CHEMICAL ENGINEERINGTRANSACTIONS 
 

VOL. 51, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors:Tichun Wang, Hongyang Zhang, Lei Tian 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN978-88-95608-43-3; ISSN 2283-9216 

Location-Routing Model for Post-disaster Initial Stage 
Relief Supplies Based on Priority Level 

Shihong Hea, Lei Zhang*b 
aSchool of Logistics Management and Engineering, Guangxi Teachers Education University, Nanning, R.P. China 
bPostdoctoral Research Station of Management Science and Engineering, Fuzhou University, Fuzhou, R.P. China 
530088979 @qq.com 

According to the location-routing problem that the total relief supplies are limited and insufficient in initial 
stages of post-disaster, the priority allocation coefficient of each point is determined with variable set theory 
and then the allocation amount of relief supplies in each stricken point is obtained. Considering the 
construction time of relief facilities and relief transportation capacity constraints, the location- routing model is 
proposed with the goal of minimum time in the entire rescue process. And then genetic algorithm is used to 
solve the facility location and relief supplies distribution routing. At last, the effectiveness and feasibility of the 
model and algorithm are verified with numerical example. 

1. Introduction  

In recent years, strong earthquakes occurred frequently in China. For example, an 8.0 earthquake took place 
on May 12, 2008 in Wechuan, Sichuan Province, a 7.1 earthquake took place on April 17, 2010 in Yushu, 
Qinghai Province, a 5.8 earthquake took place on March 10, 2011 in Yinjiang, Yunnan Province, a 5.6 
earthquake took place on September 7, 2012 in Yiliang, Yunnan Province, a 5.6 earthquake took place on 
March 29, 2013 in Jichang, Xinjiang Province, 7.0 earthquake took place on April 20, 2013 in Ya’an, Sichuan 
Province. It is of great possibility that the earthquakes with strong and irreparable damage will occur in the 
next 50 years in China (Nie et al., 2001). As the key of post-disaster rescue, to timely and reasonably allocate 
the relief supplies and to meet the demand for relief supplies quickly in limited time, space and resource 
constraint have great significance to save the stricken lives and to reduce the impact of disasters(Lang, et al. 
2014; Zheng and Ma, 2014).Domestic and foreign scholars have made certain achievements on the problems 
of emergency facilities location(Ma, et al. 2015; Ni, et al. 2015; Zhu, 2015; Yuan et al., 2015) and relief 
supplies’ routing optimization(Tzeng and Cheng, 2007; Shen et al., 2009; Widener and Horner, 2011) of post-
disaster.  
The urgency degree and demand for relief supplies at each point are different after the earthquake occurs. 
The amount of relief supplies in initial stage of post-disaster is quite limited, so the priority level analysis for the 
relief supplies demand in stricken area is the premise of rational allocation of relief supplies. However, most of 
the existing literatures set the demand of each stricken point as identified demand or random demand, seldom 
of them took the priority level of post-disaster demand for relief supplies into consideration. Therefore, this 
paper aims to sort the priority level of relief supplies in each stricken point based on the key factor of stricken 
area’s demand and takes the connectivity of transportation network and the timeliness of relief supplies into 
consideration. A collaborative optimization model of emergency facility location-routing of post-disaster is 
proposed, genetic algorithm is used to solve the model and then determine the rational facility location and 
distribution routing for relief supplies. 

2. Problem Description and Explanation  

2.1 Problem Description 

In the initial stage of earthquake, the relief supplies often cannot meet all the demand of stricken points, in this 
case the points in emergency need are sorted by priority level and thus to determine the reasonable prior 
allocation for supplies at each stricken point. Taking the time constraint into consideration, the logistic network 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651163

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: He S.H., Zhang L., 2016, Location-routing model for post-disaster initial stage relief supplies based on priority level, 
Chemical Engineering Transactions, 51, 973-978  DOI:10.3303/CET1651163   

973



structure of relief supplies has been built to determine the distribution points, delivery centers and distribution 
route with appropriate scale and amount of post-disaster relief supplies. In limited space and resource 
constraint, the emergency system will transport the relief supplies from periphery distribution points in stricken 
area to emergency delivery centers and then distribute the supplies to each stricken point to meet the demand 
with minimum time. Due to the transportation infrastructures are destroyed after earthquake and the relief 
supplies transported from emergency distribution centers to emergency delivery centers is of large quantity, 
the helicopters can be applied to supplies’ distribution and the road transportation with stronger flexibility can 
be utilized between emergency delivery centers and each stricken point. 

2.2 Symbol explanation 
The mathematical notation and formulation are as follows: 
I represents the stricken point set of post-disaster, i I. 
K represents the distribution point set of relief supplies of post-disaster, k K. 
L represents the emergency delivery center set of post-disaster, l L. 
N represents the emergency delivery center and stricken point set, n N. 
F represents the helicopter set, fF. 
V represents the transport vehicle set, vV. 
Y represents the total amount of relief supplies for pending deployment. 
iab represents the relative optimal membership degree vector of relief supplies demand. 
cij’ represents the eigen value of stricken point i at target j. 
cij represents the value of relative optimal membership degree, and it’s the value after the normalized 
treatment for cij’. 
wj represents the weight of key factor j of supplies demand. 
tk represents the time spent to build the distribution point k. 
tl represents the time spent to build the emergency delivery center l. 
sf represents the maximum transport capacity of helicopter f. 
sv represents the maximum transport capacity of vehicle v. 
hf represents the average flight speed of helicopter f. 
hv represents the average driving speed of vehicle v. 
i represents the allocation coefficient of priority level at point i. 
di represents the prior allocation amount of relief supplies at point i.  
e represents the distance between the nodes. 
zk represents a 0-1variable that whether to establish distribution point. 
zl represents a 0-1variable that whether to establish emergency delivery center. 
zkf represents a 0-1variable that whether the transport helicopter is allocated to distribution point. 
zlv represents a 0-1variable that whether the transport vehicle is allocated to delivery center. 
yiv represents a 0-1variable that whether the supplies are distributed by transport vehicle v at stricken point i. 
xklf represents a 0-1variable that whether the helicopter transport from distribution point k to delivery center l . 
cinv represents a 0-1variable that whether the vehicle transport between the nodes. 

3. Model Building 

3.1 How to determine the priority level of relief supplies 
The uncertainty to forecast the relief supplies’ demand of post-disaster is the key of allocation when the 
supplies is insufficient. Through the example of supplies’ distribution like Wenchuan earthquake, literature[2] 

verified that the allocation decision model based on variable set theory is of high reliability. This paper aims to 
take the stricken population, the disaster extent and the size of stricken area as the key factor of relief 
supplies’ demand of post-disaster and utilize the variable set theory to determine the priority level order of 
relief supplies for each stricken point. The variable optimization model is proposed as follows. 

1 2 
i i

d Y ,i , , ,m
    

(1) 

2 2

1 1

2 2

1 1 1

                      1 2
iab

a b
i m

iab

i a b

i , , ,m







 

  

 



     (2)

 

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 

 

1

1

1

1

1
                 

1

1

                                                              1 2 1 2 1 2

iab a

n bb

j ij

j

n bb

j ij

j

w c

w c

i , , ,m; a , ;b ,








 
      
  

 
 

 
  
  

  





    
(3)

 

 

   
                  1 2 1 2

ij ij
j

ij

ij ij
j j

c min c
c i , , ,m; j , , n

max c min c

 
  

 
    

(4)
 

 

   
                  1 2 1 2

ij ij
j

ij

ij ij
j j

max c c
c i , , ,m; j , , n

max c min c

 
  

 
    

(5)
 

The cost-focused target eigenvalue is calculated through Eq (4) and the benefit-focused target eigenvalue is 
calculated through Eq (5) with the goal of united type and non-dimensionalization. 

3.2 Location-routing model building 

After determining the prior allocation of relief supplies of each stricken point, the optimization model of 
location-routing of post-disaster is proposed with the goal of least time consuming in order to determine the 
emergency facilities location and the distribution routing. The objective function includes the time consuming 
of emergency distribution point construction and delivery center construction, the time consuming that relief 
supplies transported from distribution point to delivery center and the time that the emergency delivery center 
takes to distribute the relief supplies for each stricken point. 

  kl nn
k k l l klf inv

k K l L f F k K l L v V n N n Nf v

e e
min M t z t z x x

h h



       

      
   

(6)
 

The Eq (7) represents the relief supplies’ amount transported from distribution point is less than the total 
amount of relief supplies. 

f klf

k K l L f F

s x Y
  


   (7)

 

Eq (8) to (10) represent that the transport helicopter f must be allocated to the enabled distribution point k, and 
the transport helicopter shouldn’t be allocated to the distribution point k without being enabled, namely the 
transport helicopter should be allocated to enabled distribution point k only. 

0                 
klf k

f F l L

x z k K
 

   
   (8)

 

                        ,0
l L

klf k
k Kf Fx z



      (9)
 

                      ,  
kf k

z f F k Kz   
   (10) 

Eq (11) represents the capacity constraint in emergency delivery center. 

                      
f klf l l

f F k K

s x z s l L
 

  
   (11)

 

Eq (12) to (14) represent that the transport vehicle v must be allocated to the enabled delivery center l, and 
the transport vehicles shouldn’t be allocated to the delivery center l without being enabled, namely the 
transport vehicles should be allocated to the enabled delivery center l only. 

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 0               
ilv l

v V i I

l Lx z
 

  
   (12)

 

 0                  ,
ilv v l

i I

x z z v V l L


    
   (13)

 

                           ,
lv l

v V l Lz z   
   (14) 

Eq (15) represents that the delivery route of each vehicle starts from its attached emergency logistic center 
only. 

                       ,
ilv vl

i I

z v V l Lx


   
   (15)

 

Eq (16) represents the continuity of vehicles’ transport route. 

0                 , ,
nn v n nv

n N n N

x x v V n n N 
  

     
   (16)

 

Eq (17) represents that the rescue point i should be allocated to vehicle v if and only if vehicle v passes by it 
when starting from the emergency delivery center  l. 

,1         ,
inv lnv iv

n N n N

l L v Vx x y i I
 

      
   (17)

 

Eq (18) represents that the demand of each stricken point along the delivery route shouldn’t exceed the 
vehicle’s loading capacity. 

                      
i inv v

n N i I

d x s v V
 

  
   (18)

 

Eq (19) represents the 0-1 decision variable. 

, , , , , , {0,1}
k l f v iv klf inv

z z y x xz z  , , , , ,i I l L k K f F v V n N                                                 (19) 

4. Numerical Simulation 

4.1 Simulation data 
With a sudden earthquake happened somewhere in China, there has two distribution points for preparation, 
the coordinates are respectively (20,270) and(245,60) , and the time consuming of each construction is 
respectively 4 hours and 3 hours; There has four emergency delivery centers points for preparation, the 
coordinates are respectively(200,180), (50,75), (180,90)and(100,250), and the time consuming of construction 
is respectively 2 hours, 1.5 hours, 2 hours and1 hours, and the capacity is respectively 25000 units, 35000 
units, 25000 units and 30000 units; There has five helicopters and the capacity is 30000 units, the flight speed 
is 300km/h;  There has 15 transport vehicles, among which 12 vehicles have a capacity of 8000 units and the 
remaining 3 vehicles have a capacity of 6000 units, the driving speed is 80km/h; There has 30 stricken points 
and the basic information of each point is shown in Table 1. In the initial stage of post-disaster the stock of 
relief supplies is just 100,000 units, determine the priority level of relief supplies and make location distribution 
with the goal of minimum time consuming according to the basic information of each stricken point. 

4.2 Simulation results 

The parameters are set as follows:Pop=100, GGAP=0.9, maxgen=300, pc=0.7, pm=0.08. The genetic 
algorithm is implemented with Matlab7.0, the total time consuming of post-disaster emergency delivery based 
on priority level reaches 45.2 h.From the genetic algorithm convergence Figure 1, it is indicated that the 
algorithm is of good convergence effect. 
 
 
 
 
 
 

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Table 1: Basic Information of Each Stricken Point 

Number 1 2 3 4 5 6 7 8 

Stricken 
population(10,000) 3.8 2.7 3.7 4.9 2.2 3 1.7 2.1 

Stricken area 
(10,000km) 0.7 2.3 0.9 3.9 3.1 2.8 0.5 0.4 

Afflicted strength 5.3 5.3 5.3 5.2 5.6 5.2 5.9 5.9 

Coordinate x 
(km) 44 64 75 101 61 70 118 66 

Coordinate y 
(km) 63 128 117 32 107 118 90 61 

Number 9 10 11 12 13 14 15 16 

Stricken 
population(10,000) 1.9 3.3 2.3 10 1.5 1 2.9 2.6 

Stricken area 
(10,000km) 1.4 0.8 1 5 3.7 2 2.1 3.4 

Afflicted strength 5.2 5.1 5.7 7 5.3 5.5 6.5 5.7 

Coordinate x 
(km) 36 45 118 56 85 46 131 127 

Coordinate y 
(km) 124 152 204 145 144 123 164 100 

Number 17 18 19 20 21 22 23 24 

Stricken 
population(10,000) 3.4 4.2 50 6.9 3.3 7.6 4.6 6 

Stricken area 
(10,000km) 3.1 1.9 15 3.5 2.3 2.9 0.9 3.8 

Afflicted strength 5.7 5.7 7.2 6.1 5.6 6.7 6.2 5.3 

Coordinate x 
(km) 131 154 154 186 180 193 155 136 

Coordinate y 
(km) 75 159 29 74 31 36 142 149 

Number 25 26 27 28 29 30   

Stricken 
population(10,000) 6.2 3.1 4.2 3.7 4.5 1.6   

Stricken area 
(10,000km) 1.6 2.9 2.6 2.4 1.6 2.4   

Afflicted strength 5.2 6.3 5.8 6.3 6.4 6.3   

Coordinate x 
(km) 159 103 184 121 160 142   

Coordinate y 
(km) 186 196 189 160 196 143   

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Figure 1: Genetic Algorithm Convergence Diagram 

5. Conclusions 

To timely meet the need of stricken individuals for relief supplies after the earthquake occurs, this paper firstly 
identified the key factors of relief supplies’ allocation of post-disaster, construct the relative membership 
degree matrix of index and sort the demand urgency of relief supplies according to the priority level by utilizing 
variable set theory, and then determine the prior allocation amount of relief supplies of each stricken point. On 
the basis of this, the emergency facility location-distribution routing model is proposed and the genetic 
algorithm is designed to solve the model according to its characteristics. The example analysis indicates that 
the model and algorithm can be used as the auxiliary decision of relief supplies’ delivery of post-disaster. 

Acknowledgements 

This work was supported by Zhejiang Natural Science Foundation under Award Number LY15G030021, the 
project of specialty integrated reform pilotunder Award NumberZG0429. 

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0 50 100 150 200 250 300
2

4

6

8

10

12

14
x 10

5

Iteration

T
a
rg

e
t 

v
a
lu

e
change of solution

change of mean value

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