Annals of Operations Research

, Volume 129, Issue 1–4, pp 217–245 | Cite as

Emergency Logistics Planning in Natural Disasters

  • Linet Özdamar
  • Ediz Ekinci
  • Beste Küçükyazici


Logistics planning in emergency situations involves dispatching commodities (e.g., medical materials and personnel, specialised rescue equipment and rescue teams, food, etc.) to distribution centres in affected areas as soon as possible so that relief operations are accelerated. In this study, a planning model that is to be integrated into a natural disaster logistics Decision Support System is developed. The model addresses the dynamic time-dependent transportation problem that needs to be solved repetitively at given time intervals during ongoing aid delivery. The model regenerates plans incorporating new requests for aid materials, new supplies and transportation means that become available during the current planning time horizon. The plan indicates the optimal mixed pick up and delivery schedules for vehicles within the considered planning time horizon as well as the optimal quantities and types of loads picked up and delivered on these routes.

In emergency logistics context, supply is available in limited quantities at the current time period and on specified future dates. Commodity demand is known with certainty at the current date, but can be forecasted for future dates. Unlike commercial environments, vehicles do not have to return to depots, because the next time the plan is re-generated, a node receiving commodities may become a depot or a former depot may have no supplies at all. As a result, there are no closed loop tours, and vehicles wait at their last stop until they receive the next order from the logistics coordination centre. Hence, dispatch orders for vehicles consist of sets of “broken” routes that are generated in response to time-dependent supply/demand.

The mathematical model describes a setting that is considerably different than the conventional vehicle routing problem. In fact, the problem is a hybrid that integrates the multi-commodity network flow problem and the vehicle routing problem. In this setting, vehicles are also treated as commodities. The model is readily decomposed into two multi-commodity network flow problems, the first one being linear (for conventional commodities) and the second integer (for vehicle flows). In the solution approach, these sub-models are coupled with relaxed arc capacity constraints using Lagrangean relaxation. The convergence of the proposed algorithm is tested on small test instances as well as on an earthquake scenario of realistic size.

emergency planning linear and integer multi-period multi-commodity network flows vehicle routing Lagrangean relaxation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aggarwal, C.C., M. Oblak, and R.R. Vemuganti. (1995). “A Heuristic Solution Procedure for Multi-Commodity Integer Flows.” Computers and Operations Research 22, 1075–1087.Google Scholar
  2. Awerbuch, B. and T. Leighton. (1993). “Multi-Commodity Flows: A Survey of Recent Research.” In Proceedings of ISAAC '93, pp. 297–302.Google Scholar
  3. Barnhart, C. and Y. Sheffi. (1993). “A Network Based Primal-Dual Heuristic forMulti-Commodity Network Flow Problems.” Transportation Science 27, 102–117.Google Scholar
  4. Barnhart, C. (1993). “Dual Ascent Methods for Large-Scale Multi-Commodity Network Flow Problems.” Naval Research Logistics 40, 305–324.Google Scholar
  5. Barnhart, C., C.A. Hane, and P.H. Vance. (1996). “Integer Multi-Commodity Flow Problems.” Centre for Transportation Studies Working Paper, Centre for Transportation Studies, MIT.Google Scholar
  6. Bodin, L.D. (1990). “Twenty Years of Routing and Scheduling.” Operations Research 38, 571–579.Google Scholar
  7. Brunetta, L., M. Conforti, and M. Fischetti. (1995). “A Polyhedral Approach to an Integer Multi-Commodity Flow Problem.” Preprint No. 18, Department of Mathematics, Padova University.Google Scholar
  8. Desrochers, M., J.K. Lenstra, M.W.P. Savelsbergh, and F. Soumis. (1988). “Vehicle Routing with Time Windows.” In B.L. Golden and A.A. Assad (eds.), Vehicle Routing: Methods and Studies. Amsterdam: Elsevier Science.Google Scholar
  9. Desrochers, M., J.K. Lenstra, and M.W.P. Savelsbergh. (1990). “A Classification Scheme for Vehicle Routing and Scheduling Problems.” European Journal of Operational Research 46, 322–332.Google Scholar
  10. Desrochers, M. et al. (1998). “Towards a Model and Algorithm Management System for Vehicle Routing and Scheduling Problems.” Working Paper, GERAD, Montreal, Canada.Google Scholar
  11. Dror, M. and P. Trudeau. (1990). “Split Delivery Routing.” Naval Research Logistics 37, 383–402.Google Scholar
  12. Equi, L., G. Gallo, S. Marziale, and A. Weintraub. (1996). “A Combined Transportation and Scheduling Problem.” Working Paper, Pisa University, Pisa, Italy.Google Scholar
  13. Frangioni, A. (1997). “Dual Ascent Methods and Multi-Commodity Flow Problems.” PhD Dissertation TD 5/97, Department of Informatics, Pisa University, Pisa, Italy.Google Scholar
  14. Fisher, M. (1981). “The Lagrangean Relaxation Method for Solving Integer Problems.” Management Science 27, 1–18.Google Scholar
  15. Fisher, M. (1995). “Vehicle Routing.” In M.O. Ball et al. (eds.), Handbooks in OR and MS, Vol. 8. Amsterdam: Elsevier Science.Google Scholar
  16. Fisher, M., B. Tang, and Z. Zheng. (1995). “A Network Flow Based Heuristic for Bulk Pick Up and Delivery Routing.” Transportation Science 29, 45–55.Google Scholar
  17. Gendreau, M., F. Guertin, J.-Y. Potvin, and E. Taillard. (1999). “Parallel Tabu Search for Real-Time Vehicle Routing and Dispatching.” Transportation Science 33, 381–390.Google Scholar
  18. Held, M. et al. (1974). “Validation of Sub-Gradient Optimization.” Mathematical Programming 6, 62–88.Google Scholar
  19. Jimenez, F. and J.L. Verdegay. (1999). “Solving Fuzzy Solid Transportation Problems by an Evolutionary Algorithm Based Parametric Approach.” European Journal of Operational Research 117, 485–510.Google Scholar
  20. Jones, K.L. et al. (1993). “Multi-Commodity Network Flows: The Impact of Formulation on Decomposition.” Mathematical Programming 62, 95–117.Google Scholar
  21. Kennington, J.L. and M. Shalaby. (1977). “An Effective Sub-Gradient Procedure for Minimal Cost Multi-Commodity Flow Problems.” Management Science 23, 994–1004.Google Scholar
  22. Laporte, G. (1992). “The Vehicle Routing Problem: An Overview of Exact and Approximate Algorithms.” European Journal of Operational Research 59, 345–358.Google Scholar
  23. Mathies, S. and P. Mevert. (1998). “A Hybrid Algorithm for Solving Network Flow Problems with Side Constraints.” Computers and Operations Research 25, 745–756.Google Scholar
  24. Orlin, J.B. (1993). “A Faster Strongly Polynomial Minimum Cost Flow Algorithm.” Operations Research 41, 338–350.Google Scholar
  25. Rathi, A.K., R.L. Church, and R.S. Solanki. (1993). “Allocating Resources to Support a Multicommodity Flow with Time Windows.” Logistics and Transportation Review 28, 167–188.Google Scholar
  26. Ribeiro, C. and F. Soumis. (1994). “A Column Generation Approach to theMulti-Depot Vehicle Scheduling Problem.” Operations Research 42, 41–52.Google Scholar
  27. Rodriguez, P. et al. (1998). “Using Global Search Heuristics for the Capacity Vehicle Routing Problem.” Computers and Operations Research 25, 407–417.Google Scholar
  28. U.S. Geological Survey Information Services. (1999). “Implications for Earthquake Risk Reduction in the United States from the Kocaeli, Turkey, Earthquake of August 17, 1999.” USGS Circular # 1193.Google Scholar
  29. Venkataramanan, M.A., J.J. Dinkel, and J. Mote. (1989). “A Surrogate and Lagrangean Approach to Constrained Network Problems.” Annals of OR 20, 283–302.Google Scholar
  30. Ziliaskopoulos, A. and W. Wardell. (2000). “An Intermodal Optimum Path Algorithm for Multimodal Networks with Dynamic Arc Travel Times and Switching Delays.” European Journal of Operational Research 125, 486–502.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Linet Özdamar
    • 1
  • Ediz Ekinci
    • 2
  • Beste Küçükyazici
    • 3
  1. 1.School of Mechanical and Production Engineering, Systems and Engineering Management DivisionNanyang Technological UniversitySingapore
  2. 2.Turkish Armed ForcesTurkey
  3. 3.Department of Systems EngineeringYeditepe UniversityTurkey

Personalised recommendations