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.
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.
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.
Anaya-Arenas, A. M., Renaud, J., & Ruiz, A. (2014). Relief distribution networks: A systematic review. Annals of Operations Research, 223(1), 53–79.
Anily, S., & Federgruen, A. (1993). Two-echelon disribution systems with vehicle routing costs and central inventories. Operations Research, 41(1), 37–47.
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.
Balcik, B., Beamon, B. M., & Smilowitz, K. (2008). Last mile distribution in humanitarian relief. Journal of Intelligent Transportation Systems, 12(2), 51–63.
Beamon, B. M., & Balcik, B. (2008). Performance measurement in humanitarian relief chains. International Journal of Public Sector Management, 21(1), 4–25.
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.
Bertazzi, L., & Speranza, M. G. (2012). Inventory routing problems: An introduction. EURO Journal on Transportation and Logistics, 1(4), 307–326.
Bertazzi, L., & Speranza, M. G. (2013). Inventory routing problems with multiple customers. EURO Journal on Transportation and Logistics, 2(3), 255–275.
Bramel, J., & Simchi-Levi, D. (1995). A location based heuristic for general routing problems. Operations Research, 43(4), 649–660.
Burkart, C., Nolz, P. C., & Gutjahr, W. J. (2017). Modelling beneficiaries’ choice in disaster relief logistics. Annals of Operations Research, 256(1), 41–61.
Campbell, A. M., & Savelsbergh, M. W. P. (2004). A decomposition approach for the inventory-routing problem. Transportation Science, 38(4), 488–502.
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.
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.
Clarke, G., & Wright, J. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12(4), 568–581.
Coelho, L. C., Cordeau, J.-F., & Laporte, G. (2014). Thirty years of inventory routing. Transportation Science, 48(1), 1–19.
Coelho, L. C., & Laporte, G. (2013). The exact solution of several classes of inventory-routing problems. Computers & Operations Research, 40(2), 558–565.
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.
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.
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.
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.
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.
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.
Ekici, A., Ozener, O. O., & Kuyzu, G. (2015). Cyclic delivery schedules for an inventory routing problem. Transportation Science, 49(4), 817–829.
Ferrer, J. M., Ortuno, M. T., & Tirado, G. (2016). A GRASP metaheuristic for humanitarian aid distribution. Journal of Heuristics, 22(1), 55–87.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Mirzaei, S., & Seifi, A. (2015). Considering lost sale in inventory routing problems for perishable goods. Computers & Industrial Engineering, 87, 213–227.
Monnot, J. (2005). Approximation algorithms for the maximum Hamiltonian path problem with specified endpoint(s). European Journal of Operational Research, 161(3), 721–735.
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.
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.
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.
Raa, B. (2015). Fleet optimization for cyclic inventory routing problems. International Journal of Production Economics, 160, 172–181.
Raa, B., & Dullaert, W. (2017). Route and fleet design for cyclic inventory routing. European Journal of Operational Research, 256(2), 404–411.
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.
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.
Tomasini, R., & Van Wassenhove, L. (2009). Humanitarian logistics. Basingstoke: Palgrave Macmillan.
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.
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.
Van Wassenhove, L. N. (2006). Humanitarian aid logistics: Supply chain management in high gear. Journal of the Operational Research Society, 57(5), 475–489.
Viswanathan, S., & Mathur, K. (1997). Integrating routing and inventory decisions in one-warehouse multiretailer multiproduct distribution systems. Management Science, 43(3), 294–312.
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.
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.
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.
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.
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.
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.
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.
Zobel, C. W., Altay, N., & Haselkorn, M. P. (Eds.). (2016). Advances in managing humanitarian operations., International series in operations research & management science Berlin: Springer.
Acknowledgements
This research is supported by TUBITAK Grant 115M535.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-018-2781-7