Article Contents
Article Contents

# Disaster relief routing in limited capacity road networks with heterogeneous flows

• * Corresponding author: Dilek Tuzun Aksu
• 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.

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

 Citation:

• Figure 1.  Road network of Fatih County in Istanbul

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)

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

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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