem, S.M.J.: A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty. OR Spektrum 35, 905–933 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • CBS News: Typhoon Haiyan slams into northern Vietnam, 10 Nov 2013. Available online at http://www.cbsnews.com/news/typhoon-haiyan-slams-into-northern-vietnam

  • Chen, F., Federgruen, A.: Mean-variance analysis of basic inventory models. Working Paper, Columbia Business School, Columbia University, New York (2000)

    Google Scholar 

  • Chicago Tribune: Typhoon Haiyan: Desperate Philippine survivors turn to looting, 13 Nov 2013. Available online at http://http://www.chicagotribune.com/news/chi-philippines-typhoon-haiyan-20131113,0,4099086,full.story

  • Das, R.: Advancement on uncertainty modeling in humanitarian logistics for earthquake response. PhD dissertation, The Graduate School of Science and Engineering, Department of International Development Engineering, Tokyo Institute of Technology (2014)

    Google Scholar 

  • de la Fuente, A.: Government expenditures in pre and post-disaster risk management. The World Bank, Washington, DC (2011)

    Google Scholar 

  • Dong, J., Zhang, D., Nagurney, A.: A supply chain network equilibrium model with random demands. Eur. J. Oper. Res. 156, 194–212 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Dupuis, P., Nagurney, A.: Dynamical systems and variational inequalities. Ann. Oper. Res. 44, 9–42 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  • Falasca, M., Zobel, C.W.: A two-stage procurement model for humanitarian relief supply chains. J. Humanitarian Logist. Supply Chain Manag. 1 (2), 151–169 (2011)

    Article  Google Scholar 

  • Fugate, W.: The state of FEMA – leaning forward: go big, go early, go fast, be smart. A report by the US Department of Homeland Security. Available online at: www.fema.gov/pdf/about/state_of_fema/state_of_fema.pdf (2012)

  • Hale, T., Moberg, C.: Improving supply chain disaster preparedness: a decision process for secure site location. Int. J. Phys. Distrib. Logist. Manag. 35 (3), 195–207 (2005)

    Article  Google Scholar 

  • Harris, G.: Nepal’s bureaucracy blamed as quake relief supplies pile up. The New York Times, 4 May 2015

    Google Scholar 

  • Huang, M., Smilowitz, K., Balcik, B.: Models for relief routing: equity, efficiency and efficacy. Transp. Res. E 48, 2–18 (2012)

    Article  Google Scholar 

  • Kim, S.H., Cohen, M., Netessine, S.: Performance contracting in after-sales service supply chains. Manag. Sci. 53, 1843–1858 (2007)

    Article  MATH  Google Scholar 

  • Liu, Z., Nagurney, A.: Risk reduction and cost synergy in mergers and acquisitions via supply chain network integration. J. Financ. Decis. Making 7 (2), 1–18 (2011)

    Google Scholar 

  • Lorch, D.: Rural Nepal still waiting for relief after devastating earthquake. USA Today, 5 May 2015

    Google Scholar 

  • Luke, S., McVicker, L.: Local Nepal earthquake survivor: “it was utter chaos.” San Diego News, 29 April 2015

    Google Scholar 

  • Markowitz, H.: Portfolio selection. J. Financ. 56 (6), 2019–2065 (1952)

    Google Scholar 

  • Markowitz, H.: Portfolio Selection: Efficient Diversification of Investment. Wiley, New York (1959)

    Google Scholar 

  • Matopoulos, A., Kovacs, G., Hayes, O.: Local resources and procurement practices in humanitarian supply chains: an empirical examination of large-scale house reconstruction projects. Decis. Sci. 25 (4), 621–646 (2014)

    Article  Google Scholar 

  • Mete, H.O., Zabinsky, Z.B.: Stochastic optimization of medical supply location and distribution in disaster management. Int. J. Prod. Econ. 126, 76–84 (2010)

    Article  Google Scholar 

  • Nagurney, A.: Network Economics: A Variational Inequality Approach, second and revised edition. Kluwer Academic, Dordrecht (1999)

    Book  Google Scholar 

  • Nagurney, A., Masoumi, A.H.: Supply chain network design of a sustainable blood banking system. In: Boone, T., Jayaraman, V., Ganeshan, R. (eds.) Sustainable Supply Chains: Models, Methods and Public Policy Implications, pp. 49–72. Springer, London (2012)

    Chapter  Google Scholar 

  • Nagurney, A., Qiang, Q.: Fragile Networks: Identifying Vulnerabilities and Synergies in an Uncertain World. Wiley, Hoboken, NJ (2009)

    Book  MATH  Google Scholar 

  • Nagurney, A., Qiang, Q.: Fragile networks: identifying vulnerabilities and synergies in an uncertain age. Int. Trans. Oper. Res. 19, 123–160 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Nagurney, A., Zhang, D.: Projected Dynamical Systems and Variational Inequalities with Applications. Kluwer Academic, Boston, MA (1996)

    Book  MATH  Google Scholar 

  • Nagurney, A., Yu, M., Qiang, Q.: Supply chain network design for critical needs with outsourcing. Pap. Reg. Sci. 90 (1), 123–143 (2011)

    Article  Google Scholar 

  • Nagurney, A., Yu, M., Qiang, Q.: Multiproduct humanitarian healthcare supply chains: a network modeling and computational framework. In: Proceedings of the 23rd Annual POMS Conference, Chicago, IL (2012a)

    Google Scholar 

  • Nagurney, A., Masoumi, A.H., Yu, M.: Supply chain network operations management of a blood banking system with cost and risk minimization. Comput. Manag. Sci. 9 (2), 205–231 (2012b)

    Google Scholar 

  • Nagurney, A., Masoumi, A.H., Yu, M.: An integrated disaster relief supply chain network model with time targets and demand uncertainty. In: Nijkamp, P., Rose, A., Kourtit, K. (eds.) Regional Science Matters: Studies Dedicated to Walter Isard, pp. 287–318. Springer International Publishing, Cham (2015)

    Google Scholar 

  • NOAA: WMO retires Ingrid and Manuel for Atlantic and Eastern North Pacific basins, 10 April 2014

    Google Scholar 

  • Ortuño, M.T., Tirado, G., Vitoriano, B.: A lexicographical goal programming based decision support system for logistics of humanitarian aid. TOP 19 (2), 464–479 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Ortuño, M.T., Cristóbal, P., Ferrer, J.M., Martín-Campo, F.J., Muñoz, S., Tirado, G., Vitoriano, B.: Decision aid models and systems for humanitarian logistics: a survey. In: Vitoriano, B., Montero, J., Ruan, D. (eds.) Decision Aid Models for Disaster Management and Emergencies. Atlantis Computational Intelligence Systems, vol. 7, pp. 17–44. Springer Business + Science Media, New York (2013)

    Chapter  Google Scholar 

  • Ozbay, K., Ozguven, E.E.: Stochastic humanitarian inventory control model for disaster planning. In: Proceedings of the Transportation Research Board 86th Annual Meeting, Washington, DC (2007)

    Google Scholar 

  • Pasch, R.J., Zelinsky, D.A.: Hurricane Manuel. National Hurricane Center, Tropical cyclone report. EP132013, revised 14 April 2014

    Google Scholar 

  • Qiang, Q., Nagurney, A.: A bi-criteria indicator to assess supply chain network performance for critical needs under capacity and demand disruptions. Transp. Res. A 46 (5), 801–812 (2012)

    Google Scholar 

  • Rottkemper, B., Fischer, K., Blecken, A.: A transshipment model for distribution and inventory relocation under uncertainty in humanitarian operations. Socio Econ. Plan. Sci. 46, 98–109 (2012)

    Article  Google Scholar 

  • Schneeweis, T., Crowder, G., Kazemi, H.: The New Science of Asset Allocation Risk Management in a Multi-Asset World. Wiley, Hoboken, NJ (2010)

    Book  Google Scholar 

  • The International Bank for Reconstruction and Development/The World Bank: FONDEN: Mexico’s natural disaster fund - a review, Washington, DC (2012)

    Google Scholar 

  • Toyasaki, F., Wakolbinger, T.: Impacts of earmarked private donations for disaster fundraising. Ann. Oper. Res. 221 (1), 427–447 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Tzeng, G.-H., Cheng, H.-J., Huang, T.: Multi-objective optimal planning for designing relief delivery systems. Transp. Res. E 43 (6), 673–686 (2007)

    Article  Google Scholar 

  • UNHCR: United Nations High Commissioner for Refugees UNHCR Handbook for Emergencies, 3rd edn. UNHCR, Geneva (2007)

    Google Scholar 

  • United Nations: Global assessment report on disaster reduction (2011)

    Google Scholar 

  • USAID: United States Agency for International Development, Office of Foreign Disaster Assistance, Field operations guide for disaster assessment and response, Version 4.0 (2005)

    Google Scholar 

  • Van Wassenhove, L.N.: Blackett memorial lecture. Humanitarian aid logistics: supply chain management in high gear. J. Oper. Res. Soc. 57 (5), 475–489 (2006)

    Google Scholar 

  • Vitoriano, B., Ortuño, M., Tirado, G., Montero, M.: A multi-criteria optimization model for humanitarian aid distribution. J. Glob. Optim. 51, 189–208 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Vitoriano, B., Montero, J., Ruan, D. (eds.): Decision Aid Models for Disaster Management and Emergencies. Atlantis Computational Intelligence Systems, vol. 7. Springer Business + Science Media, New York (2013)

    Google Scholar 

  • Walton, R., Mays, R., Haselkorn, M.: Defining “fast”: Factors affecting the experience of speed in humanitarian logistics. In: Proceedings of the 8th International ISCRAM Conference, Lisbon, May 2011

    Google Scholar 

Download references

Acknowledgements

This paper is dedicated to the students in Professor Anna Nagurney’s Humanitarian Logistics and Healthcare class in 2015 at the Isenberg School of Management and to all the victims of natural disasters over the centuries as well as to humanitarian professionals.

Professor Anna Nagurney thanks Professor Panos M. Pardalos of the University of Florida and Professor Ilias Kootsireas of Wilfrid Laurier University for the great collaboration on the co-organization of the 2nd International Conference on Dynamics of Disasters in Kalamata, Greece.

The authors also thank the speakers and participants in the conference for comments and stimulating discussions on themes of the conference.

The authors acknowledge helpful comments from two anonymous reviewers on an earlier version of this paper and acknowledge Professor Kotsireas for handling the reviewing process.

Author information

Authors and Affiliations

  1. Department of Operations and Information Management, Isenberg School of Management, University of Massachusetts, Amherst, MA, 01003, USA

    Anna Nagurney

  2. Department of Electrical and Computer Engineering, University of Hartford, West Hartford, CT, 06117, USA

    Ladimer S. Nagurney

Authors
  1. Anna Nagurney
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ladimer S. Nagurney
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anna Nagurney .

Editor information

Editors and Affiliations

  1. Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Department of Operations and Information Management, University of Massachusetts, Amherst, Massachusetts, USA

    Anna Nagurney

  3. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Nagurney, A., Nagurney, L.S. (2016). A Mean-Variance Disaster Relief Supply Chain Network Model for Risk Reduction with Stochastic Link Costs, Time Targets, and Demand Uncertainty. In: Kotsireas, I., Nagurney, A., Pardalos, P. (eds) Dynamics of Disasters—Key Concepts, Models, Algorithms, and Insights. DOD 2015 2016. Springer Proceedings in Mathematics & Statistics, vol 185. Springer, Cham. https://doi.org/10.1007/978-3-319-43709-5_12

Download citation

Publish with us

Policies and ethics

Search

Navigation