Abstract
Fast and equitable distribution of the humanitarian relief supplies is key to the success of relief operations. Delayed and inequitable deliveries can result in suffering of affected people and loss of lives. In this study, we analyze the routing operations for the delivery of relief supplies from a distribution center to the dispensing sites. We assume that the relief supplies to be distributed arrive at the distribution center in batches and are consumed at the dispensing sites with a certain daily rate. When forming delivery schedules, we use the ratio of the inventory to the daily consumption rate at the dispensing sites as our decision criterion. This ratio is called the slack and can be considered as the safety stock (when positive) in case of a delay in the deliveries. Negative value for the slack means the dispensing site has stock-outs. Our objective is to maximize the minimum value of this slack among all dispensing sites. This is equivalent to maximizing the minimum safety stock or minimizing the maximum duration of the stock-outs. Due to multi-period structure of the problem, it is modeled as a variant of the Inventory Routing Problem. To address the problem, we propose a general framework which includes clustering, routing and improvement steps. The proposed framework considers the interdependence between all three types of decisions (clustering, routing and resource allocation) and makes the decisions in an integrated manner. We test the proposed framework on randomly generated instances and compare its performance against the benchmark algorithms in the literature. The proposed framework not only outperforms the benchmark algorithms by at least 1% less optimality gap but also provides high-quality solutions with around 2–3% optimality gaps.
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References
Afshar A, Haghani A (2012) Modeling integrated supply chain logistics in real-time large-scale disaster relief operations. Socio Econ Plan Sci 46(4):327–338
Al-Monitor (2019) Why Iranian authorities failed to minimize flood damage. https://www.al-monitor.com/pulse/originals/2019/04/iran-floods-response-disaster-management-prevention.html
Altay N, Green W (2006) OR/MS research in disaster operations management. Eur J Oper Res 175(1):475–493
Anaya-Arenas A, Renaud J, Ruiz A (2014) Relief distribution networks: a systematic review. Ann Oper Res 223(1):53–79
Archetti C, Bertazzi L, Hertz A, Speranza M (2012) A hybrid heuristic for an inventory routing problem. INFORMS J Comput 24(1):101–116
Balcik B, Beamon B (2008) Facility location in humanitarian relief. Int J Log Res Appl 11(2):101–121
Balcik B, Beamon B, Smilowitz K (2008) Last mile distribution in humanitarian relief. J Intell Transp Syst 12(2):51–63
Beamon B, Balcik B (2008) Performance measurement in humanitarian relief chains. Int J Public Sector Manag 21(1):4–25
Berkoune D, Renaud J, Rekik M, Ruiz A (2012) Transportation in disaster response operations. Socio Econ Plan Sci 46(1):23–32
Bertazzi L, Speranza M (2012) Inventory routing problems: an introduction. EURO J Transp Log 1(4):307–326
Bertazzi L, Speranza M (2013) Inventory routing problems with multiple customers. EURO J Transp Log 2(3):255–275
Bramel J, Simchi-Levi D (1995) A location based heuristic for general routing problems. Oper Res 43(4):649–660
Campbell A, Jones P (2011) Prepositioning supplies in preparation for disasters. Eur J Oper Res 209(2):156–165
Campbell A, Vandenbussche D, Hermann W (2008) Routing for relief efforts. Transp Sci 42(2):127–145
Cankaya E, Ekici A, Ozener O (2019) Humanitarian relief supplies distribution: an application of inventory routing problem. Ann Oper Res 283(1–2):119–141
Coelho L, Cordeau J-F, Laporte G (2014) Thirty years of inventory routing. Transp Sci 48(1):1–19
Ekici A, Ozener O, Kuyzu G (2015) Cyclic delivery schedules for an inventory routing problem. Transp Sci 49(4):817–829
Elci O, Noyan N, Bulbul K (2018) Chance-constrained stochastic programming under variable reliability levels with an application to humanitarian relief network design. Comput Oper Res 96:91–107
Haghani A, Oh S (1996) Formulation and solution of a multi-commodity, multi-modal network model for disaster relief operations. Transp Res Part A Policy Pract 30(3):231–250
Holguin-Veras J, Jaller M, Wassenhove LV, Perez N, Wachtendorf T (2012) On the unique features of post-disaster humanitarian logistics. J Oper Manag 30(7–8):494–506
Holguin-Veras J, Taniguchi E, Jaller M, Aros-Vera F, Ferreira F, Thompson R (2014) The Tohoku disasters: chief lessons concerning the post disaster humanitarian logistics response and policy implications. Transp Res Part A Policy Pract 69:86–104
Huang M, Smilowitz K, Balcik B (2012) Models for relief routing: equity, efficiency and efficacy. Transp Res Part E Log Transp Rev 48(1):2–18
International Federation of Red Cross and Red Crescent Societies (2000) Introduction to disaster preparedness: disaster preparedness training programme. https://www.ifrc.org/Global/Publications/disasters/all.pdf
Jung J, Mathur K (2007) An efficient heuristic algorithm for a two-echelon joint inventory and routing problem. Transp Sci 41(1):55–73
Li J, Chu F, Chen H (2011) A solution approach to the inventory routing problem in a three-level distribution system. Eur J Oper Res 210(3):736–744
Lin Y, Batta R, Rogerson P, Blatt A, Flanigan M (2012) Location of temporary depots to facilitate relief operations after an earthquake. Socio Econ Plan Sci 46(2):112–123
Montjoy A, Brown S, Herrmann J (2009) Solving the inventory slack routing problem for medication distribution planning. Technical report, University of Maryland
Nair D, Rey D, Dixit V (2017) Fair allocation and cost-effective routing models for food rescue and redistribution. IISE Trans 49(12):1172–1188
Naji-Azimi Z, Renaud J, Ruiz A, Salari M (2012) A covering tour approach to the location of satellite distribution centers to supply humanitarian aid. Eur J Oper Res 222(3):596–605
National Academies of Sciences, Engineering, and Medicine (2016) The nation’s medical countermeasure stockpile: opportunities to improve the efficiency, effectiveness, and sustainability of the CDC Strategic National Stockpile: workshop summary. The National Academies Press, Washington, DC
Nolz P, Semet F, Doerner K (2011) Risk approaches for delivering disaster relief supplies. OR Spectr 33(3):543–569
Noyan N, Kahvecioglu G (2018) Stochastic last mile relief network design with resource reallocation. OR Spectr 40(1):187–231
Orgut I, Ivy J, Uzsoy R, Wilson J (2016) Modeling for the equitable and effective distribution of donated food under capacity constraints. IIE Trans 48(3):252–266
Ozdamar L, Demir O (2012) A hierarchical clustering and routing procedure for large scale disaster relief logistics planning. Transp Res Part E Log Transp Rev 48(3):591–602
Ozdamar L, Ekinci E, Kucukyazici B (2004) Emergency logistics planning in natural disasters. Ann Oper Res 29(1–4):217–245
Ozguven E, Ozbay K (2013) A secure and efficient inventory management system for disasters. Transp Res Part C Emerg Technol 29:171–196
Perez-Rodriguez N, Holguin-Veras J (2016) Inventory-allocation distribution models for postdisaster humanitarian logistics with explicit consideration of deprivation costs. Transp Sci 50(4):1261–1285
Raa B, Dullaert W (2017) Route and fleet design for cyclic inventory routing. Eur J Oper Res 256(2):404–411
Rath S, Gutjahr W (2014) A math-heuristic for the warehouse location-routing problem in disaster relief. Comput Oper Res 42:25–39
Rawls C, Turnquist M (2010) Pre-positioning of emergency supplies for disaster response. Transp Res Part B Methodol 44(4):521–534
Shen Z, Dessouky M, Ordonez F (2009) A two-stage vehicle routing model for large-scale bioterrorism emergencies. Networks 54(4):255–269
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. Transp Sci 45(3):335–345
Sphere Association (2018) The sphere handbook: humanitarian charter and minimum standards in humanitarian response, Geneva. www.spherestandards.org/handbook
Tan M, Davey M, Weaver M (2015) Nepal earthquake: tensions rise over slow pace of aid. The Guardian. https://www.theguardian.com/world/live/2015/apr/29/nepal-earthquake-humanitarian-crisis-engulfing-8-million-people-rolling-report. Accessed on 15 Aug 2017
The Guardian (2019) At least 62 people killed in Iran floods as US accused of blocking aid. https://www.theguardian.com/world/2019/apr/04/iran-floods-death-toll-reaches-62
The Washington Post (2017) Puerto Rico’s roadways alone are a disaster, and it will cost at least \$240 million to fix them. https://www.washingtonpost.com/news/dr-gridlock/wp/2017/09/29/puerto-ricos-roadways-alone-are-a-disaster-and-it-will-cost-at-least-240-million-to-fix-them/
Torre L, Dolinskaya I, Smilowitz K (2012) Disaster relief routing: integrating research and practice. Socio Econ Plan Sci 46(1):88–97
Tzeng G, Cheng H, Huang T (2007) Multi-objective optimal planning for designing relief delivery systems. Transp Res Part E Log Transp Rev 43(6):673–686
United Nations Office for the Coordination of Humanitarian Affairs (2012) Japan: post-earthquake coordination saves lives. https://www.unocha.org/story/japan-post-earthquake-coordination-saves-lives
Vitoriano B, Ortuno M, Tirado G, Montero J (2011) A multi-criteria optimization model for humanitarian aid distribution. J Glob Optim 51(2):189–208
Yang X, Feng L (2013) Inventory routing problem: routing and scheduling approach with the objective of slack maximization. J Transp Res Board Transp Res Rec 2378(1):32–42
Yang X, Zhu S (2016) Solution to the multidepot inventory slack-routing problem at the planning stage. J Comput Civ Eng 30(1):04014115
Yi W, Kumar A (2007) Ant colony optimization for disaster relief operations. Transp Res Part E Log Transp Rev 43(6):660–672
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This research is supported in part by The Scientific and Technological Research Council of Turkey (TÜBİTAK) Grant 115M535.
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Ekici, A., Özener, O.Ö. Inventory routing for the last mile delivery of humanitarian relief supplies. OR Spectrum 42, 621–660 (2020). https://doi.org/10.1007/s00291-020-00572-2
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DOI: https://doi.org/10.1007/s00291-020-00572-2