Introduction
Disaster prevention defines three major missions: fire prevention,
disaster rescue and emergently medical service relating to the lives of
people. (1) People expect that the fire department can adopt proper
countermeasures for disaster prevention and they also hope that fire
branches can dispatch rescue teams efficiently to execute their
missions. Currently, the performances of fire branches commonly adopt
single or few rules to measure the performances of fire prevention,
hazardous materials management, disaster rescue and duty supervision,
but emergently medical services, educational training, fire
investigation and general administration are not taken into
consideration. Current performances tend to cause arguments because of
lacking objectivity and justice. Therefore, the most important thing to
do is to look for a proper measure with objectivity and justice to
evaluate the performance efficiencies of fire branches and then adjust
reasonable resources for those inefficient fire branches.
In 1978, Harry pointed out that efficiency, effectiveness and
productivity are three major parts of performance. (2) In 1988, Fortuin
(3) placed the organizational goal in two categories: efficiency and
effectiveness. The efficiency is defined as the ratio between input and
output, (4) and the effectiveness is defined as the achieving level of
the expected production output by a production system. (5) In fact,
efficiency and effectiveness represent different levels of performance,
and there is no guarantee that both of them can be achieved
simultaneously. However, an efficient organization must handle both of
them well, and use the most efficient way to pursue maximum
effectiveness. (6)
There are many measures of performance evaluation: the Ratio
Approach, the Regression Analysis, the Multiple Criteria Analysis, the
Analytic Hierarchy Process, the Balanced Scorecard, the Delphi Hierarchy
Process, the Total Factor Productivity (TFP), and the Data Envelopment
Analysis (DEA). (7) Among these methods, the DEA is the most suitable
way to measure the performance efficiency of nonprofit organizations
because of its multi-indication character. The performance efficiencies
of fire branches have to be reasonably measured by multiple inputs and
outputs, and the function relationship between inputs and outputs are
unknown in advance. (8) In this research, DEA is selected as the
measuring method of performance efficiencies for fire branches because
of its characteristic of multi-indication, and thus the relative
efficiency of each fire branch can be determined by comparing the
quantitative data of inputs and outputs. (9)
The Data Envelopment Analysis (DEA) was proposed from Charnes,
Cooper and Rhodes in 1978. Originally, the DEA is applied to measure the
performance efficiency of the public or nonprofit organization, but
later is applied to many beneficial organizations. The model of DEA is
shown by the ratio of output/input and has the same meaning of the
so-called TFP. (10) The DEA is based on the concepts of Pareto
Optimality and Frontier to calculate the relative efficiencies of the
whole decision making units (DMUs) in order to determine their
performances, especially for the similar decision making units. (11) In
fact, the DEA uses the separated programming via the fractional
programming and then transfers the process to linear programming in
order to find out the values of the relative efficiencies for the whole
decision making units (DMUs) and to determine the inefficient DMUs. (12)
This study is trying to measure the relative efficiency for each fire
branch under the double duties of disaster prevention and the security
of peoples' life and property. Besides, not only can the DEA
strengthen the justice on the judgment of performance efficiency for
each fire branch and provide an excellent referenced guideline for the
resource allocation of each fire branch, but it also can offer the new
thinking to measure the performance efficiencies of fire branches.
This study aims to assess the performance efficiencies of fire
branches by using 35 fire branches of Tainan County Fire Bureau as an
example. Currently, the Tainan County Fire Bureau consists of office
duty and field duty sectors, including six sections, one fire center,
three fire corps and 35 fire branches. The employees in the fire branch
are regarded as long-term workers (13) because each fire branch has to
operate all day, and thus the employees in the fire branch should be
trained to handle multiple tasks, including water supply, etc. According
to relevant laws and ordinances, the manpower of the fire branch is
arranged relative to the population and the size of the area. (14) The
current allocation of fire protection resources merely considers the
location and its associated response time. (15)
The resource allocation for each fire branch has no rules to be
followed, and the current allocation depends on the resource
distributor; the differing characteristics of the city and country, the
governmental budget subsidiaries and the scale of fire branch are not
considered. Therefore, the current method often causes a biased
assessment of performances. This study, however, considers the aspects
of control area, loadings on fire duties and government budget in order
to establish a reasonable method to assess the performances of fire
branches.
The DEA is conducted in the first-stage of this study. The second
stage, according to the future estimated trend of output to select a
proper strategy, is (ORA)--where output trend is steady or
decreasing--which is also called or Multi-Stage Resource Allocation
Approach (MSRAA). In MSRAA, output tendency is increasing. The solutions
of ORA are recommended from the contribution index of each input item.
The MSRAA is a quantitative approach presented in this study to allocate
resources and will be then described in detail in this study. Through
the two approaches of ORA and MSRAA, the decision maker can adopt
different strategies based on the assessment of the future output trend.
Furthermore, these two strategies will function as a referenced
guideline to resolve the long-term existing difficulties in a way that
reasonably eliminates or allocates resources while making decisions.
The Determination of Input and Output Items
This study focuses on the investigation of the performance
efficiency for each fire branch; the production function of DMU is not
assumed, so that the DEA is chosen as the assessing measure of
performance efficiency in this study. In fact, the DEA includes two
different models: Charnes, Cooper and Rhodes, and Banker, Charnes and
Cooper. Both of them have two options--input orientation and output
orientation. Because a fire branch tries to minimize its input usage of
resources to maintain current performance, this study adopts the
input-oriented model of Charnes, Cooper and Rhodes to conduct the
efficiency analysis for each fire branch. In 1989, Golany and Roll
thought that the selection of input and output items was very important
while executing DEA. (16) Generally speaking, the determination of the
input and output items for the DEA model should be paid more attention.
So, the common way to determine the input and output items is to
interview with organization officers and then to analyze the
organization and management objectives, literature reviews, and
experiences. (17)
Therefore, four input items (the number of on-duty personnel, the
on-duty cost, the total vehicle displacement and the vehicle maintenance
fee) and five output items (the number of fire cases, the number of
rescue cases, the number of public service cases, the number of listed
fire protected spaces and the number of fire hydrants) were selected as
variables in this article for assessing efficiency.
The definition of each variable is given in table 1, and the input
and output values for each DMU are listed in table 2. Table 3 describes
the correlation coefficiencies between input items and output items of
DMUs. From table 3, there exist positive correlations between each input
item and each output item. This means that the relationship between each
variable complies with the characteristic of "isotonicity,"
which is the basic assumption of Data Envelopment Analysis. Backward
elimination (18) can then be applied in order to delete the input and
output items with zero weight in sequence until the weight of each left
item is nonzero (i.e. if the weights of input/output items are zero,
those items are eliminated). After executing the backward elimination,
the previous selected items cannot be deducted from this study. The
weights of input and output items for each DMU are listed in table 4.
Empirical Analysis
Frontier software was applied to investigate 35 fire branches of
Tainan Fire Bureau in Taiwan by using the input and output data from
2003 to perform the efficiency analysis and potential improvement
analysis. The efficiency analysis is described below.
The production efficiency derived from the Charnes, Cooper and
Rhodes model of DEA includes the technical efficiency and the scale
efficiency. The production efficiency, the technical efficiency, the
scale efficiency and the return to scale of each fire branch in Tainan
County are listed in table 5. For example, the production efficiency of
Baihe branch is 0.6656, its technical efficiency is 0.6775 and the scale
efficiency is 0.982. It reveals that the production inefficiency of
Baihe branch is mainly due to its technical factor because its technical
efficiency (0.6775) is smaller than the scale efficiency (0.982). The
analyzing results of DEA for those 35 fire branches in Tainan County are
described as follows:
Firstly, the production efficiencies from 14 branches among 35
branches are equal to one. Secondly, regarding to the technical
efficiency, there are 21 fire branches whose technical efficiencies
are equal to one. Thirdly, the scale efficiencies of 14 fire
branches among 35 branches are equal to one. Fourthly, for
analyzing the return to scale, there are three fire branches which
have been categorized into the decreasing return to scale (DRS).
Those three DRS branches mean that they can try to decrease their
scale for efficiency improvement. Fourteen fire branches are in the
category of constant return to scale (CRS); this indicates that
these 14 branches have already reached the optimal production
scale. The 18 fire branches left are in the category of increasing
return to scale (IRS) meaning that those 18 IRS branches can try to
amplify their scales for efficiency improvement. The detailed
information of DRS, CRS and IRS for those 35 fire branches is
listed in table 5.
Resource Strategies
Based on future output trends, this section presents two
strategies, the MSRAA and the ORA.
When the future output trend is steady or deceasing, it can be
inferred from the potential improved targets and the improved ranges of
input/output items that the relatively inefficient units do not require
further inputs; on the contrary, they should properly trim their
resources. The target values and improved ranges of input/output items
for each fire branch are listed in table 6. The ORA strategy is to trim
the values of input items on the basis of the DEA report because the
output items of each fire branch cannot be changed by us. Taking the
Shanhua branch as an example, its present input values (the number of
on-duty personnel, the on-duty cost, the total vehicle displacement, the
vehicle maintenance fee) are 10, 181.817, 26.002 and 224.685
respectively. The contribution indexes (shown in table 7) of these four
input items are 0%, 96.3%, 0% and 3.7% in order, and the target values
of input items (shown in table 6) are 8.71, 177.38, 23.23, and 219.2
respectively. Based on the contribution indexes, the ORA strategy
recommends that Shanhua branch has to improve "the on-duty
cost" to its target value of 177.38 first because its contribution
index of 96.3 percent is the largest, then improve "the vehicle
maintenance fee" to the target value of 219.2 because such
item's contribution index 3.7 percent is just below the
contribution index of the on-duty cost. This way, the relative
efficiency of the Shanhua branch is improved. The detailed information
of contribution indexes for each DMU is listed in table 7.
On the other hand, if the future output trend is increasing, the
MSRAA strategy is performed. The aim of MSRAA is to balance the workload
of relative efficient branches with other inefficient branches when the
future estimated output trend is increasing. Thus, the workloads of
those efficient branches can be deducted if resources can be added into
them.
The main ideas of MSRAA are as follows:
1. A unit of allocated resources is defined and relative efficient
DMUs are grouped. Those efficient DMUs are regarded as candidate DMUs to
supplement resources because their work loading is higher than those
inefficient branches while the future trend is increasing.
2. The allocated capacity (the number of candidate DMUs) is
checked. (If allocable resources are greater than or equal to the
allocated capacity, a unit allocated resource is added into each
candidate DMU and then one can proceed to step five; otherwise go to the
next step.)
3. Compute the total improved performance efficiencies of the whole
DMUs by adding a unit allocated resource to a candidate DMU
individually, and order these candidate DMUs in accordance with their
total improved performance efficiencies. To be more specific, the most
improved one is assigned the number "one," followed by the
less improved ones--"two," "three," and the like. If
a "tie" occurs, a DMU with less resources has the priority.
4. Based on the order of the previous step, resources are assigned
to those candidate DMUs one by one according to their order (from the
least to the greatest) until the entire allocable resources are
exhausted.
5. Calculate the relative efficiencies of the whole DMUs where
resources are added and regroup these newer efficient DMUs as the
candidate DMUs (the allocated capacity). If remaining resources exist,
these remaining resources are considered as the allocable resources for
the next step. Now return to the step 2 to check the allocated capacity
or go to the final step.
6. Generate the suggested resource allocations in the final step,
and the MSRAA is complete.
An Exemplified Case of Resource Strategy
Bryan (19) mentioned that while the population keeps increasing,
the losing costs of fire cases including the control cost of fire and
the system cost of fire would increase. Therefore, fire branches of
Tainan County, where there is a positive population growth, still need
to supplement resources. Taking the supplementation of firefighters as
an example, there are 20 firefighters to be assigned to fire branches,
and a firefighter is determined as an allocated unit. In the first
stage, there are 14 efficient fire branches evaluated from the DEA
report, and these 14 efficient fire branches (i.e. the allocated
capacity is 14) are considered as the initial set for the first stage.
Assign 14 firefighters into fire branches in the initial set (each fire
branch has assigned a firefighter) because the allocable resources (20
persons) is greater than the allocated capacity (14), and then calculate
the relative efficiencies of fire branches after adding 14 firefighters
in the initial set for the first stage. The aforementioned calculations
are listed in table 8. At this time, the remaining number of
firefighters is six (i.e. the allocable firefighters for the next stage
is six). From the fluctuation of relative efficiencies, it is found that
the Syuejia branch, the Rende branch, and the Gueiren branch would turn
into inefficiencies after adding a firefighter for each. Such phenomenon
means that the original on-duty firefighters of these three branches
before adding firefighters have achieved the optimal scale. Therefore,
there are 11 branches (14 - 3 = 11) whose relative efficiencies are
still 100 percent after adding a firefighter. Order the above-mentioned
11 branches as the initial set of the second stage, and then the
resource allocation (RA) set of the second stage is determined. The
allocable resources of the second stage are six firefighters (20 - 14 =
6). Table 9 shows the detailed process to assign the remaining six
firefighters consecutively to the most prior six branches in the RA set
at the second stage, and then calculate the performance efficiencies of
the whole fire branches (35 fire branches). After conducting the MSRAA,
these 20 firefighters are reasonably allocated into fire branches that
are really in need of resources. After adding those 20 firefighters by
using MSRAA, the number of efficient fire branches has been increased
from 14 to 18 branches (shown in table 10). It indicates that the
workloads of fire branches in Tainan county have been slightly balanced.
The entire relative efficiencies of each stage for conducting the MSRAA
are listed in table 10.
Conclusions
Nowadays, performance evaluation is an important topic in the field
of management sciences. This topic is highly valued by administrative
organizations and/or businesses because a great performance is always
the guarantee of management. (20) Performance evaluations also are
important measures for organizations that want to see how they've
executed or organized certain goals, and how they've stimulated the
morale and the efficiency of the workplace. The aspects of
effectiveness, efficiency and productivity would impact the operation of
organizations if resources were not reasonably allocated. Fortunately,
the proposed strategies in this study will help to solve such difficult
and complicated problems.
By the investigation of the changes of future output trends in this
study, decision makers can quickly determine their resource strategy,
ORA or MSRAA. If the future estimated output trend is decreasing or
steady, the inputs of those relatively inefficient branches require a
proper reduction, but how to accurately and reasonably adjust those
input items and the priority of them have been fully discussed in this
article. The proposed ORA strategy enables decision makers to determine
the reduction of resources for each relatively inefficient branch based
on the contribution indexes of input items. And, since the future
estimated output trend is increasing, resources of input items are
encouraged to supplement, and accurately and reasonably allocate
resources into right branches has to be considered. Indeed, the MSRAA is
capable of reasonably allocating resources. These two resource
strategies can help decision makers quickly obtain a referenced
guideline for resources allocation on the basis of the relative
efficiency for each DMU.
As a matter of fact, a fire branch has the responsibility of public
safety, and therefore its scale of fire resources has to be seriously
considered. If the input resources of relatively inefficient branches
are greatly reduced, the public safety of locality will be affected.
Consequently, the decision maker has to consider the appropriate scale
of fire resources for each fire branch while performing the ORA
strategy, Based on the increasing population of Tainan County, the
future fire protection duties will accordingly become heavier.
Therefore. the proposed MSRAA strategy in this study will play an
important role in the allocation of future fire protection resources.
Although this study takes the allocation of fire manpower as an example
to demonstrate the MSRAA strategy, the input resources such as the
number of fire vehicles (total vehicle displacement), the maintenance
fees, and the on-duty cost all can be allocated through the proposed
MSRAA strategy. In sum, this study provides an efficiency-based
quantitative approach to adjust or allocate fire protection resources,
and further establish an executive prototype of the new era to pursue
higher efficiency.
Chun-Hsiung Lan
3F, No.221
Nanya W. Rd. Sec.2
Panchiao 220
Taiwan R.O.C.
chlan@mail.nhu.edu.tw
Liang-Lun Chuang
Tainan County Fire Bureau
Tainan County, 730
Taiwan R.O.C.
pb35kimo@yahoo.com.tw
Chi-Chung Chang
Nanhua University
Dalin, Chiayi 622
Taiwan R.O.C.
mgenera1168@yahoo.com.tw
Notes
(1) National Fire Agency Ministry of Interior R.O.C:
http://www.nfa.gov.tw.
(2) Harry, P.H. (1978). The Status of Productivity Measurement in
the Public Sector. Public Administration Review, 38(1): 28.
(3) Fortuin, L. (1988). Performance Indicators-Why, Where and How,
European Journal of Operational Research, 34:1-9.
(4) Farrell, M.J. (1957). The Measurement of Productivity
Efficiency, Journal of the Royal Statistical Society, Series A, 120(3):
253-281.
(5) Szilagyi, jr. A.D. (1984). Management and Performance, 2nd ed.,
New Jersey: Scott, Foresman and Company.
(6) Robbins, S.P. (1994). International Management, 4th ed., New
York: Prentice-Hall.
(7) Clarke, R. L. (1992). Evaluating USAF Vehicle Maintenance
Productivity Over Time: An Application of Data Envelopment Analysis.
Decision Science, 23(2): 376-384.
(8) Banker, R.D. and Morey, R.C. (1986). Efficiency Analysis for
Exogenously Fixed Inputs and Outputs, Operations Research, 34(4):
513-521.
(9) Insurance Service Office. (1980). Fire Suppression Rating
Schedule, edition 6-80, P30.
(10) Gleason, J.M. and Dariod, T.B. (1982). "Toward Valid
Measures of Public Sector Productivity: Performance Measures in Urban
Transi," Management Science, 28(4): 237-243.
(11) Banker, R.D., Charnes, A. and Cooper, W.W. (1984). Some Models
For Estimating Technical and Scale Inefficiencies in Data Envelopment
Analysis, Management Science, 30(9): 1078-1092.
(12) Charnes, A., Cooper, W.W., and Rhodes, E. (1978). Measuring
the efficiency of decision making units, European Journal of Operational
Research, 2: 429-444.
(13) Traut, OA., Larsen, R., and Feimer, S. (2000). Hanging on or
fading out? : Job satisfaction and the long-term worker, Public
Personnel Management, 29(3): 343-351.
(14) Schaenman, P.S. (1974). Measuring Fire Protection Productivity
in Local Government, Boston: National Fire Protection Association.
(15) Coleman, R.J., Granito, J.A., and Hickey, H.E. (1979),
Managing Fire Services International City/County Management Association,
42-43.
(16) Golan, B. and Roll, Y (1989). An Application Procedure for
DEA, OMEGA, 17(3): 237-250.
(17) Kao, C. (2000), Data Envelopment Analysis in Resource
Allocation: An Application to Forest Management. International Journal
of Systems Science, 31(9): 1059-1066.
(18) Hwang, S.N. and Chang, T.Y. (2003). Using Data Envelopment
Analysis to Measure Hotel Managerial Efficiency Change in Taiwan,
Tourism Management, 24(4): 357-369.
(19) Bryan, J.L. (1979). Managing Fire Service, International City
Management Association ICMA, p. 363.
(20) Thompson, J.R. and LeHew, C. (2000). Skill-based pay as an
organizational innovation, Review of Public Personnel Administration,
20(1): 20-40.
Chun-Hsiung Lan is a professor and a chairman of the Graduate
Institute of Management Sciences at Nanhua University in Taiwan. He
earned his Ph.D. at Tamkang University's Department of Management
Sciences in Taiwan. His research interests are in the fields of
efficiency management, resource strategy, operations research, calculus
of variations and soft computing. He has published many international
journal papers regarding the aforementioned fields of study.
Liang-Lun Chuang is the director of the Tainan County Fire
Bureau's Emergency and Rescue Command Center, located in Taiwan,
and a Ph.D. student at the Graduate Institute of Management Sciences at
Nanhua University, Taiwan. He received his bachelor's degree from
the Department of Fire Sciences at Central Police University, Taiwan in
1990, and completed his master's degree at Nanhua University
(Taiwan) in 2004. His research interests lie in the fields of efficiency
management and forest fire rescue.
Chi-Chung Chang is a manager of Quick Service Restaurant in Taiwan
and a Ph.D. student at the Graduate Institute of Management Sciences at
Nanhua University, Taiwan. He received his bachelor's degree from
the National Taiwan University of Sciences and Technology, Taiwan, in
1984, and completed his master's degree at Nanhua University
(Taiwan) in 2004. His research interests lie in the fields of efficiency
management and operations research.
Table 1: The Definitions of Input and Output Items
input/
No. output Name of Item Definitions
01 input number of on-duty The monthly average on-duty persons
personnel of the fire branch during the
period of assessment (person)
02 input on-duty cost The business expenses and vehicle
fuel expenses of the fire branch
during the period of assessment
(thousand dollars)
03 input total vehicle The displacement of fire vehicles
displacement of the fire branch during the
period of assessment (cc /1000)
04 input vehicle The maintenance fee of fire
maintenance fee vehicles of the fire branch during
the period of assessment (thousand
dollars)
01 output number of fire The number of fire cases occurred
cases within the control area of the fire
branch during the period of
assessment (case)
02 output number of The number of emergency rescue
emergency rescue cases of the fire branch during
cases the period of assessment (case)
03 output number of The number of public services,
public-service such as bee capture, snake capture,
cases water supply, etc, made by the fire
branch during the period of
assessment (case)
04 output number of listed The total number of protected
fire protected spaces listed in the fire branch
spaces during the period of assessment
(house)
05 output number of fire The number of fire hydrants listed
hydrants in the fire branch during the
period of assessment (hydrant)
Table 2: The Values of Input and Output Items for Each DMU
DMUs Input 1 Input 2 Input 3 Input 4
Sinying 18 336.165 53.819 449.005
Fire Branch
Liouying 6 129.276 18.952 170.932
Fire Branch
Yanshuei 7 145.558 18.952 170.932
Fire Branch
Baihe 10 223.796 37.953 232.998
Fire Branch
Houbi 7 132.648 18.952 179.245
Fire Branch
Dongshan 7 138.794 18.952 179.245
Fire Branch
Dongyuan 5 99.457 10.726 108.867
Fire Branch
Syuejia 7 160.664 37.953 224.469
Fire Branch
Jiangjyun 5 89.125 10.726 100.540
Fire Branch
Beimen 6 117.883 18.952 169.570
Fire Branch
Jiali Fire 8 186.725 29.729 366.802
Fire Branch
Sigang 6 99.530 10.726 125.492
Fire Branch
Cigu 6 123.401 18.952 199.746
Fire Branch
Madou 16 315.491 46.179 316.562
Fire Branch
Siaying 6 133.056 18.952 170.932
Fire Branch
Lioujia 7 164.292 18.952 179.245
Fire Branch
Guantian 7 177.484 18.952 179.392
Fire Branch
Shanhua 10 181.817 26.002 224.685
Fire Branch
Danei 6 102.197 18.952 179.245
Fire Branch
Anding 5 114.020 10.726 83.928
Fire Branch
Yujing 7 156.231 18.952 170.932
Fire Branch
Nansi 6 130.523 10.726 100.554
Fire Branch
Nanhua 6 120.707 10.726 108.867
Fire Branch
Sinhua 8 157.979 18.952 170.932
Fire Branch
Shansun 10 210.668 18.952 145.994
Fire Branch
Gueiren 9 231.614 27.178 270.124
Fire Branch
Wunsian 7 164.243 18.364 179.245
Fire Branch
Rende 7 184.667 46.179 286.750
Fire Branch
Guanmiao 9 218.04 18.952 241.310
Fire Branch
Yongkan 9 174.008 16.452 140.756
Fire Branch
Sinshih 8 182.156 18.364 162.620
Fire Branch
Nanke 13 209.819 23.319 107.506
Fire Branch
Dawan 8 195.469 37.953 286.750
Fire Branch
Yanhang 10 157.374 18.952 249.623
Fire Branch
Fusing 17 289.29 46.179 283.312
Fire Branch
DMUs Output 1 Output 2 Output 3 Output 4 Output 5
Sinying 212 1658 175 533 664
Fire Branch
Liouying 91 596 87 123 207
Fire Branch
Yanshuei 119 762 115 187 237
Fire Branch
Baihe 125 810 76 175 232
Fire Branch
Houbi 77 545 49 120 134
Fire Branch
Dongshan 59 432 45 69 105
Fire Branch
Dongyuan 19 224 52 16 35
Fire Branch
Syuejia 79 607 83 231 265
Fire Branch
Jiangjyun 51 360 26 71 205
Fire Branch
Beimen 59 241 69 40 113
Fire Branch
Jiali Fire 128 1069 98 210 383
Fire Branch
Sigang 81 564 31 109 175
Fire Branch
Cigu 102 457 49 80 162
Fire Branch
Madou 144 1220 191 242 189
Fire Branch
Siaying 53 654 82 84 117
Fire Branch
Lioujia 91 575 82 91 122
Fire Branch
Guantian 110 668 85 235 187
Fire Branch
Shanhua 92 836 120 160 317
Fire Branch
Danei 30 253 48 24 63
Fire Branch
Anding 99 600 34 156 135
Fire Branch
Yujing 38 451 93 95 91
Fire Branch
Nansi 16 321 42 56 65
Fire Branch
Nanhua 18 212 75 34 54
Fire Branch
Sinhua 178 1049 140 280 205
Fire Branch
Shansun 40 391 72 55 97
Fire Branch
Gueiren 203 1221 105 278 309
Fire Branch
Wunsian 141 859 76 216 117
Fire Branch
Rende 163 819 128 247 209
Fire Branch
Guanmiao 236 798 80 187 238
Fire Branch
Yongkan 168 1124 86 160 326
Fire Branch
Sinshih 124 917 96 227 139
Fire Branch
Nanke 40 342 88 53 327
Fire Branch
Dawan 89 1012 67 405 213
Fire Branch
Yanhang 119 894 54 484 219
Fire Branch
Fusing 157 1263 82 240 182
Fire Branch
Table 3: Correlation Coefficiencies Between Input and Output Variables
Number of On-Duty Total Vehicle Vehicle Number
On-Duty Cost Displacement Maintenance of Fire
Personnel Fee Cases
Number of 1 0.923 0.733 0.641 0.484
On-Duty
Personnel
On-Duty Cost 0.923 1 0.812 0.746 0.627
Total Vehicle 0.733 0.812 1 0.850 0.499
Displacement
Vehicle 0.641 0.746 0.850 1 0.632
Maintenance
Fee
Number of Number of Number of Number of
Emergency Public- Listed Fire Fire
Rescue Service Protected Hydrants
Cases Cases Spaces
Number of 0.685 0.634 0.532 0.599
On-Duty
Personnel
On-Duty Cost 0.774 0.730 0.600 0.607
Total Vehicle 0.682 0.661 0.612 0.578
Displacement
Vehicle 0.774 0.631 0.732 0.676
Maintenance
Fee
Table 4: The Weights of Input and Output Items for Each Fire Branch
Fire Branch Input 1 Input 2 Input 3 Input 4
Sinying 0.646659 1.00E-06 0.214788 0.138553
Fire Branch
Liouying 2021684 1.00E-06 1.00E-06 0.685738
Fire Branch
Yanshuei 1.973753 1.00E-06 1.00E-06 0.610545
Fire Branch
Baihe 1.423995 1.00E-06 1.00E-06 0.402548
Fire Branch
Houbi 1.00E-06 2.234261 1.00E-06 1.00E-06
Fire Branch
Dongshan 1.324998 1.174018 1.00E-06 1.00E-06
Fire Branch
Dongyuan 1.00E-06 1.00E-06 5.017617 1.00E-06
Fire Branch
Syuejia 1.776252 1.00E-06 1.00E-06 0.618562
Fire Branch
Jiangjyun 1.712203 1.00E-06 1.00E-06 2.341881
Fire Branch
Beimen 1.00E-06 2.851680 1.00E-06 1.00E-06
Fire Branch
Jiali 2.249996 1.00E-06 1.00E-06 1.00E-06
Fire Branch
Sigang 1.00E-06 3.125864 0.373861 1.00E-06
Fire Branch
Cigu 1.109726 1.716473 1.00E-06 1.00E-06
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Madou 1.00E-06 1.00E-06 1.00E-06 1.418376
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Siaying 2.999997 1.00E-06 1.00E-06 1.00E-06
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Lioujia 2.463639 1.00E-06 0.119034 1.00E-06
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Guantian 2.032505 1.00E-06 0.151452 0.391078
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Shanhua 1.00E-06 1.781181 1.00E-06 0.073213
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Danei 1.00E-06 3.289379 1.00E-06 1.00E-06
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Anding 1.00E-06 1.00E-06 1.00E-06 5.349879
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Yujing 2.497762 1.00E-06 0.081352 1.00E-06
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Nansi 1.00E-06 1.00E-06 5.017616 1.00E-06
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Nanhua 1.00E-06 1.00E-06 5.017616 1.00E-06
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Sinhua 1.00E-06 1.00E-06 2.839749 1.00E-06
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Shansun 1.00E-06 1.00E-06 1.00E-06 3.075498
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Gueiren 1.999996 1.00E-06 1.00E-06 1.00E-06
Fire Branch
Wunsian 2.217190 1.00E-06