Disaster relief routing in limited capacity road networks with heterogeneous flows

Linet Ozdamar; Dilek Tuzun Aksu; Elifcan Yasa; Biket Ergunes

doi:10.3934/jimo.2018011

Article Contents

2018, Volume 14, Issue 4: 1367-1380. Doi: 10.3934/jimo.2018011

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Disaster relief routing in limited capacity road networks with heterogeneous flows

Department of Industrial and Systems Engineering, Yeditepe University, 26 Agustos Yerlesimi, Kayisdagi Cad., 34755 Atasehir, Istanbul, Turkey

* Corresponding author: Dilek Tuzun Aksu
* Corresponding author: Dilek Tuzun Aksu

Received: August 31, 2016

Revised: September 30, 2017

Early access: January 2018

Published: October 2018

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Abstract

In the aftermath of a major earthquake, delivery of essential services to survivors is of utmost importance and in urban areas it is conducted using road networks that are already stressed by road damages, other urban traffic and evacuation. Relief distribution efforts should be planned carefully in order to create minimal additional traffic congestion. We propose a dynamic relief distribution model where relief trucks share limited capacity road networks with counterflows resulting from car traffic. We develop a MIP model for this problem and solve it by decomposing the road network geographically and solving each subnetwork iteratively using the Relax and Fix method.

Keywords:

Mathematics Subject Classification: Primary: 90C35, 90C11, 90C06, 90B06, 90B20.

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Figure 1. Road network of Fatih County in Istanbul

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Table .

Algorithm 1

1: Initialize $k=0$
2:While $(k < \frac{T}{\Delta t})$ do
3:     $k++$
4:     Define $y_{ijcq}$ and $v_{ijcq}$ for $q=(k-1)\Delta t+1, ..., k\Delta t$ as integers, let $y_{ijcq}$ and $v_{ijcq}$ be positive float variables for $q= k\Delta t+1, ..., T$
5:     Solve Model R
6:     Fix $y_{ijcq}$ and $v_{ijcq}$ for $q=(k-1)\Delta t+1, ..., k\Delta t$ at their optimal integer values
7: end while
8: Report final solution
9: End (Algorithm1)

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Table 1. Performance of the RF Algorithm as a function of $\Delta t$

Region	Method	Obj.	CPU(secs.)	Rel.Gap	% Dev
1 (56 links)	No RF	1948.89	590.48	0.001	-
	RF ($\Delta t$=2)	1928.38	680.01		-1.052
	RF ($\Delta t$=4)	1931.90	415.80		-0.872
	RF ($\Delta t$=8)	1932.05	374.31		-0.864
2 (54 links)	No RF	2055.46	3609.47	0.017	-
	RF ($\Delta t$=2)	2037.86	734.53		-0.856
	RF ($\Delta t$=4)	2052.20	489.48		-0.159
	RF ($\Delta t$=8)	2053.23	744.67		-0.108
3 (65 links)	No RF	1659.32	3611.89	0.021	-
	RF ($\Delta t$=2)	1667.39	999.43		0.486
	RF ($\Delta t$=4)	1655.30	636.56		-0.242
	RF ($\Delta t$=8)	1656.58	645.14		-0.165
4 (52 links)	No RF	3967.29	3609.02	0.003	-
	RF ($\Delta t$=2)	3964.52	713.17		-0.070
	RF ($\Delta t$=4)	3961.60	424.16		-0.143
	RF ($\Delta t$=8)	3967.04	278.05		-0.006
5 (46 links)	No RF	2969.91	3610.08	0.009	-
	RF ($\Delta t$=2)	2969.68	304.56		-0.008
	RF ($\Delta t$=4)	2973.97	164.88		0.137
	RF ($\Delta t$=8)	2972.40	140.04		0.084
6 (63 links)	No RF	1347.78	3612.22	0.018	-
	RF ($\Delta t$=2)	1346.13	948.06		-0.122
	RF ($\Delta t$=4)	1353.34	533.05		0.413
	RF ($\Delta t$=8)	1353.42	472.09		0.418
7 (64 links)	No RF	1834.74	3608.97	0.011	-
	RF ($\Delta t$=2)	1822.31	999.92		-0.677
	RF ($\Delta t$=4)	1824.13	539.54		-0.578
	RF ($\Delta t$=8)	1830.28	475.05		-0.243

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Table 2. Comparison of solution quality for various decomposition strategies

Subnetworks	Obj.	CPU	Rel.Gap	No. of Links
67	3527.10	7251.00	0.03	127
6+7	3182.52	7221.19
6+7 (RF)	3183.70	947.14
12	3998.60	7241.77	0.02	110
1+2	4004.35	4199.95
1+2 (RF)	3985.28	1118.97
45	8499.28	7232.73	0.01	98
4+5	6937.20	7219.10
4+5 (RF)	6939.44	418.10
37	3744.10	7243.97	0.10	129
3+7	3494.06	7220.86
3+7 (RF)	3486.86	1120.19
34	5621.70	7246.52	0.01	117
3+4	5626.61	7220.91
3+4 (RF)	5623.62	923.19
345	9050.53	10897.60	0.12	163
34+5	8591.61	10856.60
3+4+5	8596.52	10830.99
3+4+5 (RF)	8596.02	1063.23
456	9713.23	10905.90	0.08	161
45+6	9847.06	10844.95
4+5+6	8284.98	10831.32
4+5+6 (RF)	8292.86	890.18
567	5520.59	10914.90	0.24	173
5+67	6497.01	10861.08
5+6+7	6152.43	10831.27
5+6+7 (RF)	6156.10	1087.18
123	650.07	10939.80	1.00	175
12+3	5657.92	10853.66
1+2+3	5663.67	7811.84
1+2+3 (RF)	5641.86	1764.11
12345	1145.08	18450.00	1.00	273
12+345	13049.13	18139.37
123+45	9149.35	18172.53
1+2+3+4+5	12600.87	15030.94
1+2+3+4+5 (RF)	12581.30	2182.21
34567	1170.16	18560.90	1.00	290
34+567	11142.29	18161.42
37+456	13457.33	18149.87
3+4+5+6+7	11779.04	18052.18
3+4+5+6+7 (RF)	11779.72	2010.37

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References

	A. Afshar and A. Haghani , Modeling integrated supply chain logistics in real-time large-scale disaster relief operations, Socio-Economic Planning Sciences, 46 (2012) , 327-338. doi: 10.1016/j.seps.2011.12.003.
	V. Akbari and F. S. Salman , Multi-vehicle synchronized arc routing problem to restore post-disaster network connectivity, European Journal of Operational Research, 257 (2017) , 625-640. doi: 10.1016/j.ejor.2016.07.043.
	M. Albareda-Sambola , A. Alonso-Ayuso , L. F. Escudero , E. Fernandez and C. Pizarro , Fix-and-relax-coordination for a multi-period location-allocation problem under uncertainty, Computers & Operations Research, 40 (2013) , 2878-2892. doi: 10.1016/j.cor.2013.07.004.
	A. M. Anaya-Arenas , J. Renaud and A. Ruiz , Relief distribution networks: A systematic review, Annals of Operations Research, 223 (2014) , 53-79. doi: 10.1007/s10479-014-1581-y.
	J. Araoz , E. Fernandez and C. Zoltan , Privatized rural postman problems, Computers & Operations Research, 33 (2006) , 3432-3449. doi: 10.1016/j.cor.2005.02.013.
	J. Araoz , E. Fernandez and O. Meza , Solving the prize-collecting rural postman problem, European Journal of Operational Research, 196 (2009) , 886-896. doi: 10.1016/j.ejor.2008.04.037.
	C. Archetti , D. Feillet , A. Hertz and M. G. Speranza , The undirected capacitated arc routing problem with profits, Computers & Operations Research, 37 (2010) , 1860-1869. doi: 10.1016/j.cor.2009.05.005.
	B. Balcik , B. M. Beamon and K. Smilowitz , Last mile distribution in humanitarian relief, Journal of Intelligent Transportation Systems, 12 (2008) , 51-63. doi: 10.1080/15472450802023329.
	T. A. Baldo , M. O. Santos , B. Almada-Lobo and R. Morabito , An optimization approach for the lot sizing and scheduling problem in the brewery industry, Computers & Industrial Engineering, 72 (2014) , 58-71. doi: 10.1016/j.cie.2014.02.008.
	P. Beraldi , G. Ghiani , E. Guerriero and A. Grieco , Scenario-based planning for lot-sizing and scheduling with uncertain processing times, International Journal of Production Economics, 101 (2006) , 140-149. doi: 10.1016/j.ijpe.2005.05.018.
	D. Berkoune , J. Renaud , M. Rekik and A. Ruiz , Transportation in disaster response operations, Socio-Economic Planning Sciences, 46 (2012) , 23-32. doi: 10.1016/j.seps.2011.05.002.
	V. Campos , R. Bandeira and A. Bandeira , A method for evacuation route planning in disaster situations, Procedia-Social and Behavioral Sciences, 54 (2012) , 503-512. doi: 10.1016/j.sbspro.2012.09.768.
	A. M. Caunhye , X. Nie and S. Pokharel , Optimization models in emergency logistics: A literature review, Socio-Economic Planning Sciences, 46 (2012) , 4-13. doi: 10.1016/j.seps.2011.04.004.
	A. Y. Chen , F. Pena-Mora and Y. Ouyang , A collaborative GIS framework to support equipment distribution for civil engineering disaster response operations, Automation in Construction, 20 (2011) , 637-648. doi: 10.1016/j.autcon.2010.12.007.
	T. Cova and J. Johnson , A network flow model for lane-based evacuation routing, Transportation Research Part A: Policy and Practice, 37 (2003) , 579-604. doi: 10.1016/S0965-8564(03)00007-7.
	J. Cui, S. An and M. Zhao, A generalized minimum cost flow model for multiple emergency flow routing Mathematical Problems in Engineering 2014 (2014), Article ID 832053, 12 pages. doi: 10.1155/2014/832053.
	C. F. Daganzo , The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory, Transportation Research Part B: Methodological, 28 (1994) , 269-287. doi: 10.1016/0191-2615(94)90002-7.
	L. E. de la Torre , I. S. Dolinskaya and K. R. Smilowitz , Disaster relief routing: Integrating research and practice, Socio-Economic Planning Sciences, 46 (2012) , 88-97.
	L. Escudero , A. Garin , M. Merino and G. Perez , BFC-MSMIP: An exact branch-and-fix coordination approach for solving multistage stochastic mixed 0--1 problems, TOP, 17 (2009) , 96-122. doi: 10.1007/s11750-009-0083-6.
	D. Feillet , P. Dejax and M. Gendreau , The profitable arc tour problem: Solution with a branch-and-price algorithm, Transportation Science, 39 (2005) , 539-552. doi: 10.1287/trsc.1040.0106.
	C. M. Feng and C. C. Wen , A fuzzy bi-level and multi-objective model to control traffic flow into disaster area post earthquake, Journal of the Eastern Asia Society for Transportation Studies, 6 (2005) , 4253-4268.
	D. Ferreira , R. Morabito and S. Rangel , Relax and fix heuristics to solve one-stage one machine lot-scheduling models for small-scale soft drink plants, Computers & Operations Research, 37 (2010) , 684-691. doi: 10.1016/j.cor.2009.06.007.
	S. Gupta , M. Starr , R. Zanjirani Farahani and N. Matinrad , Disaster management from a POM perspective: Mapping a new domain, Production and Operations Management, 25 (2016) , 1611-1637. doi: 10.1111/poms.12591.
	A. Haghani and S. C. Oh , Formulation and solution of a multi-commodity, multi-modal network flow model for disaster relief operations, Transportation Research Part A: Policy and Practice, 30 (1996) , 231-250. doi: 10.1016/0965-8564(95)00020-8.
	F. Liberatore , M. T. Ortuno , G. Tirado , B. Vitoriano and M. P. Scaparra , A hierarchical compromise model for the joint optimization of recovery operations and distribution of emergency goods in Humanitarian Logistics, Computers & Operations Research, 42 (2014) , 3-13. doi: 10.1016/j.cor.2012.03.019.
	G. J. Lim , S. Zangeneh , M. R. Baharnemati and T. Assavapokee , A capacitated network flow optimization approach for short notice evacuation planning, European Journal of Operational Research, 223 (2012) , 234-245. doi: 10.1016/j.ejor.2012.06.004.
	Y. H. Lin , R. Batta , P. A. Rogerson , A. Blatt and M. Flanigan , A logistics model for emergency supply of critical items in the aftermath of a disaster, Socio-Economic Planning Sciences, 45 (2011) , 132-145. doi: 10.1016/j.seps.2011.04.003.
	Y. Liu , X. R. Lai and G. L. Chang , Two-level integrated optimization system for planning emergency evacuation, J. Of Transportation Engineering, 132 (2006) , 800-807. doi: 10.1061/(ASCE)0733-947X(2006)132:10(800).
	E. Miller-Hooks and S. S. Patterson , On solving quickest time problems in time-dependent, dynamic networks, Journal of Mathematical Modelling and Algorithms, 3 (2004) , 39-71. doi: 10.1023/B:JMMA.0000026708.57419.6d.
	M. Najafi , K. Eshghi and W. Dullaert , A multi-objective robust optimization model for logistics planning in the earthquake response phase, Transportation Research Part E: Logistics and Transportation Review, 49 (2013) , 217-249. doi: 10.1016/j.tre.2012.09.001.
	L. Ozdamar and O. Demir , A hierarchical clustering and routing procedure for large scale disaster relief logistics planning, Transportation Research Part E: Logistics and Transportation Review, 48 (2012) , 591-602. doi: 10.1016/j.tre.2011.11.003.
	L. Ozdamar , E. Ekinci and B. Kucukyazici , Emergency logistics planning in natural disasters, Annals of Operations Research, 129 (2004) , 217-245. doi: 10.1023/B:ANOR.0000030690.27939.39.
	L. Ozdamar and M. A. Ertem , Models, solutions and enabling technologies in humanitarian logistics, European Journal of Operational Research, 244 (2015) , 55-65. doi: 10.1016/j.ejor.2014.11.030.
	B. Vitoriano , M. T. Ortuno , G. Tirado and J. Montero , A multi-criteria optimization model for humanitarian aid distribution, Journal of Global Optimization, 51 (2011) , 189-208. doi: 10.1007/s10898-010-9603-z.
	B. Vitoriano , T. Ortuno and G. Tirado , HADS, a goal programming-based humanitarian aid distribution system, Journal of Multi-Criteria Decision Analysis, 16 (2009) , 55-64. doi: 10.1002/mcda.439.
	S. Yan and Y. L. Shih , Optimal scheduling of emergency roadway repair and subsequent relief distribution, Computers & Operations Research, 36 (2009) , 2049-2065. doi: 10.1016/j.cor.2008.07.002.