Maximal Service Area Problem for Optimal Siting of Emergency Facilities

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Maximal service area problem for optimal siting of emergency facilitiesVini Indriasaria; Ahmad Rodzi Mahmudb; Noordin Ahmadc; Abdul Rashid M. Shariffd

a GIS and Geomatic Engineering, Universiti Putra Malaysia, Malaysia b Department of CivilEngineering, Universiti Putra Malaysia, Malaysia c Geomatics Engineering Unit, Universiti PutraMalaysia, Malaysia d Department of Biological and Agricultural Engineering, Universiti PutraMalaysia, Malaysia

Online publication date: 01 March 2010

To cite this Article Indriasari, Vini , Mahmud, Ahmad Rodzi , Ahmad, Noordin and Shariff, Abdul Rashid M.(2010)'Maximal service area problem for optimal siting of emergency facilities', International Journal of GeographicalInformation Science, 24: 2, 213 — 230To link to this Article: DOI: 10.1080/13658810802549162URL: http://dx.doi.org/10.1080/13658810802549162

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Research Article

Maximal service area problem for optimal siting of emergency facilities

VINI INDRIASARI{, AHMAD RODZI MAHMUD*{, NOORDIN AHMAD§

and ABDUL RASHID M. SHARIFF"

{GIS and Geomatic Engineering, Universiti Putra Malaysia, Malaysia

{Department of Civil Engineering, Universiti Putra Malaysia, Malaysia

§Geomatics Engineering Unit, Universiti Putra Malaysia, Malaysia

"Department of Biological and Agricultural Engineering, Universiti Putra Malaysia,

Malaysia

(Received 4 June 2008; in final form 1 October 2008 )

Geographic information systems (GIS) have been integrated to many applica-

tions in facility location problems today. However, there are still some GIS

capabilities yet to be explored thoroughly. This study utilizes the capability of

GIS to generate service areas as the travel time zones in a facility location model

called the maximal service area problem (MSAP). The model is addressed to

emergency facilities for which accessibility is an important requirement. The

objective of the MSAP is to maximize the total service area of a specified number

of facilities. In the MSAP, continuous space is deemed as the demand area, thus

the optimality was measured by how large the area could be served by a set of

facilities. Fire stations in South Jakarta, Indonesia, were chosen as a case study.

Three heuristics, genetic algorithm (GA), tabu search (TS) and simulated

annealing (SA), were applied to solve the optimization problem of the MSAP.

The final output of the study shows that the three heuristics managed to provide

better coverage than the existing coverage with the same number of fire stations

within the same travel time. GA reached 82.95% coverage in 50.60 min, TS did

83.20% in 3.73 min, and SA did 80.17% in 52.42 min, while the existing coverage

only reaches 73.82%.

Keywords: Facility location; Emergency facilities; Service area; Geographic

information systems; Network analysis

1. Introduction

Studies about facility location problems, also known as Location Science, have

appeared in the literature since the beginning of the 1970s (e.g. Church and ReVelle

1974, Toregas and ReVelle 1972, Toregas et al. 1971), and even earlier (e.g. Hogg

1968). Problems in facility location were usually denoted as optimization problems

in operations research (OR) framework which should be solved by certain

algorithms in order to optimize single or multiple objective functions. The objective

is either to minimize costs or to maximize benefits. The problems include locating

hospitals, schools, power plants, ambulances, fire stations, pipelines, conservation

areas and warehouses. Early facility location modeling could only work with small

dataset and involve simple functions to measure spatial interaction between facilities

*Corresponding author. Email: [email protected]

International Journal of Geographical Information Science

Vol. 24, No. 2, February 2010, 213–230

International Journal of Geographical Information ScienceISSN 1365-8816 print/ISSN 1362-3087 online # 2010 Taylor & Francis

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and demands. Currently, with the advent of geographic information systems (GIS)

and sophisticated computer technology, decision making in facility site selection can

be enhanced into a larger dataset with more complicated data structures, more

accurate spatial measurement, spatial analysis and spatial modeling. GIS capability

to represent spatial objects as points, line, or polygons has increased the flexibility of

entity representations in facility location modeling no longer limited to points as it

has been (Miller 1996). Furthermore, GIS capability to perform surface modeling

allows location science to extend its version into three-dimensional problems.

Several studies have integrated GIS into location modeling (e.g. Murray and

Tong 2007, Liu et al. 2006, Li and Yeh 2005, Aertz and Heuvelink 2002, Yeh and

Cow 1996). However, there are still some GIS capabilities yet to be explored

thoroughly, requiring further investigation into how they may be effectively

implemented to improve solutions for facility location problems. This study tries to

enhance the location selection process by utilizing the GIS capability to generate

service areas as travel time zones, within an emergency facility context. The objective

of this study is to establish service coverage modeling in a continuous demand

region, with road accessibility considerations. This study emerges from the fact that

most conventional models only define a facility’s service area simply as a circular-

shaped region based on a specified radius. Such a definition might be appropriate

for facilities which are not influenced by topographical barriers, like sirens or

telecommunication transmitters. But for particular facilities like fire stations,

ambulances and delivery services, accessibility is an important requirement.

Through a network analysis, GIS allows the service area to be calculated by taking

into account the road access, barriers and road network attributes. This advantage

from GIS should be incorporated in the service area calculation to obtain a more

realistic model.

1.1 Emergency facility location problem

Facility location modeling introduced in this paper is addressed to emergency

facilities. Not all location models are suitable to be adopted for emergency facilities.

In fact, certain models are only appropriate for certain types of facilities. To select

an appropriate model, we should understand the objective of the model and the

nature of facility services. For example, we have location models concerning

minimizing distance called the P-median problem (PMP) and P-center problem

(PCP). The PMP has the objective to minimize the total or average distance between

facilities and demands assigned to them, whereas the PCP has the objective to

minimize the farthest distance (Klose and Drexl 2005, Hamacher and Nickel 1998).

We also have other models concerning optimizing service coverage, such as the

location set covering problem (LSCP) and maximal covering location problem

(MCLP). In the LSCP, the optimum number of facilities is one aspect of the solution

to the problem, and the constraint requires for all demands must be covered by at

least one facility (Toregas and ReVelle 1972). In the MCLP, the number of facilities

is known a priori and the objective becomes to maximize services for demands

(Church and ReVelle 1974). Which model is suitable for emergency facilities?

Emergency facilities have a unique characteristic in the way they measure benefits.

Typically, the objective of facility location problem is either to minimize costs or

maximize benefits. In the case of emergency services, the objective is often stated as

the minimization of losses to the public (Aly and White 1978). This objective is

equivalent to the maximization of benefits. Typical illustrations of emergency

214 V. Indriasari et al.


facilities are ambulances, fire stations, police stations, warning sirens, health clinics,

hospitals, police patrol cars and civil defense stations. In the case of ambulance

services, sick or injured people are to be delivered to the hospital. Fire stations are to

be located in order to minimize losses resulting from fire, such as property loss, loss

of lives and psychological damages. In the case of police services, protections against

criminal actions are to be provided.

It is obvious that in any case, the response time or distance traveled is a crucial

parameter to measure the quality of emergency services (Toregas et al. 1971).

Longer response will result in more losses, indicating the poor service. Conversely,

quicker response will save more properties and lives from losses and damages.

Therefore, emergency facility location problems are typically modeled under time or

distance constraint. This nature of emergency services affects the types of models

that should be adopted for locating emergency facilities. For instance, it may make

more sense to a city fire department to locate fire stations so that a response is

possible to every property in less than 5 min, than to worry about minimizing the

average response time (Longley et al. 2005). Given this consideration, coverage

location problems such as the MCLP and LSCP are more appropriate than the PMP

which seeks to minimize the total/average distance. In fact, both the LSCP and

MCLP and their variants appear as dominant approaches applied to solve

emergency facility location problems. ReVelle and Snyder (1995), for example,

developed an extension of the MCLP for integrated fire and ambulance siting, and

Chrissis (1980) modified the LSCP into a dynamic model for locating fire stations.

1.2 The maximal covering location problem

This study is interested to further develop the MCLP for optimal siting of

emergency facilities by integrating GIS in the service coverage modeling. The MCLP

was first introduced by Church and ReVelle (1974). It seeks the maximum

population that can be served by a limited number of facilities within a stated

service distance or time. A mathematical formulation of this problem is stated as

follows:

MCLP: Maximize z~X

i [ I

wixi ð1Þ

subject to:P

j [Ni

yj§xi Vi [ I ð2Þ

Pj [ J

yj~p ð3Þ

xi [ 0, 1f g, yj [ 0, 1f g Vi [ I , Vj [ J ð4Þ

where:

i,I the index and set of demand nodes

j,J the index and set of potential facility sites

Ni {j g J|dij(S}5the set of all node j which is within S of node i

dij the shortest distance/time between node i and node j

S the desired service distance/time for every demand node i

wi the population to be served at node i

Maximal service area problem 215


p the number of facilities to be sited

xi~1 if demand node i is covered by one or more facilities

0 otherwise

�

yj~1 if a facility is sited at the node j

0 otherwise

�

2. The maximal service area problem

The location model developed in this study is called the maximal service area

problem (MSAP), as its objective is to maximize the total service area of a fixed

number of facilities. The MSAP is created as a modification of the MCLP which

makes use of the capability of GIS to generate service areas of facilities as travel time

zones. In general, the service area of a facility can be defined as: (1) the area that is

closer in distance, time or cost to that facility than to any other facility; or (2) the

area that can be reached from the facility within a specified distance, time or cost. It

may be generated in planar region or based on the network. In the MCLP, a

demand node is said to be covered when the closest facility to that node is at a

distance or time less than or equal to S. Conversely, a demand node is said to be

uncovered when the closest facility to that node is at a distance or time greater than

S. The value of S can be chosen differently for each demand node i. Ni is the set of

facility sites eligible to cover demand node i. We can term the area within radius of S

from a facility as the service area of that facility, and the shape of this service area is

circular. Distances between demand nodes and facilities are typically measured as

straight-line distances by calculating the difference of location coordinates between

the two entities with the well-known Pythagorean formula. Such calculation can be

done without GIS.

In GIS, it is possible to generate various types of service areas according to the

nature of facility services. Figure 1 depicts various ways to define the service area.

Circular coverage is appropriate to define services provided by a warning siren or

radar station (e.g. Murray and O’Kelly 2002), assuming that the topographical

variation is not an issue. Thiessen polygon, which is very useful for proximity

mapping, may be conveniently adopted to define the service area of schools, where

students are to be allocated to the nearest school from their homes; or warehouses,

where retail stores should be supplied by the nearest warehouse. In surface

modeling, the viewshed of an observer point can be defined as the service area of the

observer point. Viewshed identifies regions of visibility from one or more observer

points. It typically works with raster digital elevation model. Each cell in the output

raster receives a value that indicates how many observer points can be seen from

each location. All cells that cannot see the observer point are given a value of zero.

Viewshed can be applied for locating transmission towers and designing a forest fire

watch tower. The travel time zone, or in some texts referred to as travel time band, is

a polygon layer, overlaid on the network, indicating band of travel time. Since

emergency facilities are typically modeled under time or distance constraint, the

travel time zones are the most appropriate way to define their service areas. In the

travel time zones, service area polygons are generated based on the network through



a network analysis in a vector GIS environment. Network analysis in GIS takes into

account network attributes such as road width, speed limit, barriers, turn restriction

and one way restriction. Most GIS packages which support network analysis can

generate travel time zones. Some of these are TransCAD, ArcGIS Network Analyst,

GRASS with its v.net.alloc and v.nec.iso functions, SANET with its Voronoi

function and TNTMips Network Analysis with its allocation functionality.

Similar to the MCLP, the MSAP is designed as a discrete model where a specified

number of facility sites that achieve the best objective function value of the model

are selected out of a finite set of candidate sites. The entire region of the study area is

deemed as the demand region. Thus, the demand is continuous. In the MSAP, the

facility does not have capacity constraints which limit demand quantities it can

serve, or the capacity is not taken into consideration. As such, the model is

uncapacitated.

The objective of the MSAP is to reach the largest possible area of services from a

specified number of facilities. Totaling service area from multiple facilities cannot be

done simply by summing areas of service area polygons through the mathematical

addition operation, as the polygons are overlaid one on top of another (figure 2(a)).

Instead, all of the service area polygons must be dissolved into a single polygon first,

and then the area of the single polygon reflects the total service area of facilities

(figure 2(b)). The dissolving process and area calculation must be done in the GIS,

and surely will take a significant amount of time when run iteratively.

A method is introduced to overpass the dissolving process and area calculation in

the implementation of the mathematical modeling by using surrogate information.

Figure 1. Various ways to define service area: (a) circular coverage; (b) Thiessen polygons;(c) viewshed; (d) travel time zones.



First, the continuous space of the demand region is partitioned into pieces of

discrete objects (figure 3(a)). The number of demand objects intersecting with a set

of service area polygons is then used as the surrogate information to measure the

total service area (figure 3(b)). We could easily understand that the larger number of

demand objects falling within the service area polygons indicates the larger total

service area. The service area polygons need not be dissolved in this way, thus the

computation time can be significantly shortened. As our interest in the MSAP is the

area of services, in this way we only have information of the number of demand

objects covered by multiple facilities. This means we calculate the percentage of

coverage as a ratio of the number of demand objects covered to the number of total

demand objects in the study area. The value of this percentage may not be exactly

the same as the ratio of the area of demand region covered to the area of the whole

demand region, which is our interest. But in a fine resolution of demand objects, the

former percentage will be close to the latter, and hence is sufficient to measure the

solution quality of the problem.

Either regular points or polygons can be used for discretization, with various

arrangements supported by the software. However, when evaluating a service from a

facility to polygon-based demands, some work must be done to specify conditions in

which polygons are said to be covered, as some polygons may only be partially

covered. For instance, coverage will be provided if the closest point of the polygon

falls within the service area of a facility. The center point of a polygon and the

percentage of a polygon covered can also be used to define coverage (Murray et al.

2008). These steps are unnecessary when regular points are used, as there is no issue

of partial coverage in point representations. In our approach, we only consider the

Figure 2. Calculation of total service area from multiple facilities. (a) Service area polygonsfrom multiple facilities are overlaid one on top of another. (b) The service area polygons aredissolved into a single polygon; the area of the single polygon reflects the total service area.

Figure 3. Calculation of total service area from multiple facilities through discretization ofdemand region. (a) The planar space of demand region is represented by discrete objects. (b)The number of demand objects falling within the service area polygons of facilities is used assurrogate information to measure the total service area.



points inside or outside the polygon. Hence, to simplify the implementation of

mathematical modeling, regular points are used for discretization of demand region.

When point objects are used, the optimization problem of the MSAP becomes to

maximize the number of demand points falling within the service area polygons of a

set of facilities. The problem is then formulated as follows:

MSAP: Maximize z~X

i [ I

wixi ð5Þ

subject to:Pj [ J

aijyj§xi Vi [ I ð6Þ

Pj [ J

yj~p ð7Þ

xi [ 0, 1f g, yj [ 0, 1f g Vi [ I , Vj [ J ð8Þ

where:

aij~1 if demand object i falls within service area polygon of facility j

0 otherwise

�

Other notations have been defined previously.

In essence, this formula is the same as that of the MCLP, except for the constraint

in equation (6) where information of aij is obtained from the GIS. This is where the

integration of GIS distinguishes the MSAP from the original MCLP. To evaluate

the coverage of facilities over demand points, the GIS functionality is used to

examine whether the points fall within the service area polygons of facilities, and

these service area polygons are generated also by the GIS through a network

analysis as explained earlier. The weight wi in the MCLP represents the population

aggregated in the demand object. Since no data aggregation takes place in the

MSAP, this coefficient may be replaced by the risk level of the demand point. For

example, high-risk points have a higher weight than do low-risk points. For this

study, there is no distinction of risk levels among demand points. Thus, the value of

wi is set to 1 or simply ignored.

3. Solution algorithms

Coverage location problems, like MCLP and MSAP, are concerned with the

problem of selecting p facility sites out of n candidate sites that achieve the best

objective function value of the problem. In mathematics, such a problem is

considered as a combinatorial problem. The number of possible combinations is

calculated by the formula:

Cnp~

n!

p! n{pð Þ! ð9Þ

From that formula, we can see that the number of possible combinations C grows

exponentially as the number of facility sites p and the number of candidate sites n

increase. For a large dataset, it is impractical to investigate all possible combinations

(brute search) to find the best solution, as the run time needed is extremely

enormous. Even the most sophisticated computer cannot complete the search within



a reasonable time. Unfortunately, most facility location problems involve a large set

of demand nodes and candidate facility sites. Therefore, we need to solve these

problems using techniques other than brute search. Two classifications of solution

techniques are available for this purpose – exact algorithms and heuristics. While

exact algorithms guarantee the optimal solution, heuristics only provide a near

optimal solution, as the solution is not proved to be the best. The most popular

exact algorithms are branch and bound and cutting plane (Wang 2006). Instead of

exhaustively searching the entire solution space to find the best solution, exact

algorithms use an intelligent search by discarding feasible solutions that have been

proved not to provide the optimal solution without having to search all of them.

Techniques to prove these non optimal solutions vary amongst algorithms.

Although able to find the real optimal solution, Schietzelt and Densham (2003)

stated that exact algorithms have relatively restricted importance for facility location

problems. They have been successfully applied to reduce problem sizes within hybrid

approaches and as validation methods for solutions previously found by heuristics.

Generally, however, their scope is limited by the inferior performance. Solution

times tend to increase exponentially with problem size. Therefore, developing more

efficient heuristics remains a great challenge. Church and Sorensen (1996) have

established criteria for selecting and developing appropriate heuristic to solve

facility location problems. These criteria involve the robustness of heuristic process,

ease of understanding, speed or efficiency of technique and ease of development and

integration. Among heuristics that have been applied in facility location problems

are tabu search (Jaeggi et al. 2008, Sun 2006), simulated annealing (Murray and

Church 2004, Aerts and Heuvelink 2002, D’Amico 2002), genetic algorithm (Li and

Yeh 2005, Jaramillo et al. 2002) and ant colony algorithm (Chan and Kumar 2008,

Liu et al. 2006, Zecchin et al. 2006). For this paper, genetic algorithm (GA) was

employed to solve the MSAP. Other heuristics, tabu search (TS) and simulated

annealing (SA), were also tested for comparison. Assuming that the reader is

familiar with these heuristics, we will not be discussing their theoretical descriptions

within this paper, and will directly address our problem.

3.1 Genetic algorithms

Search techniques in GA are based on the mechanism of natural selection and

natural genetics. Our GA is designed as follows:

1. Encoding: Each solution is encoded by a bit string as the chromosome

structure (figure 4). Each bit represents a candidate site, thus the length of bits

equal to the number of candidate sites. A bit value of 1 means that the facility

is located at the corresponding site; a bit value of 0 means otherwise. Since the

number of facilities to be sited p is a fixed variable in the MSAP, there are

Figure 4. Genetic representation of solution for the MSAP.



always p bits which have the value of 1 in any chromosome. We refer thesebits as 1-value bits.

2. Population size: Practically, a population size around 100 individuals is quite

common (Sivanandam and Deepa, 2007). But in our GA, the fitness values of

all individuals are not too much diverse. Hence, 50 individuals will suffice to

explore the whole search space, as a larger population size might not provide

significant improvement to the solution yielded. Moreover, by using a smaller

population size, we gain the advantage of faster processing time.

3. Fitness function: The fitness function value of each chromosome is identical tothe objective function of the MSAP. That is, the number of demand points

covered by each individual.

4. Parent selection: We prefer that better individuals will be selected as the

parents for reproduction more often than the worse ones. Actually, the

roulette wheel and stochastic universal sampling techniques could meet this

purpose. However, as the interval of fitness function values of the solutions is

relatively small, those techniques become less significant because each solution

will have a nearly equal chance to be picked. Thus we use the tournamentselection instead.

5. Reproduction: Reproductions are typically performed by crossover and

mutation. But in our case, the number of 1-value bits in the individual

chromosome must be maintained. Due to this constraint, any crossover

operator can not be applied as it might violate the constraint. Therefore,

chromosomes of offspring are copied directly from chromosomes of parents,

and then the bits in the chromosomes are shuffled by mutation. The mutation

is performed by relocating one or more facilities to other free sites. Eachrelocation will swap one bit from 0 to 1 and another bit from 1 to 0. An

integer number between 1 and p/2 is randomly generated to determine how

many facilities will be relocated in each mutation.

6. Replacement: At each time step, offspring as many as the population size are

created in the reproduction process. These offspring replace less fit individuals

in the existing population to form a new generation. In this way, the best

solutions will survive on the population and the average fitness value of the

population improves over generations.7. Convergence criteria: The search is terminated by two stopping conditions –

maximum generations and stall generations. The algorithm stops either when

50 generations have evolved or if there is no improvement in the objective

function for five consecutive generations.

3.2 Tabu search

TS is aimed to overcome the problem of a local search procedure becoming trapped

at a local optimum by permitting non-improving moves whenever a local optimum

is encountered. It achieves this by recording the recent history of searches in a tabu

list and ensuring that future moves do not search this part of the search space, at

least not for a specified number of iterations (de Smith et al. 2007). Our TS is

designed with single tabu list (short-term memory) and single aspiration criteria. The

details are as follows:

1. Move: The move from one solution to the next solution is performed by

dropping and adding sites that yield the best coverage change. The best



change does not necessarily an increase of coverage. When a local optimum is

encountered, any future move will only cause a decrease of coverage. At thissituation, the best change is the one that causes the smallest decrease.

2. Short-term memory: Short-term memory is a tabu list containing a series ofrecently dropped sites. The tabu restriction prevents these sites from being

added back to a solution for a specified number of iterations. We permit only

10 sites to be tabu at any given time. As a result, each dropped site remains

tabu for 10 iterations and then is removed from tabu list, releasing it from its

tabu status. There are 63 candidate sites in the solution space, and only 17 of

them are picked at each solution. With 10 sites retained in the tabu list, 36 free

sites are left admissible to be added. This number is considered sufficient for

diversification.

3. Aspiration criteria: The aspiration criterion to override the tabu status that

allows the move to add a site in the tabu list will be satisfied only when theresulting coverage is larger than the best coverage achieved in the current

search cycle.

4. Stopping rule: The search terminates when a maximum number of moves is

reached.

3.3 Simulated annealing

In our SA, each solution consists of a set of sites representing open facilities. At each

iteration, the current set is perturbed by randomly replacing several sites with other

free sites. Energy level C is defined as the coverage achieved by each solution. Thenew set will replace the current set if C(i + 1) is higher than C(i), where C(i + 1) is the

coverage of the new set and C(i) is the coverage of the current set. If C(i + 1) is lower

than C(i), the acceptance of replacement is subject to the following condition:

expC iz1ð Þ{C ið Þ

T ið Þ

� �wR ð10Þ

R is a random number uniformly distributed in the range [0,1]. T is a temperature

gradually cooled over time by a factor a as shown in formula (11), where 0,a,1.We use a50.9 in our SA. For initiation, T is set in such a way that the probability of

non-improving replacements being accepted is about 90%.

T sz1ð Þ~a�T sð Þ ð11Þ

To avoid too lengthy iterations within each temperature stage, T is controlled by

two parameters. It will decrease either when 100 solutions have been evaluated or

when the energy level has reached a constant value. The algorithm will terminate

when the system has been frozen. The freezing temperature at which the system isdeemed frozen is stipulated such that only about 1% of non-improving replacements

will be accepted.

4. Application

4.1 Study area and data

Fire stations in South Jakarta, Indonesia, are chosen to evaluate the effectiveness of

the MSAP. The road network dataset for performing the network analysis was

specially prepared. The ArcGIS 9.2 package was utilized to build the road network



dataset. In ArcGIS, the road network connectivity is established either at endpoint

or at any vertex of the line object representing the road (figure 5). For this study, the

former connectivity rule was selected. Thus, the road data must be prepared so that

endpoints are present at all intended junctions. In certain cases where the

connectivity does not exist in the junction, such as in flyovers or underpasses, the

line must go through the junction so that the connectivity will not be established at

the junction.

There are five classes of roads in South Jakarta (table 1) which are classified by

similarities in physical characteristics and traffic condition. This classification is

used to stipulate the road hierarchies. The speed for each class is the average speed

between day and night estimated roughly through a driving test for a whole week.

The higher hierarchy road has the higher speed. The tollroad is excluded when

building the road network dataset, as fire vehicles do not typically use the toll road

as their routes due to limited entrances, unless the fire incident occurs along it.

Attributes of road data contain a Meters field representing the road segment length,

and a Minutes field representing the travel time to traverse the road segment. From

Meters and Speed fields, values of the Minutes field can be calculated. The Minutes

field is then used as the network impedance in the network analysis.

There are 63 candidate sites available in the study area, consist of 46 proposed

sites and 17 sites of existing fire stations. The proposed sites were obtained through

the site suitability evaluation performed as a multi-criteria decision making

(MCDM) problem in a raster GIS environment. A series of suitability criteria,

such as proximity to high-hierarchy road, distance to existing fire stations, ability to

cover fire risk zones and proximity to water sources were evaluated to determine

suitable sites for locating new fire stations. The number of existing fire stations is

used as the number of facilities to be sited in the MSAP (p), so that the output can be

Figure 5. Network connectivity rules in ArcGIS. (a) At endpoint; Junctions j1, j2, j3 and j4are only created at endpoints of lines L1 and L2. No connectivity established at the sharedvertex of crossing lines L1 and L2. (b) At any vertex; A junction j5 is created at the sharedvertex of lines L1 and L2. The connectivity is established at the junction, and the two lines aresplit into four edges by the junction.

Table 1. Road network classification.

Class Hierarchy Speed (km/h)

Tollroad 1 75Trunkroad 2 55Thoroughfare 3 45Main road 4 35Local street 5 25



compared with the existing condition. Thus, we are going to select 17 fire station

sites out of 63 candidate sites in such a way that the total service area is maximal.

4.2 Service area computation

Service area polygons of fire stations are generated using the new service area

function in ArcGIS Network Analyst extension. There are two types of network

nodes in this function – facilities and barriers. Candidate sites of fire stations shown

in figure 6 are loaded as facilities in the service area computation. The service area is

defined as travel time zones away from facilities. Some necessary parameters must

be set first, such as in which band the travel time zones will be generated, how the

polygon should be constructed, and what restrictions should be applied. In this case,

the zones are generated within 4 min travel time, slightly faster than the standard

5 min travel time used in the country. For the one-way restriction, according to the

local regulation, on duty fire vehicles and ambulances are allowed to traverse

Figure 6. Candidate facility sites.



a one-way road in the opposite direction and exempted from turn restrictions.

Therefore one-way restriction is unnecessary to be applied (unchecked).

The facilities are not located exactly on the network. In a network analysis, a

facility must be linked to the nearest point on the network edge to become a network

node, before its service area can be generated. Hence, we use the search tolerance

parameter to determine the radius within which the facilities will be linked to the

network edge. If with 100 m search tolerance some facilities are not linked because

they have no network within the distance, this value needs to be increased until all

facilities are linked. Parameter settings for the service area computation are shown

in table 2.

Some information must be prepared prior to the optimal site search process. These

include the discretization of demand entity from planar space into regular points to

implement the formulated mathematical model. For this study, the spacing of demand

points was set to 200 m which results in a total 3614 demand points. To obtain

information of aij required in the mathematical model, the ‘Spatial Join’ function in

ArcGIS was utilized. This function analyzed whether the demand points fall within

the service area polygons of facilities. One demand point might fall within many

service area polygons. Likewise, one service area polygon might contain many

demand points. If the row of a pair of demand point i – facility j exists, the value of aij

in equation (6) will equal to 1, indicating that demand point i is covered by facility j.

4.3 Results

The location modeling was loosely-coupled with the GIS. That is, all the necessary

data were exported from the GIS into an external database. Following this, the

heuristics were run outside GIS using this database, and finally, the outputs were

sent back to GIS for visualization and area calculation. All heuristics were coded in

Perl programming language and executed on a computer environment with Intel

Core 2 Duo 1.73 GHz processor and 2 GB RAM. Since GA and SA are stochastic

procedures, they were run multiple times to study their robustness in producing

Table 2. Parameter settings for service area computation.

Parameters Value

Network LocationsLocation type FacilitiesSearch tolerance 100 mSnap to Closest

Analysis settingsImpedance MinutesDefault breaks 4Direction Away From FacilitiesAllow U-turns EverywhereIgnore invalid locations checkedOneway restriction unchecked

Polygon GenerationPolygon type DetailedTrim polygons 100 mMultiple facilities options OverlappingOverlap type Disks



good solutions. In this case, each of them was run five times. Results of five tests

using these two heuristics are shown in table 3. It is seen that on average, GA wasbetter in term of solution quality, but SA was slightly faster in terms of computation

time. The average of coverage achieved by GA is 2997.8 while the average of

coverage achieved by SA is 2729.8. The average of time consumed by GA is

51.17 min. In all tests, the algorithm terminated after completing the maximum 50

generations. The average of time consumed by SA is 47.49 min, with numbers of

iterations elapsed varying amongst tests.

Of three heuristics applied, TS appears to be the best both in term of solution

quality and computation time. By implementing only short-term memory process,TS managed to complete 50 iterations in 3.72 min and yielded 3010 coverage.

Comparison of performance between GA, TS and SA is shown in figure 7. The

coverage and time of GA and SA are taken from their best solutions of all tests

conducted, i.e. Test 1 for GA and Test 5 for SA. The graph depicts the coverage

achieved by each heuristic over time.

The objective function of the MSAP in equation (5), z, is defined as the number of

demand points falling within the service area polygons of a set of facilities. Since the

Table 3. Comparison of performance between GA and SA in five tests.

Test

GA SA

Coverage Time (min) Coverage Time (min)

1 3001 50.60 2733 50.782 2990 50.87 2639 44.023 3001 50.72 2709 46.584 2998 52.38 2673 43.655 2999 51.28 2895 52.42Average 2997.8 51.17 2729.8 47.49

Figure 7. Comparison of performance between GA, TS and SA.



value of z only acts as the surrogate information to measure the total service area,

we need to calculate the actual area of demand region covered to verify how close

the z value reflects the total service area. The area calculation was done in the GIS

and the result is shown in table 4. For this calculation, service area polygons of the

facilities were dissolved into a single polygon, and then clipped by the study area

polygon to remove parts of the polygon lying outside the study area. As was

expected, for facility sets obtained by all heuristics, percentages based on the area of

demand region covered A are slightly different from (mostly lower than) percentages

based on z value. This also occurs to the existing coverage. Yet their differences d are

very small, around 0.1%. This is due to relatively fine resolution of points used for

discretization of demand region.

Maps of coverage area from all heuristics are shown in figure 8. It can be seen that

the sets of facility sites gained by GA and TS are nearly the same. There are only two

differences – sites 15 and 51 in GA set do not exist in TS set, and are replaced by

sites 3 and 45. SA set differs enough from the others. It only has six sites in common,

i.e. sites 9, 17, 27, 32, 44 and 61. This is no wonder as the coverage of GA and TS is

quite close, while coverage of SA is a bit far below them. All heuristics managed to

provide better coverage than the existing coverage. Based on A values, GA provided

an increase of 9.26%, TS did 9.51% and SA did 6.48%. In GA and TS coverage, Site

23 and 24 appear to provide a significant increase of coverage in the southern part of

the study area.

5. Conclusions

Through the use of GIS, this study has been able to extend the conventional facility

location models that employed concentric circle analysis to a more complex and

realistic model – the MSAP. By taking advantage of GIS capability to calculate the

service area as the travel time zones, the model takes into account the road

accessibility in the selection of facility locations. GIS simulates the real road

network of the area being analyzed. Hence the solution gained by using GIS is more

accurate than otherwise.

The objective of the MSAP is to achieve a maximal total service area from a

specified number of facilities. Calculation of total service areas from multiple

facilities cannot be done merely by creating simple summary of service area

polygons, as the polygons are overlaid one on top another. This study has managed

to solve this issue by dividing the planar space of demand region into discrete

regular points. The use of regular points as the surrogate information to measure the

total service area was introduced as an alternative method of calculation. The

method was found to be helpful to ease the implementation of mathematical

modeling of the MSAP. Using points for discretization instead of polygons also

Table 4. Comparison of coverage between existing and three heuristics based on the numberof demand points covered (z) and area of demand region covereda.

Facility set z A (km2) d (%)

Existing 2668 (73.82%) 106.41 (73.69%) 0.13GA 3001 (83.04%) 119.78 (82.95%) 0.09TS 3010 (83.29%) 120.15 (83.20%) 0.09SA 2895 (80.11%) 115.76 (80.17%) 20.06

aTotal number of demand points53614; total area of demand region5144.40 km2



obviates the issue of partial coverage. In a fine resolution of demand points, thepercentage of total service area based on the number of demand points covered is

very close to the percentage based on the area of demand region covered. Hence, the

Figure 8. Coverage area of existing fire stations and three heuristics: (a) existing coverage;(b) coverage by GA; (c) coverage by TS; (d) coverage by SA.



aforementioned method of calculation may be conveniently applied to measure the

solution quality of the problem.

Fire stations in South Jakarta, Indonesia, were chosen to implement the MSAP.

Three heuristics, GA, TS and SA, have been applied to solve the optimization

problem of the MSAP. Of three heuristics applied, TS was the most superior both in

term of solution quality and computation time. It reached 83.20% coverage in

3.73 min only. GA and SA were comparable in computation time, but GA was

better in solution quality. The best solution of GA reached 82.95% coverage in

50.60 min, and the best solution of SA reached 80.17% coverage in 52.42 min. Hence

all three heuristics managed to provide better coverage than the existing coverage

which only reaches 73.82%, with 17 fire stations within 4 min travel time.

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230 Maximal service area problem


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Maximal Service Area Problem for Optimal Siting of Emergency Facilities