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**The optimal location of**

**airport fire stations: a**

**fuzzy multi**

**‐objective**

**programming and revised**

**genetic algorithm approach**

Gwo‐Hshiung Tzeng a_{ & Yuh‐Wen Chen }b
a

Energy and Environmental Research Group , Institute of Traffic and Transportation, College of Management, National Chiao Tung University , 4F‐114, Sec. 1, Chung Hsiao W. Rd., Taipei 100, Taiwan, ROC Phone: 886(2)23120519 Fax: 886(2)23120519 E-mail:

b

Energy and Environmental Research Group , Institute of Traffic and Transportation, College of Management, National Chiao Tung University , 4F‐114, Sec. 1, Chung Hsiao W. Rd., Taipei 100, Taiwan, ROC

Published online: 26 Apr 2007.

**To cite this article: Gwo‐Hshiung Tzeng & Yuh‐Wen Chen (1999) The optimal**
location of airport fire stations: a fuzzy multi‐objective programming and revised
genetic algorithm approach, Transportation Planning and Technology, 23:1, 37-55,
DOI: 10.1080/03081069908717638

**To link to this article: **http://dx.doi.org/10.1080/03081069908717638

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### THE OPTIMAL LOCATION OF AIRPORT

### FIRE STATIONS: A FUZZY

### MULTI-OBJECTIVE PROGRAMMING

### AND REVISED GENETIC

### ALGORITHM APPROACH

GWO-HSHIUNG TZENG* and YUH-WEN CHEN

*Energy and Environmental Research Group, Institute of*
*Traffic and Transportation, College of Management,*

*National Chiao Tung University, 4F-114, Sec. 1,*
*Chung Hsiao W. Rd., Taipei 100, Taiwan, ROC*

*(Received 14 September 1998; Revised 17 February 1999; In final form 31 May 1999)*

As the global aviation business expands rapidly, issues of aviation safety become corre-spondingly important. In turn, aviation safety should be more emphasized. The crashes of China Airlines planes at Nagoya (Japan) international airport in 1994, and near Taipei's international airport in 1998, caused airport authorities around the world to pay closer attention to rescue and fire-protection plans at their airports. Our research reveals that the location and number of fire stations at an international airport is an important factor in its fire protection capability. However, if the sites of the fire stations are not appropriately planned and located, fire engines and crews cannot arrive at the accident area in a timely manner. Similarly, if the number of fire stations at an airport is not sufficient, fires caused by aircraft accidents may take longer to be extinguished, resulting in more injuries and fatalities. Therefore, a location model based on a fuzzy multi-objective approach is pro-posed in this paper. This model can help in determining the optimal number and sites of fire stations at an international airport, and can also assist the relevant authorities in drawing up optimal locations for fire stations. Finally, because of the combinatorial com-plexity of our model, a genetic algorithm (GA) is employed and compared with the enu-meration method. The study results show that our revised GA is comparatively effective in resolution and that our model can be applied to the optimal location of other emergency facilities.

*Keywords: Fuzzy; Multi-objective; Aircraft accidents; Airport; Fire station;*

Location; Combinatorial optimization; Genetic algorithm

* Corresponding author. Tel./Fax: 886(2)23120519. Fax: 886(2)23120082. E-mail: ghtzeng@cc.nctu.edu.tw.

**37**

**1. INTRODUCTION**

In many countries, the number of aircraft taking off and landing has increased proportionally to their gross domestic product (GDP). For example, the traffic at Taipei's international airport in Taiwan has increased greatly since 1988, and in 1998 exceeded 80,000 aircraft movements. Thus, in the event of an accident, if an airport authority's response is not instantaneous, injuries and deaths may be greatly increased. Emergency action includes mainly the fire protection and rescue plans, both of which are executed in a timely manner by fire-fighters based at fire stations at an airport. Thus, the relevant authori-ties have the duty not only to provide adequate resources for fire fighting and rescue but also must have the capacity to direct these resources instantaneously to the accident area.

To assist the relevant authorities in such a timely fire protection and rescue response, the well-considered location of fire stations at an airport is needed. An appropriate fire station location can bring the following benefits: (a) it can shorten the distance between fire stations and the high-risk areas so as to improve reaction time efficiency; (b) fire stations can be located by considering the interaction between all fire stations -this can minimize overlap of fire station services, so as to utilize effici-ently fire station resources; and (c) it can help determine the reasonable number of fire stations at an airport by considering an economical trade-off between accident-loss cost and total setup cost of fire stations. Using the above criteria, this study constructs a location model to pro-mote the reaction efficiency of fire stations.

Previous research has included determining ambulance-hospital
*locations (Berlin et al., 1976), locating facilities by fuzzy multi-criteria*
*(Bhattacharya et al., 1992), achieving maximal covering for locations*
*(Church et al., 1991), analyzing the trade-off between cost and *
*acces-sibility (Current et al., 1987), studying the US essential air service *
pro-gram (Flynn and Ratick, 1988), locating new facilities in a competitive
environment (Hakimi, 1983), expanding facilities with multiple fuzzy
goals (Hannan, 1981), finding the location for emergency facilities
(Toregas, 1971), locating the treatment sites of hazardous wastes
using multi-criteria methods (Giannikos, 1998), and discussing
effi-ciency in a constrained continuous location problem (Ndiaye and
Michelot, 1998). On the basis of this review, the location model of fire

stations proposed in this study is implemented using a fuzzy
multi-objective approach in which we simultaneously integrate the optimal
number and sites of fire stations at Taipei's international airport. To
solve our model with combinatorial complexity, a genetic algorithm
(GA) is also used because it has proved to be suitable for solving
*combinatorial optimization problems (Sakawa, 1993; Sakawa et ah,*
1997), and is effective for solving a large-scale location problem of the
type considered here (Goldberg, 1989; Michalewicz, 1996). Our GA is
similar in spirit to that of Sakawa's work (1997), but is revised to fit our
location model.

This paper is organized as follows: the introduction has briefly pre-sented the problem background, the study's purpose, a review of the relevant literature and selection of methods for solving our location model. In Section 2, the International Civil Aviation Organization (ICAO) standards of fire protection are discussed. In Section 3, the mathematical model is constructed and a revised GA is proposed. In Section 4, our revised GA is employed and Taipei's international air-port is used to illustrate the practicability and efficiency of our model. A comparison of resolution efficiencies between the enumeration method and our revised GA is also performed. Finally, some conclu-sions are presented in Section 5.

**2. FIRE-PROTECTION STANDARDS SUGGESTED BY ICAO**

Today's wide-bodied jets carry hundreds of passengers on each flight. If such an aircraft crashes at or near an airport, inappropriate or inade-quate strategies in fire fighting and rescue could have disastrous con-sequences. Since fire station staff at airports are responsible for putting out fires and rescuing lives, a well-performed fire-protection strategy and well-considered location of fire stations can significantly help the relevant authorities improve this reaction efficiency. First, a well-performed fire-protection strategy has to be implemented based on the standards suggested by ICAO. The ICAO concept classifies airports into specified levels according to the number of aircraft movements. Each level, in turn, corresponds to a level of necessary fire-protection resources (e.g., number of fire engines, amount of fire extinguishers, etc.).

Briefly, the ICAO standards are as follows:
*(a) Categories of fire protection*

The categories are classified into 10 levels, depending on the number of aircraft movements, and the length and width of the aircraft body -these categories are shown in Table I.

It is obvious that a larger aircraft will be categorized at a higher fire-protection level. This also implies that we need more fire-fire-protection resources for rescuing passengers in a larger aircraft body.

*(b) Extinguishers to be equipped*

Table II gives the minimum number of extinguishers needed in an air-port at each fire-protection level (from 1 to 10). Level A contains the strictest standard for fire-protection levels.

TABLE I Airport category of fire-protection ability

*Airport*
*catGQorv*
l
2
3
4
5
6
7
8
9
10

*Airport category Length of aircraft (m) 1*

1
2
3
4
5
6
7
8
9
10
Source: ][CAO, 1995.
0-9
9-12
12-18
18-24
24-28
28-39
39-49
49-61
61-76
76-90
*Width of aircraft (m)*
2
2
3
4
4
5
5
7
7
8

TABLE II Airport category of necessary extinguishers

*Water*
(1)
350
1000
1800
3 600
8100
11800
18200
27300
36400
48200
*A level*
*Discharging*
*rate*
(1/min)
350
800
1300
2600
4500
6 000
7900
10800
13 500
16600
*B level*
*Water Discharging*
(1)
230
670
1200
2400
5400
7900
12100
18200
24 300
32 300
*rate*
(1/min)
230
550
900
1800
3000
4000
5300
7200
9000
11200
*Complementary*
*Chemical*
*powder*
(kg)
45
90
135
135
180
225
225
450
450
450
*Halons*
(kg)
45
90
135
135
180
225
225
450
450
450
*agents*
*Carbon*
*dioxide*
(kg)
90
180
270
270
360
450
450
900
900
900
Source: ICAO, 1995.

*(c) Reaction time*

The acceptable reaction time for any aircraft accident should be no longer than 3 min. This reaction time is the time necessary for 50% of available fire engines to arrive at the accident area and implement fire fighting and rescue plans.

According to our survey, the current reaction time at Taipei's inter-national airport (see Fig. 5) meets these criteria.

*(d) Fire stations*

The number of fire stations should be adequately established. Further-more, the siting of fire stations should allow fire engines access to the accident area in minimum time.

To sum up, the ICAO standards provide guidelines for promoting the reaction efficiency of fire fighting and rescue plans but ICAO do not instruct the relevant authorities how to decide on the optimal number and siting of fire stations at an airport. Thus, the problem we try to solve in this study is to find the optimal number and sites of fire stations at an airport so as to meet ICAO standards. This problem will be formulated mathematically in next section.

**3. MODEL CONSTRUCTION AND RESOLUTION**

To integrate the optimal number and sites of fire stations, many objec-tives need to be considered. The concept and formulation of our loca-tion model is illustrated as follows:

**3.1. Model Construction**

A location model is established for optimizing the number and sites of fire stations. Decision variables for this model are of the binary (0-1) type - a fire station will be set up at the corresponding coordinate if this variable equals 1. Objectives and constraints of our model are as follows:

*(a) Minimizing the total setup cost of fire stations and total loss cost*
*of an accident*

An insufficient number of fire stations will lead to inefficient reaction times — the loss caused by reacting inefficiently is defined as the total

loss cost (TLC) in this study. If no fire station is set up at an airport, the total loss cost will be equal to TLC; on the contrary, the TLC can be reduced when more fire stations are set up. Meanwhile, too many fire stations will result in wasting fire-protection resources. Therefore, there will be an optimal number of fire stations after the trade-off between total setup cost (TSC) of fire stations and total loss cost (TLC), weighted by some negative exponential form. The conceptual cost resulting from the TSC of fire station plus the weighted TLC should be minimized. This formulation is expressed in Eq. (1).

Min/i = x SC + TLC x e (i)

*where Sy. the decision variable, if a fire station is set up on a x-y*
*coordinate (i,j), then S,y= 1, otherwise, S,*y*=0; and ^2l52jSy> ^* S C :

the setup cost for a single fire station; TLC: the total loss cost. More-over, although Eq. (1) is subjectively established by assumption, Eq. (1) is theoretically reasonable because /i has a U-shaped curve - this represents a trade-off between the TSC and weighted TLC. A simple example in Fig. 1 indicates that the optimal number of fire stations is two when TLC = 7 and SC = 1.

*(b) Minimizing the longest distance from the fire station to any point at*
*the airport*

This objective is designed to increase the accessibility from any fire station to any point at or near the airport. This objective is shown

Cost _{5}
4
3
2
1
0
*7SC+Weighted TLC*
*TSC*
*Weighted TLC*
1 2 3 4
Number of Firestations

FIGURE 1 The trade-off between TSC and Weighted TLC.

in Eq. (2).

### Min/

2*= Yl JMax|x-i| + b'-y|} (2)*

*where Sy: the decision variable, if a fire station is set up on a x-y*
*coordinate (ij), then Sy = 1, otherwise, Sy = 0; x, y: if Sy = 1, then x = i*
*and y =j.*

*(c) Minimizing the longest distance from any fire station to the*
*high-risk area*

The distance from any fire station to the high-risk area should be mini-mized in order to increase reaction efficiency. This objective function is shown in Eq. (3).

M i n /3*= Max JT^nj x {\x - i\ + \y-j\} (3)*

*where Sy. the decision variable, if a fire station is set up on a x-y *
*coor-dinate (i,j), then Sy = 1, otherwise, Sy = 0;x,y:if Sy = 1, then x = i and*
*y=j. ry. the risk rank for x-y coordinate (i,j). The risk rank r,y is*
computed based on accident statistics for different areas at or near an
airport - in this case, Taipei's international airport (this will be
dis-cussed in detail in Section 4).

In addition to the aforementioned three objectives, the first constraint
*in our model applies to the summation of Sy being greater than or equal*
to 1. This implies that we should set up at least one fire station at the
airport. This is shown in Eq. (4).

*where Sy. the decision variable, if a fire station is set up on a x-y*
*coordinate (/,/), then Sy= 1, otherwise, Sy = 0. Secondly, from a *
*theo-retical point of view, there should be a reasonable distance (drab) between*

*any two fire stations; e.g., fire station a and fire station b. This distance*
*should not only be not too long (dlah) for fire stations to support each*

*other but also should not be so short (d*b) as to cause overlapping of*

*fire station services. Expressions drah, dlah and dsab* are utilized to construct

**E E ^**

**1**

** w**

Achievement Level

Distance between any

FIGURE 2 The achievement level of distance constraint between any two fire stations.

*fuzzy constraints. The membership function n<](dab) of distance between*

any two fire stations is shown in Eq. (5) and Fig. 2.

*\, \{dah=drab,*
*( 4 , - dah)l{d[h - drab), if d'ah > dab*
*(dah - dsab)/{drah - d*a*
0,
*dab,*
*if dsab < dab*
otherwise.
(5)

*Let {Sjj} denote the set of Sy — 1, let also a and b be any two different*
elements taken from {Sy}, then the aforementioned constraint is shown
in Eq. (6).

*\xa ~ xb\ + \ya - yb\ « d'ab* (6)

*where xa: the / value of element a taken from {5,y}; xh: the i value of*

*element b taken from {Sy}; ya: they value of element a taken from {%};*

*yb: they" value of element b taken from {Sy}; «: the symbol of fuzzy*

*equality. Furthermore, the / and j values are expressed in x—y *
coordi-nate form. This presentation coincides with the grid map for rescuing
people at an airport. In the next section, Taipei international airport is
taken to represent a numerical example, which shows the establishment
and working of our model.

**3.2. Fuzzy Multi-objective Optimization Model**

A fuzzy multi-objective approach is employed for the following reasons. First, the model should be simultaneously optimized for the number and siting of fire stations at an airport. Thus, techniques for optimizing only

one single objective are not suitable for such a problem (Cohon, 1976;
Fendel and Spronk, 1983; Yu, 1985; Zeleny, 1982). Second, the fuzzy
multi-objective approach is quite simple when compared with
tradi-tional weighting methods for multi-objective optimization (Bellman
*and Zadeh, 1970; Fedrizzi et al., 1991; Lai and Hwang, 1994; Sakawa,*
*1993; Sakawa et al., 1997). Finally, the fuzzy multi-objective approach is*
more efficient when compared with traditional methods related to
util-ity functions in multi-objective optimization (Chen and Hwang, 1992;
Sakawa, 1993).

The basic concept of fuzzy multi-objective optimization is to find the
maximal achievement level among constraints of conflicting objectives
(Sakawa, 1993). Using Eqs. (l)-(3) as an example, and assuming that
*the optimistic value of the &th objective (k = 1,2,3) is f^ while the*
pessimistic value is/^r, the achievement level can then be expressed as
in Fig. 3 (Hannan, 1981).

*Where Hk(fk) represents the fuzzy membership function of fk, it*

*also reveals the achievement level otfk. By using the A transformation*

*(Sakawa, 1993; Sakawa et al., 1997), and A = Min A, Eqs. (l)-(6) can be*
rewritten as in Eq. (7).
Maximise A
subject to
*fk ~fk*
A < *k= 1,2,3* **(7)**
and Eqs. (4)-(6).

To solve the model in Eq. (7), a two-step optimization approach can
reduce the resolution complexity. The first step is to compute the
*optimal number of fire stations in the first objective (k= 1); the second*

*Mk(fk) t*
**1.0**

**0**

** r r f**

**r r f**

*Jk Jk Jk*

*FIGURE 3 The achievement level for fuzzy objectives (k = 1,2,3).*

step is to optimize Eq. (7) with the optimal number of fire stations from the first step. (In Section 4.2, our revised GA and enumeration method are both applied and compared for their resolution efficiency).

**3.3. Model Resolution by Revised GA**

To solve the mathematical model in Eq. (7), a two-step approach is
necessary. The first step is to decide the optimal number of fire stations
at the airport; the second step then uses the results from the first step
to maximize the global A under other constraints. For this study, a GA
is also developed for the following reasons: (a) the concept of GA is
comparatively easy to follow by those who lack a strong background
in mathematics; (b) the GA is fully transferable - the other problems
which are similar to our study can apply almost the same, steps for
resolution; and (c) our model is an NP-hard problem, and the GA has
been proved to be effective in solving such combinatorial optimization
*problems (Sakawa et ai, 1997). The traditional and basic notion of gene*
type in GA, e.g., 0010 (Goldberg, 1989), is also applied to form our gene
population. But considering the characteristics of our model, we omit
the crossover in GA to prevent infeasible solutions and promote
self-evolution efficiency - this revised approach is also called the simple GA
(SGA). Thus, gene type, reproduction, mutation and performance
evaluation are re-defined as follows:

*(a) Gene type*

From Fig. 4, we observe that the range of the x-axis is from 0 to 16, while
the range of the y-axis is from 0 to 7; therefore there are 136 (17 x 8 =
136) available sites to set up fire stations at the airport. A 0-1 string of
136 bits is proposed to indicate whether or not to set up a fire station at
*any specified location (i,j). All Sy are listed from left to right, and the*
*corresponding x-y coordinates (i,j) to Sy are (0,0),(1,1),(1,2),...,*
*(16,7), respectively. Thus, if Sy = 0, no fire station is located on the*
*corresponding x-y coordinate (i,j); if Sy<= 1, a fire station is set up on*
*the corresponding x-y coordinate (i,j). This gene notation is shown as*
follows:

*Gene Type (136 bit string): 1 0 1 . . . 1*

*Corresponding Coordinate (ij): (0,0), (1,1), (1,2),..., (16,7).*

150
120
90-
60-30
30
60-90
120-
150-• **•**
**| 65 cases |**
**•**
**•**
**•**
**• •**
**•**
**•**
**• •**
**•**
**•**
**Undershoot**
•

### vl.V

### •

### •••

• • • • • • • • • • * • •*• \*•*• • • •

*mm* •*• ft •

*^*ft * • • ft ft • • • •

*L*Along runway • • •

**. | 148 cases |***

*L7T.*

_{•}

_{•}

**••**

« . . . « «
Overrun
**Threshold** **Runway end**

FIGURE 4 Statistical analysis of air crashes around the airport in the world (source: ICAO, 1995).

*(b) Reproduction*

The reproduction probability (RP) is designed to give a higher repro-duction-chance to the gene, which will make A have a larger value in a gene population. In view of any gene (g) in the gene population, this reproduction probability is shown in Eq. (8).

^ Vg. (8)

*(c) Mutation*

The mutation is defined as the recombination for a randomly selected gene. First, two cut-points are randomly selected. Secondly, the content between two cut-points is preserved and shifted to the left-hand side. Finally, the gene is recombined from left to right. Mutation in this study is shown as follows:

*Parent Gene: 1010010001-1 Offspring Gene 1: 1001010001...1*
*(d) Performance evaluation*

The self-evolution mechanism in generations is the important
char-acteristic in GA. A generation in this study is defined as a process to
make the gene population undergo rank-selection once, reproduction
once and mutation once (no crossover is applied). The rank selection
*applied in this study tries to find the optimal sets of x-y coordinates,*
which will finally make A have the largest value among all possible
values of A in Eq. (7).

**4. NUMERICAL EXAMPLE: CASE OF TAIPEI'S**
**INTERNATIONAL AIRPORT**

This section follows the procedural steps for a practical application of our location model to Taipei's international airport - this will validate the model's practical applicability and effectiveness.

**4.1. Problem Description and Data Collecting**

*First, in order to compute the risk rank rtj of Eq. (3), the accidents at or*

near Taipei's international airport from January 1,1996 to December 31,

1997 are collected and analyzed statistically. Because different kinds of accident occur at the airport, the accident frequency by type is calcu-lated and summarized in Table III.

Secondly, in Fig. 4, the areas where accidents occur are taken from ICAO is statistical and geographical analysis and combined with Table III. Thus, after a conditional probability and normalized com-putation, the accident frequency rate is obtained for different areas, and this risk-rank table for Taipei's international airport is established, as shown in Table IV.

*Thirdly, ry is assigned to the corresponding area at or near the *
air-port - this is shown in the grid map of Fig. 5. The lower value of

TABLE III Statistical analysis of accident at or near Taipei's international airport

*Accident*

1. Airplane mechanical failure
2. Airplane engine failure
3. Airplane landing failure
4. Airplane flap failure
5. Airplane tire failure
6. Airplane going off runway
7. Oil or fuel leakage
8. Building fire
9. Ground crew accident
10. Passenger accident
11. Runway poorly maintained
12. Hijack accident
13. Bomb threat
14. Others
Total
*Frequency*
30
36
6
8
9
2
41
29
12
40
11
2
3
37
266
*Frequency rate %*
11.28
13.53
2.26
3.01
3.38
0.75
15.41
10.90
4.51
15.04
4.14
0.75
1.13
13.91
100
*Accident area*
Runway/aprons
Runway/aprons
Runway/aprons
Runway/aprons
Runway/aprons
Runway
Aprons
Building
Aprons
Building/aprons
Runway
Aprons/runway
Building/aprons
Building/aprons
—

TABLE IV The risk rank of areas at the Taipei's international airport

*Accident area* *Risk rank rtj= l/AFR* *Accident frequency*

*rate % AFR*

1. Runway end to nearby areas 2. Approach over 500 m to

runway end

3. Approach less than 500 m 4. Building and aprons 5. Others 1 2 3 4 5 1.00 0.50 0.33 0.25 0.20

**p. g_**

Firestations: *x-axis*

FIGURE 5 The risk rank cubic map of Taipei's international airport.

*Yjj indicates that there is more chance for accidents to occur in the area of*
*the x-y coordinate (ij).*

Finally, the TLC and SC are computed as follows:
*(a) Computing TLC*

If there is only one fire station at the airport, the passengers in an air crash have a significantly lower chance of survival due to lack of suf-ficient rescue and fire-fighting resources. We compute the cost by esti-mating the number of deaths multiplied by the insurance payment for each. Assuming that there are 250 deaths in an air accident, and life insurance will pay NT$ 13.5 million dollars for each death, the TLC is computed to be about NTS 3.4 billion dollars (the exchange rate in 1997 was one USS equals 32 NTS dollars).

*(b) Computing SC*

If we try to set up one fire station at the airport, the capital equipment costs (e.g., fire engines, buildings, extinguishers, etc.) and operating costs (e.g., salary and life insurance of fire-fighters, training costs, etc.) are estimated by the relevant authorities at Taipei's international airport to be NTS 165 million dollars; therefore the SC is estimated to be NTS 165 million dollars.

Since TLC equals NTS 3.4 billion dollars and SC equals NTS 165
million dollars, the optimal number of fire stations at Taipei's
*inter-national airport would be three by optimizing the first objective (k = 1).*
Moreover, after consulting fire-fighters at the airport, the distances are
*set to drah = %,dlab= 15 and dsah = 1, respectively. Nevertheless, the *

risk-weighted grid map of Taipei's international airport will be our initial input for optimizing Eq. (7). Moreover, the GA and enumeration method are implemented for comparison.

**4.2. Model Resolution by Revised GA and Enumeration Method**

To solve the mathematical model in Eq. (7), we first apply GA to solve
this location problem. Because the traditional and basic notion of gene
*type in GA is binary, e.g., 0-1 type, and the decision variable Sy is*
also 0-1 type, Goldberg's encoding can be applied in a direct sense.
*After computing the optimal value of f\, and the ceiling and *
*bot-tom values for f2* and /3, Eq. (7) can be rewritten as in Eq. (9)

by the A transformation
Maximise A
subject to
51 - 3 0 '
A< 3 4 8 1~ ^ (9)
- 3 4 8 1 - 1 4 2 7 '
A
*A < Hd{dn),*
**A < n****d****(d****2i****),**

*The rank selection applied in this study tries to find three sets of x-y*
coordinates: namely, the ones which make A have the largest value
among all possible values of A. Thus, A is our performance index used to
evaluate any solution (gene) in the GA. The gene population is sorted
by the A value of each gene in descending order. Twenty runs of this GA
derived a satisfactory solution after 30 generations. The final result is
shown in Table V. In computing terms, it took 20.33 min to find the
above results using a Pentium PC computer.

Since the enumeration method can find exactly the optimal location of fire stations at the international airport, this method is used for

TABLE V Fire station sites proposed by GA and corresponding A value

*Fire station*
(1,6)
(6,1)
(1,1)
(9,4)
(5,6)
(12,0)
(5,0)
(5,1)
(7,1)
(11,6)

*Fire station sites proposed by GA*

*1 Fire station 2*
(9,6)
(9,3)
(6,5)
(1,6)
(13,6)
(5,3)
(9,4)
(4,7)
(4,4)
(11,0)
*Fire station 3*
(6,2)
(0,3)
(7,0)
(5,0)
(9,4)
(11,6)
(2,6)
(0,3)
(11,7)
(5,3)
*A value*
0.75
0.71
0.71
0.71
0.70
0.70
0.70
0.68
0.60
0.60

comparison with the GA. This enumeration method proceeds by exam-ining all possible combinations of available setup sites for three fire stations so as to achieve the maximal A value. It took 73.57 minutes to find an optimal A of 0.78.

**4.3. Results and Discussion**

*From the GA, three sets of fire-station site are obtained, whose x-y*
coordinates are (1,6), (9,6) and (6,2). The final achievement level is
0.75. These three fire stations can be identified in Fig. 5 by the
trian-gular symbols. Comparing the GA and enumeration methods, GA
used less computing time than the enumeration method (20.33 min vs.
73.57 min), yet still yielded a satisfactory achievement level between
conflicting objectives (A = 0.75 vs. A = 0.78). Therefore, the GA
demon-strated its feasibility and effectiveness in this study. Furthermore, the
GA should be able to solve efficiently larger-scale location problems
of other emergency facilities. This means that many optimal sites (e.g.,
three or many more than three sites) for any emergency facility can be
easily derived from our model, which is very easy to operate and can be
a powerful decision support when deciding location problems.

**5. CONCLUSIONS**

The tragic crash of the China Airlines aircraft near Taipei's interna-tional airport in February 1998 stimulated relevant authorities around the world to study more advanced topics for promoting the reaction efficiency of fire protection and rescue at airports. The siting and num-ber of fire stations are factors heavily affecting reaction efficiency. The location model developed in this paper, using a fuzzy multi-objective approach in order to decide the optimal number and sites of fire stations, has shown that it can be applied successfully at Taipei's international airport. Furthermore, because of the combinatorial com-plexity in resolution, the GA was employed and proved to be effective when compared with the enumeration method. In addition, our model has the potential to be expanded to devise solutions for the optimal location of other emergency facilities.

Secondly, this study still leaves much room for modification and further development. For example, re-formulating and validating the risk-cost, constructing fuzzy risk-weights to reflect the uncertainty of accidents, dynamically updating the parameters in the model for sen-sitivity analysis, and expanding the scale of this model so as to optimize any similar location model for other facilities.

Finally, this study can be regarded as providing a basis for the development of a decision support system (DSS) which, combined with a geographic information system (GIS), could assist decision making for emergency location problems or rescue problems in real situations.

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