Bi-objective Optimization Model for Determining Shelter

Location-allocation in Humanitarian Relief Logistics

Panchalee Praneetpholkrang

1 a

, Van Nam Huynh

1 b

and Sarunya Kanjanawattana

2 c

School of Advanced Science and Technology, Japan Advanced Institute of Science and Technology, Ishikawa, Japan

Computer Engineering, Institute of Engineering, Suranaree University of Technology, Nakhon Ratchasima, Thailand

Keywords:

Facility Location Problem, Epsilon Constraint, Augmented, Humanitarian Logistics, Relief Chain, Disaster

Management.

Abstract:

Shelter location-allocation is very important since it affects victims’ security and the performance of the relief

supply chain. This paper proposes a bi-objective optimization model for justifying locations of shelters and

allocating appropriate shelters to all affected areas efﬁciently and effectively. The ﬁrst objective seeks to

minimize the total cost, and the second objective attempts to minimize the average victim evacuation time.

The Epsilon Constraint method is employed to deal with the bi-objective function. To avoid the inefﬁcient

solutions problem, which is likely generated by the Epsilon Constraint approach, the transformed constraint

is augmented by the positive constant value of allowance time. A case study of the ﬂood in Phun Phin, Surat

Thani, Thailand is used to demonstrate the application of the proposed model. The results obtained from this

study could help decision-makers to determine an effective shelter location-allocation plan as well as, more

broadly, to develop a disaster management strategy.

1 INTRODUCTION

In 2019, natural disasters were frequent and impacted

people and economic systems across the world. Ac-

cording to statistical data from the Centre for Re-

search on the Epidemiology of Disaster, there were

396 natural catastrophes, leading to 11,755 deaths,

95 million affected people, and $103 billion in eco-

nomic losses. The Natural Disaster 2019 report re-

veals that ﬂooding was the most frequent disaster and

the main cause of death (CRED, 2019). Humanitar-

ian logistics plays an important role in evacuating vic-

tims from the affected areas to safe zones, as well as

in distributing the necessary relief supplies to victims

efﬁciently, to the right place, and in the right quan-

tity (Manopiniwes and Irohara, 2014; Thomas, A.;

Kopczak, 2005). Furthermore, determining the lo-

cation of relief facilities such as shelters, distribution

centers, and medical centers is a critical decision that

should be taken by humanitarian logisticians as well

as related relief authorities (Maharjan and Hanaoka,

2018). In this regard, seeking proper shelters to serve

https://orcid.org/0000-0002-8119-7946

https://orcid.org/0000-0002-3860-7815

https://orcid.org/0000-0002-1862-0588

victims is the most important issue to be decided prior

to the disaster (Ozbay et al., 2019) since it affects

victims’ security and inﬂuences the success of disas-

ter management more broadly (Balcik and Beamon,

2008; Verma and Gaukler, 2015; Kongsomsaksakul

and Yang, 2005).

Considering several important criteria simultane-

ously could help related authorities to efﬁciently and

effectively develop an appropriate shelter location-

allocation plan. This research proposes a bi-objective

optimization model for determining adequate shelter

location-allocation. The considered criteria include 1)

total cost combining ﬁxed cost for opening shelters,

victim evacuation cost, and service cost; and 2) victim

evacuation time. The proposed model is tested with

a case study of the 2011 ﬂood in Phun Phin district,

Surat Thani, Thailand (Surat Thani National Statisti-

cal Ofﬁce, 2012). The remainder of this paper is or-

ganized as follows. Section 2 discusses related work

in this ﬁeld. Section 3 presents the proposed method-

ology, which encompasses parameters, model formu-

lation, and solution method. Section 4 describes the

ﬂood case study. Section 5 provides the numerical ex-

periment results. Finally, Section 6 outlines the con-

clusions made from this study.

Praneetpholkrang, P., Huynh, V. and Kanjanawattana, S.

Bi-objective Optimization Model for Determining Shelter Location-allocation in Humanitarian Relief Logistics.

DOI: 10.5220/0010183503870393

In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems (ICORES 2021), pages 387-393

ISBN: 978-989-758-485-5

387

2 RELATED WORK

The selection of appropriate locations for relief facil-

ities inﬂuences victims’ lives and the ﬂow of services

and relief supplies. Furthermore, it has a long-term

impact, affecting the success of disaster management

(Boonmee et al., 2017; Haghani, 1996). Typical re-

lief facilities include shelters, warehouses, distribu-

tion centers, medical centers, and prevention centers.

The issue is not only to select the right locations but

also to allocate the proper facilities to the affected ar-

eas (Boonmee et al., 2017).

A lot of research has been conducted related to

facility location-allocation in the area of humani-

tarian logistics and disaster management. For the

shelter location-allocation problem, the mathemati-

cal models are formulated as single objective, bi-

objective, and multi-objective functions. The typi-

cal goal is to improve either the efﬁciency or effec-

tiveness of the humanitarian logistics performances.

The models aimed at improving effectiveness are de-

veloped to minimize evacuation time, the number of

opened shelters, distance, and demand weighted dis-

tance (Kongsomsaksakul and Yang, 2005; Qin et al.,

2018; G

ormez et al., 2011; Ozbay et al., 2019; Chanta

and Sangsawang, 2012), whereas the models aimed at

improving efﬁciency are developed to minimize trans-

portation cost, the cost of opening the shelters, and

other operation costs (Horner and Downs, 2010; Pra-

neetpholkrang and Huynh, 2020). A relatively small

number of studies consider both effectiveness and ef-

ﬁciency simultaneously e.g. by maximizing demand

coverage and minimizing operating cost (Hallak et al.,

2019), minimizing distance and total cost (Rodr

ıguez-

Esp

ındola and Gayt

an, 2015), minimizing distance to-

gether with minimizing cost of opening shelters (Hu

et al., 2014), or minimizing maximum response time

and minimizing total cost (Manopiniwes and Irohara,

2017). Several pieces of research related to other

relief facilities—e.g. warehouse, distribution cen-

ter, and healthcare—have also been conducted. Such

models aim to maximize the demand coverage of the

distribution center (Balcik and Beamon, 2008). Oth-

ers attempt to maximize demand coverage, maximize

the number of healthcare facilities, and minimize total

cost (Mic¸ and Koyuncu, 2019), or to minimize trans-

portation time and unmet demand, and minimize op-

eration cost for locating warehouses (Mete and Zabin-

sky, 2010). Determining both criteria simultaneously

means that, when seeking to minimize cost, the re-

sponsiveness level would be lower and vice versa.

The previous research is illustrated with case stud-

ies on ﬂoods, earthquakes, hurricanes, and conﬂict

areas; they are usually solved using various meth-

ods such as the Exact Algorithm, Weighted Sum

Method, Epsilon Constraint, and Weighted Goal Pro-

gramming. The methods that involve the assignment

of weights to indicate the relative importance of each

objective are not suitable for solving multi-objective

optimization models in the context of humanitarian

logistics, as monetary and non-monetary objective

functions are both involved. In these scenarios, vic-

tims’ welfare is very important and cannot be ignored.

On the other hand, the related authorities need to save

costs and resources to prevent scarcity during unex-

pected situations. Therefore, the decision-makers are

under pressure both in terms of victims’ welfare and

the related costs, so these must be balanced in the pro-

posed model through the use of multi-objective meth-

ods.

3 PROPOSED METHODOLOGY

The necessary data—i.e. number of victims, shel-

ter’s capacity, vehicle’s capacity, ﬁxed cost for open

shelter, ratio of required staff, and duration of dis-

aster—are gathered to formulate the mathematical

model. Unlike other prior works, this study considers

the ideal minimum distance between the affected area

and candidate shelter (m

i j

) that would be safe from

the disaster range. The m

i j

is calculated based on the

number of victims and population density. However,

the locations of selected shelters should not be farther

than the maximum acceptable distance (M

i j

). The as-

sumption of the model, model formulation, and the

solution methods are outlined in the next section.

3.1 Model Formulation

The assumptions of the model are as follows:

• The number of victims in each affected area is

known and constant

• The locations of all affected areas and candidate

shelters are ﬁxed

• The victims in each affected area will be allocated

to the same shelter

• The vehicles used in the evacuation process are

homogeneous

• The velocity of the vehicles is constant; the trafﬁc

conditions are not taken into account

Indices

I Set of affected areas

J Set of candidate shelters

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

388

Parameters

i j

Distance between area i and shelter j

Capacity of the shelter j

Number of victims in area i

Fixed cost for opening the shelter j

i j

Minimum distance between area i and shelter j

C Capacity of vehicle

i j

Maximum distance between area i and shelter j

N Number of vehicles for evacuation process

W Target time for evacuating the victims from

area i to shelter j

α Constant coefﬁcient of transportation cost per

kilometer per person

β Wage per person per day for hiring staff to work

in the shelter

γ Ratio of the required staff per victim

T Duration of the disaster occurrence

V Velocity of the vehicle that is used in evacuation

process

Decision Variables

1, if shelter j is selected or otherwise 0

i j

1, if area i is assigned to shelter j or otherwise 0

i j

Number of victims in area i that are assigned to

shelter j

Objective Functions

Minimize

∑

j∈J

+ α

∑

i∈I

∑

j∈J

i j

+ βT

∑

i∈I

i j

(1)

The ﬁrst objectives function (1) seeks to minimize

total cost, which combines ﬁxed cost for opening

shelters, victims’ transportation cost, and service cost

that is paid during the victims’ stay.

Minimize

∑

i∈I

∑

j∈J

i j

(2)

The second objective function (2) is to minimize vic-

tim evacuation time, the distance between affected ar-

eas and allocated shelters, the number of available ve-

hicles, vehicle capacity, and the velocity of the vehicle

during the ﬂood.

Subject to

∑

j∈J

i j

= 1, ∀

i∈I

(3)

Constraint (3) deﬁnes that the affected area i must be

entirely allocated to a single shelter

i j

≤ x

, ∀

i∈I, j∈J

(4)

Constraint (4) expresses that the affected area i must

be assigned to the opened shelter j

i j

≥ m

i j

, ∀

i∈I

j∈J

(5)

Constraint (5) deﬁnes that the distance between an af-

fected area i to assigned shelter j must be farther than

the minimum acceptable distance m

i j

≤ M

i j

, ∀

i∈I

j∈J

(6)

Constraint (6) limits the distance between an affected

area i to assigned shelter j to the maximum acceptable

distance M

i j

≤ W, ∀

i∈I

j∈J

(7)

Constraint (7) restricts victim evacuation time to the

target time for evacuation

∑

i∈I

i j

≤ c

, ∀

j∈J

(8)

Constraint (8) ensures that the numbers of assigned

victim do not exceed the capacity of shelter j

∈ {0, 1}, ∀

j∈J

(9)

Constraint (9) deﬁnes the binary variable; x

is 1 if

candidate shelter is selected, otherwise it is 0

i j

∈ {0, 1}, ∀

i∈I

j∈J

(10)

Constraint (10) deﬁnes the binary variable; y

i j

is 1

if affected area i is allocated to candidate shelter j,

otherwise it is 0.

3.2 Solution Approach

In solving the multi-objective optimization with

the Epsilon Constraint method, only one objective

is assigned as the primary objective function, and

the other objective functions become constraints.

Employing the Epsilon Constraint method to solve

the multi-objective problem is formulated as follows

(Deb, 2008; Mavrotas, 2009):

Objective Function

Min f

(11)

Bi-objective Optimization Model for Determining Shelter Location-allocation in Humanitarian Relief Logistics

389

Subject to

(x) ≤ ε

(12)

(x) ≤ ε

(13)

...

(x) ≤ ε

(14)

X ∈ S (15)

Where x is the vector of decision variables,

(x), ..., f

(x) and n is the objective function, and

n ≥ 2, S is the feasible region.

However, the Epsilon Constraint method requires

intensive computational effort to obtain the Pareto

solution and the obtained epsilon value is sometimes

inappropriate for use as the constraint for the pri-

mary objective function (Mavrotas, 2009; Xiujuan

and Zhongke, 2004). The objective function with

a positive constant helps to avoid the inefﬁcient

solutions problem (G

ormez et al., 2011). Therefore,

the f

that seeks to minimize victim evacuation

time is augmented by the allowance time, which

encompasses personal needs (such as restroom or

break times), fatigue, and delay. We take into account

the fatigue allowance to account for the exhaustion

of the physical and mental strength of the staff,

while the delay allowance factors in delays during

the transportation (Mital et al., 2016) for a total

allowance time of 20% of the ordinary time. The

augmented objective function is in Equation 17,

where δ is the constant coefﬁcient of allowance time

for evacuating victims. Thus, solving bi-objective

function problem with the Epsilon Constraint method

can be formulated as follows:

Objective Function

Min f

(16)

Subject to

∑

i∈I

∑

j∈J

i j

≤ ε

(17)

(3) - (11)

The numerical experiment was conducted using the

What’sBest LINDO Optimization tool on a Microsoft

Windows 10 laptop with Intel(R) Core (TM) 1.51

GHz, RAM 4.0 GB.

4 CASE STUDY

The major ﬂood in Phun Phin of Surat Thani, Thai-

land in 2011 is used as a case study to demonstrate

the application of the proposed model. Phun Phin is

located in the southern part of Thailand and experi-

ences repeated ﬂoods, especially in rainy season. The

international airport is located in this city and it is also

the main agricultural area of the southern part of Thai-

land. According to the statistical data on ﬂooding in

the area in 2011, there were ﬁve neighborhoods that

are henceforth deﬁned as affected areas. The numbers

of residents in these areas amounts to 1,965 people,

while the total estimated numbers of victims who suf-

fered from the ﬂood were 1,434 people, as illustrated

in Table 1.

There were four candidate shelters (S1-S4), con-

sisting of existing facilities such as schools, temples,

municipalities, or city halls, that were normally uti-

lized to serve as temporary shelters during such dis-

asters (Surat Thani National Statistical Ofﬁce, 2012).

Each shelter can accommodate 3,000 victims; there

was no construction cost since they were all exist-

ing infrastructure. Nevertheless, a ﬁxed cost for

opening the shelters was still required for installing

portable toilets, temporary kitchens, medical centers,

and warehouses, at an estimated 144,000 Thai Baht

per shelter.

As the locations of both the affected areas and can-

didate shelters are known, the road network distance

can be obtained through the Google Maps Distance

Matrix API. The vehicles that were used in the evacu-

ation process could transport 12 victims per trip. The

fuel consumption rate was 8 kilometers per liter. Dur-

ing the ﬂood, the vehicles’ speed was 24 kilometer per

hour, based on the estimated function of ﬂood depth

and vehicle speed (Pregnolato et al., 2017); this was

assumed to be constant. Furthermore, the government

authorities had to pay the service cost required for the

duration of the victims’ stays. This cost was estimated

based on the number of required staff i.e. one staff per

50 victims (Department of Disaster Prevention and

Mitigation, Ministry of Interior, 2011). The staff’s

wage was 380 Thai Baht per person per day. The

length of time for accomplishing the victim evacua-

tion process was set at no longer than 72 hours, which

aligns with the standard time accepted in the disaster

management ﬁeld (Ahmadi et al., 2015).

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

390

Table 1: Number of victims in each affected area.

Affected area No. of victims

A1 325

A2 310

A3 320

A4 230

A5 249

5 NUMERICAL EXPERIMENT

RESULTS

The numerical experiment commences by solving

each objective function individually, as illustrated in

the payoff table (Table 2). The individual optimal

solution was found to be is 214,547 Thai Baht,

which leads to an evacuation time of 2.67 hours.

For the second objective function, which attempts

to minimize the victim evacuation time, the optimal

solution is 2.57 hours with a total cost of 504,637

Thai Baht. Based on Table 2, the lower and upper

limit of the total cost is 214,547 Thai Baht and

504,637 Thai Baht. Meanwhile, the lower and upper

limit of the victims’ evacuation time is 2.57 hours

and 2.67 hours, respectively.

Table 2: Payoff table illustrating the individual optimal so-

lution.

Criteria

Optimal solution

Min f

Total cost (Thai Baht) 214,547 504,637

Evacuation time (Hours) 2.67 2.57

Table 3: Shelter location-allocation generated by individual

optimal solution.

Objective function Shelter location-allocation

Min f

S2: A1, A2, A3, A4, A5

Min f

S1: A4

S2: A2, A5

S4: A1, A3

If decision-makers seek to minimize the total cost,

there is only one shelter that services all affected

areas. If decision-makers prioritize minimizing

victim evacuation time, several shelters are required

to open in order to reduce the evacuation time

between the affected areas and assigned shelters. The

numerical experiment results shown in Table 2 and

Table 3 reveal the conﬂict in terms of cost, but the

total evacuation time does not vary much. However,

simultaneously considering both objective functions

to ﬁnd a compromising solution is a necessity in

determining shelter location-allocation, so further

steps are required.

Table 4: Total cost, average evacuation time, and shelter

location-allocation results.

Total Cost

(THB)

Evacuation

time (hours)

Shelter-Allocation

2.57 358,609 2.26

S2: A1, A2, A3, A4

S4: A5

2.58 358,688 2.29

S2: A2, A4, A5

S4: A1, A3

2.59 358,688 2.29

S2: A2, A4, A5

S4: A1, A3

2.60 361,281 2.47

S1: A4

S4: A1, A2, A3, A5

2.61 361,281 2.47

S1: A4

S4: A1, A2, A3, A5

2.62 361,281 2.47

S1: A4

S4: A1, A2, A3, A5

2.63 359,120 2.49

S2: A1, A2

S4: A3, A4, A5

2.64 359,189 2.55

S2: A3, A4, A5

S4: A1, A2

2.65 359,189 2.55

S2: A3, A4, A5

S4: A1, A2

2.66 361,550 2.59

S2: A1, A4

S4: A2, A3, A5

2.67 361,550 2.59

S2: A1, A4

S4: A2, A3, A5

Since there is no single optimal solution that can op-

timize the bi-objective concurrently, the f

is set to

minimize the total cost, while f

is augmented by the

20% allowance time for victims’ evacuation and al-

tered to act as an additional constraint (17). Hereafter,

refers to the values between 2.57 and 2.67 hours

that will be used to restrict f

. Thus, f

is solved with

10 sub-problems regarding the value of ε

= 2.57,

2.58, ..., 2.67 and bounded by constraints (3)-(10).

The Pareto optimal generates the highest and lowest

total cost of 358,609 and 361,550 Thai Baht, respec-

tively. The shortest average time for victim evacua-

tion is 2.26 hours and the highest is 2.59 hours. For

shelter location-allocation in each period of ε

, there

are only two shelters that are required to open to serve

the victims (Table 4). This reveals that, when the f

values are loosened and allowed to increase accord-

ing to ε

, the evacuation time and total cost increase

as well. However, relaxing the time restriction to the

highest acceptable value of 2.67 does not help to re-

duce the total cost (Figure 1).

Bi-objective Optimization Model for Determining Shelter Location-allocation in Humanitarian Relief Logistics

391

Figure 1: Pareto optimal generated by Epsilon Constraint method.

6 CONCLUSIONS

This study proposes the bi-objective optimiza-

tion model for determining the appropriate shelter

location-allocation in response to a natural disas-

ter. In this case, the proposed model aims at im-

proving the efﬁciency criterion through minimizing

the total cost—which combines the ﬁxed cost for

opening shelters, victim evacuation cost, and service

cost—while effectiveness is enhanced by minimizing

victim evacuation time—which is calculated based on

the number of available vehicles, speed, and capac-

ity of the vehicles. The Epsilon Constraint method is

selected to solve the bi-objective optimization prob-

lem since allocating a weight coefﬁcient to identify

the importance of monetary and non-monetary terms

is inappropriate for making comparisons in this ﬁeld.

The ﬁrst objective function—i.e. minimizing the to-

tal cost—is assigned as the primary objective func-

tion, whereas the second objective—i.e. minimizing

victim evacuation time—is altered to be an additional

constraint. Although the Epsilon Constraint method

is suitable for solving the problem in this study, this

method occasionally generates inefﬁcient solutions

caused by inappropriate deﬁnition of the value of the

hard constraint. To avoid generating inefﬁcient so-

lutions, the second objective function is augmented

with the positive constant value in which the addi-

tional allowance time is determined. Therein, the al-

lowance time is justiﬁed based on personal, delay, and

fatigue allowances. The application of the proposed

model is demonstrated through the real-world case

study of the 2011 ﬂood in Phun Phin district, Surat

Thani province, Thailand. The numerical experiment

results reveal that, when focused on individual solv-

ing the ﬁrst objective function, only one shelter is re-

quired to open since minimizing the total cost is the

target. On the other hand, when individual solving the

second objective function, the total cost is very high

due three shelters being required to open to minimize

the evacuation time. Hence, efforts are made to de-

termine both objective functions simultaneously. The

optimal solution obtained by solving the bi-objective

function generates the compromise solution in deter-

mining shelter location-allocation, which is that only

two shelters are required to open to serve the victims.

The results found by this study can assist decision-

makers to design appropriate measures for responding

to shelter location-allocation during ﬂooding events.

Future studies could incorporate disaster risk levels in

the proposed model as well as implement it on larger

and multiple case studies to demonstrate its broader

applicability.

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