Skip to main content
Log in

Humanitarian relief supplies distribution: an application of inventory routing problem

  • S.I.: Applications of OR in Disaster Relief Operations
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In this paper, we study the distribution of humanitarian relief supplies. In humanitarian relief, supplies including food, water and medication are received in batches/waves from the suppliers and the donors. Then, these supplies are distributed to local dispensing sites located in the affected areas. Fast and fair distribution of these relief supplies is the key to the success of humanitarian relief operations. Motivated by the practices in humanitarian relief chain, we study an application of Inventory Routing Problem where the goal is equitable distribution of these supplies to the affected areas over a planning horizon. We measure the fairness of the distribution plan by the safety stock level at a demand location, and our goal is to maximize the minimum safety stock level at any location. Such a difference in the objective requires a solution approach that is significantly different than the ones proposed in the literature for classical cost-minimization routing problems. In order to address this distribution problem, we propose a three-phase (clustering, routing and improvement) solution approach. Due to nature of the problem, routing and allocation decisions significantly affect each other. The proposed approach (i) considers the interaction between routing and resource allocation decisions in a novel way to produce equitable relief supplies distribution plans, (ii) outperforms the existing algorithms by finding solutions with around 1.4% lower optimality gap on average, (iii) provides solutions with 2.6% optimality gap on average when compared to an upper bound, and (iv) finds a solution in < 5 min.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Abdelmaguid, T. F., Dessouky, M. M., & Ordonez, F. (2009). Heuristic approaches for the inventory-routing problem with backlogging. Computers & Industrial Engineering, 56(4), 1519–1534.

    Google Scholar 

  • Aflaki, A., & Pedraza-Martinez, A. J. (2016). Humanitarian funding in a multi-donor market with donation uncertainty. Production and Operations Management, 25(7), 1274–1291.

    Google Scholar 

  • Anaya-Arenas, A. M., Renaud, J., & Ruiz, A. (2014). Relief distribution networks: A systematic review. Annals of Operations Research, 223(1), 53–79.

    Google Scholar 

  • Anily, S., & Federgruen, A. (1993). Two-echelon disribution systems with vehicle routing costs and central inventories. Operations Research, 41(1), 37–47.

    Google Scholar 

  • Archetti, C., Bertazzi, L., Hertz, A., & Speranza, M. G. (2012). A hybrid heuristic for an inventory routing problem. INFORMS Journal on Computing, 24(1), 101–116.

    Google Scholar 

  • Balcik, B., Beamon, B. M., & Smilowitz, K. (2008). Last mile distribution in humanitarian relief. Journal of Intelligent Transportation Systems, 12(2), 51–63.

    Google Scholar 

  • Beamon, B. M., & Balcik, B. (2008). Performance measurement in humanitarian relief chains. International Journal of Public Sector Management, 21(1), 4–25.

    Google Scholar 

  • Bell, W. J., Dalberto, L. M., Fisher, M. L., Greenfield, A. J., Jaikumar, R., Kedia, P., et al. (1983). Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interfaces, 13(6), 4–23.

    Google Scholar 

  • Bertazzi, L., & Speranza, M. G. (2012). Inventory routing problems: An introduction. EURO Journal on Transportation and Logistics, 1(4), 307–326.

    Google Scholar 

  • Bertazzi, L., & Speranza, M. G. (2013). Inventory routing problems with multiple customers. EURO Journal on Transportation and Logistics, 2(3), 255–275.

    Google Scholar 

  • Bramel, J., & Simchi-Levi, D. (1995). A location based heuristic for general routing problems. Operations Research, 43(4), 649–660.

    Google Scholar 

  • Burkart, C., Nolz, P. C., & Gutjahr, W. J. (2017). Modelling beneficiaries’ choice in disaster relief logistics. Annals of Operations Research, 256(1), 41–61.

    Google Scholar 

  • Campbell, A. M., & Savelsbergh, M. W. P. (2004). A decomposition approach for the inventory-routing problem. Transportation Science, 38(4), 488–502.

    Google Scholar 

  • Centre for Research on the Epidemiology of Disasters. (2017). Annual disaster statistical review 2016: the numbers and trends. https://reliefweb.int/sites/reliefweb.int/files/resources/adsr_2016.pdf. Accessed 5 Nov 2017.

  • Chapman, A. G., & Mitchell, J. E. (2018). A fair division approach to humanitarian logistics inspired by conditional value-at-risk. Annals of Operations Research, 262(1), 133–151.

    Google Scholar 

  • Chitsaz, M., Divsalar, A., & Vansteenwegen, P. (2016). A two-phase algorithm for the cyclic inventory routing problem. European Journal of Operational Research, 254(2), 410–426.

    Google Scholar 

  • Clarke, G., & Wright, J. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12(4), 568–581.

    Google Scholar 

  • Coelho, L. C., Cordeau, J.-F., & Laporte, G. (2014). Thirty years of inventory routing. Transportation Science, 48(1), 1–19.

    Google Scholar 

  • Coelho, L. C., & Laporte, G. (2013). The exact solution of several classes of inventory-routing problems. Computers & Operations Research, 40(2), 558–565.

    Google Scholar 

  • Cordeau, J.-F., Lagana, D., Musmanno, R., & Vocaturo, F. (2015). A decomposition-based heuristic for the multiple-product inventory-routing problem. Computers & Operations Research, 55, 153–166.

    Google Scholar 

  • Desaulniers, G., Rakke, J. G., & Coelho, L. C. (2016). A branch-price-and-cut algorithm for the inventory-routing problem. Transportation Science, 50(3), 1060–1076.

    Google Scholar 

  • Diabat, A., Abdallah, T., & Le, T. (2016). A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods. Annals of Operations Research, 242(2), 373–398.

    Google Scholar 

  • Dror, M., Ball, M., & Golden, B. (1985/6). A computational comparison of the algorithms for the inventory routing problem. Annals of Operations Research, 4(1), 3–23.

  • Dufour, E., Laporte, G., Paquette, J., & Rancourt, M.-E. (2018). Logistics service network design for humanitarian response in East Africa. Omega, 74, 1–14.

    Google Scholar 

  • Duhamel, C., Santos, A. C., Brasil, D., Châtelet, E., & Birregah, B. (2016). Connecting a population dynamic model with a multi-period location-allocation problem for post-disaster relief operations. Annals of Operations Research, 247(2), 693–713.

    Google Scholar 

  • Duran, S., Ergun, O., Keskinocak, P., & Swann, J. L. (2013). Humanitarian logistics: Advanced purchasing and pre-positioning of relief items. In J. Bookbinder (Ed.), Handbook of logistics (pp. 447–462)., International series in operations research & management science New York, NY: Springer.

    Google Scholar 

  • Ekici, A., Ozener, O. O., & Kuyzu, G. (2015). Cyclic delivery schedules for an inventory routing problem. Transportation Science, 49(4), 817–829.

    Google Scholar 

  • Ferrer, J. M., Ortuno, M. T., & Tirado, G. (2016). A GRASP metaheuristic for humanitarian aid distribution. Journal of Heuristics, 22(1), 55–87.

    Google Scholar 

  • Holguin-Veras, J., Perez, N., Jaller, M., Van Wassenhove, L. N., & Aros-Vera, F. (2013). On the appropriate objective function for post-disaster humanitarian logistics models. Journal of Operations Management, 31(5), 262–280.

    Google Scholar 

  • Huang, M., Smilowitz, K., & Balcik, B. (2012). Models for relief routing: Equity, efficiency and efficacy. Transportation Research Part E: Logistics and Transportation Review, 48(1), 2–18.

    Google Scholar 

  • Huang, X., & Song, L. (2016). An emergency logistics distribution routing model for unexpected events. Annals of Operations Research, 1–17.

  • International Federation of Red Cross and Red Crescent Societies. (2015). Haiti earthquake: Five-year progress report. http://www.ifrc.org/Global/Documents/Americas/201501/1287600-IFRC-Haiti%205-year%20progress%20report-EN-LR.pdf. Accessed 10 Feb 2017.

  • Jung, J., & Mathur, K. (2007). An efficient heuristic algorithm for a two-echelon joint inventory and routing problem. Transportation Science, 41(1), 55–73.

    Google Scholar 

  • Kleywegt, A. J., Nori, V. S., & Savelsbergh, M. W. P. (2004). Dynamic programming approximations for a stochastic inventory routing problem. Transportation Science, 38(1), 42–70.

    Google Scholar 

  • Larrain, H., Coelho, L. C., & Cataldo, A. (2017). A variable MIP neighborhood descent algorithm for managing inventory and distribution of cash in automated teller machines. Computers & Operations Research, 85, 22–31.

    Google Scholar 

  • Lefever, W., Aghezzaf, E.-H., & Hadj-Hamou, K. (2016). A convex optimization approach for solving the single-vehicle cyclic inventory routing problem. Computers & Operations Research, 72, 97–106.

    Google Scholar 

  • Lei, L., Pinedo, M., Qi, L., Wang, S., & Yang, J. (2015). Personnel scheduling and supplies provisioning in emergency relief operations. Annals of Operations Research, 235(1), 487–515.

    Google Scholar 

  • Li, J., Chu, F., & Chen, H. (2011). A solution approach to the inventory routing problem in a three-level distribution system. European Journal of Operational Research, 210(3), 736–744.

    Google Scholar 

  • Li, K., Chen, B., Sivakumar, A. I., & Wu, Y. (2014). An inventory-routing problem with the objective of travel time minimization. European Journal of Operational Research, 236(3), 936–945.

    Google Scholar 

  • Mirzaei, S., & Seifi, A. (2015). Considering lost sale in inventory routing problems for perishable goods. Computers & Industrial Engineering, 87, 213–227.

    Google Scholar 

  • Monnot, J. (2005). Approximation algorithms for the maximum Hamiltonian path problem with specified endpoint(s). European Journal of Operational Research, 161(3), 721–735.

    Google Scholar 

  • Montjoy, A., Brown, S., Herrmann, J. W. (2009). Solving the inventory slack routing problem for medication distribution planning. Technical report, University of Maryland.

  • Nambirajan, R., Mendoza, A., Pazhani, S., Narendran, T. T., & Ganesh, K. (2016). CARE: Heuristics for two-stage multi-product inventory routing problems with replenishments. Computers & Industrial Engineering, 97, 41–57.

    Google Scholar 

  • Pedraza-Martinez, A. J., & Van Wassenhove, L. N. (2012). Transportation and vehicle fleet management in humanitarian logistics: Challenges for future research. EURO Journal on Transportation and Logistics, 1(1–2), 185–196.

    Google Scholar 

  • Perez-Rodriguez, N., & Holguin-Veras, J. (2016). Inventory-allocation distribution models for postdisaster humanitarian logistics with explicit consideration of deprivation costs. Transportation Science, 50(4), 1261–1285.

    Google Scholar 

  • Raa, B. (2015). Fleet optimization for cyclic inventory routing problems. International Journal of Production Economics, 160, 172–181.

    Google Scholar 

  • Raa, B., & Dullaert, W. (2017). Route and fleet design for cyclic inventory routing. European Journal of Operational Research, 256(2), 404–411.

    Google Scholar 

  • Solyali, O., & Sural, H. (2011). A branch-and-cut algorithm using a strong formulation and an a priori tour-based heuristic for an inventory-routing problem. Transportation Science, 45(3), 335–345.

    Google Scholar 

  • Starr, M. K., & Van Wassenhove, L. N. (2014). Introduction to the special issue on humanitarian operations and crisis management. Production and Operations Management, 23(6), 925–937.

    Google Scholar 

  • Tomasini, R., & Van Wassenhove, L. (2009). Humanitarian logistics. Basingstoke: Palgrave Macmillan.

    Google Scholar 

  • Torre, L. E., Dolinskaya, I. S., & Smilowitz, K. R. (2012). Disaster relief routing: Integrating research and practice. Socio-Economic Planning Sciences, 46(1), 88–97.

    Google Scholar 

  • Tzeng, G., Cheng, H., & Huang, T. (2007). Multi-objective optimal planning for designing relief delivery systems. Transportation Research Part E: Logistics and Transportation Review, 43(6), 673–686.

    Google Scholar 

  • Van Wassenhove, L. N. (2006). Humanitarian aid logistics: Supply chain management in high gear. Journal of the Operational Research Society, 57(5), 475–489.

    Google Scholar 

  • Viswanathan, S., & Mathur, K. (1997). Integrating routing and inventory decisions in one-warehouse multiretailer multiproduct distribution systems. Management Science, 43(3), 294–312.

    Google Scholar 

  • Vitoriano, B., Ortuno, M. T., Tirado, G., & Montero, J. (2011). A multi-criteria optimization model for humanitarian aid distribution. Journal of Global Optimization, 51(2), 189–208.

    Google Scholar 

  • Xiang, Y., & Zhuang, J. (2016). A medical resource allocation model for serving emergency victims with deteriorating health conditions. Annals of Operations Research, 236(1), 177–196.

    Google Scholar 

  • Yang, X., & Feng, L. (2013). Inventory routing problem: Routing and scheduling approach with the objective of slack maximization. Journal of Transportation Research Board: Transportation Research Record, 2378(1), 32–42.

    Google Scholar 

  • Yang, X., & Zhu, S. (2016). Solution to the multidepot inventory slack-routing problem at the planning stage. Journal of Computing in Civil Engineering, 30(1), 1–10.

    Google Scholar 

  • Yu, Y., Chu, C., Chen, H., & Chu, F. (2012). Large scale stochastic inventory routing problems with split delivery and service level constraints. Annals of Operations Research, 197(1), 135–158.

    Google Scholar 

  • Zhang, H. (2014). Explaining the perceived justice of disaster relief policy: An empirical study based on the 2008 Wenchuan Earthquake in China. International Journal of Social Welfare, 23(2), 150–164.

    Google Scholar 

  • Zhao, Q.-H., Chen, S., & Zang, C.-X. (2008). Model and algorithm for inventory/routing decision in a three-echelon logistics system. European Journal of Operational Research, 191(3), 623–635.

    Google Scholar 

  • Zobel, C. W., Altay, N., & Haselkorn, M. P. (Eds.). (2016). Advances in managing humanitarian operations., International series in operations research & management science Berlin: Springer.

    Google Scholar 

Download references

Acknowledgements

This research is supported by TUBITAK Grant 115M535.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ali Ekici.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Çankaya, E., Ekici, A. & Özener, O.Ö. Humanitarian relief supplies distribution: an application of inventory routing problem. Ann Oper Res 283, 119–141 (2019). https://doi.org/10.1007/s10479-018-2781-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-018-2781-7

Keywords

Navigation