Optimal human resource allocation model: A case study of Taiwan fire service

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Optimal human resource allocationmodel: A case study of Taiwan fireserviceChun-Hsiung Lan a , Liang-Lun Chuang a & Yung-Fang Chen ba Graduate Institute of Management Sciences, Nanhua University ,Dalin, Chiayi , 62248 , Taiwan, R.O.C.b Department of Geography, Environment and Disaster Management ,Coventry University , Coventry , CV1 5LW , U.K.Published online: 14 Jun 2013.

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Optimal human resource allocation model: A case study of Taiwan fi re service

Chun-Hsiung Lan*

Liang-Lun Chuang

Graduate Institute of Management SciencesNanhua UniversityDalin, Chiayi 62248Taiwan, R.O.C.

Yung-Fang Chen

Department of GeographyEnvironment and Disaster ManagementCoventry UniversityCoventry, CV1 5LWU.K.

AbstractA lack of government fund results in great diff erent ratios of a fi refi ghter to the popula-

tion in major cities in Taiwan. The research proposes to develop an optimal human resource

allocation model to strike the balance between the fi re workforce and responsibilities in

emergency responses. The DEA method is used to evaluate the organizational performance

and determine the production eff iciency of the fi re services in Taiwan. Next, the Omit Re-

source Approach is used to determine eff iciency improvement and resource adjustment to

the fi re department. Last, the research uses the Total Eff iciency-Based Scale Approach to

suggest an ideal human resource allocation model.

Keywords: data envelopment analysis (DEA), omit resource approach (ORA), performance evalua-tion, total eff iciency-based scale approach (TEBSA), resource allocation, fi re department.

1. Introduction

There are three major missions of fi re department, the fi re preven-

tion, the disaster rescue, and the emergency medical service relating to

the people’s lives, and the execution performance of the above-mentioned

Journal of Statistics & Management SystemsVol. 14 (2011), No. 1, pp. 187–216

© Taru Publications

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188 C. H. LAN, L. L. CHUANG, AND Y. F. CHEN

missions is one of the indicators on political aff airs [1]. In Taiwan, the fast

growth of economic, the high utilization of lands, the massive centraliza-

tion of population and the establishment of vary factories causing the fi re

missions become more and more arduous and higher danger during the

recent thirty years, that is, overload would make fi refi ghters tiredness

and it also aff ect the organizational performance. In addition, the current

method to allocate fi re manpower is determined by the number of fi re

engines, the number of fi re engines is determined based on the popula-

tion of administrative areas. The current Taiwan fi re aff airs belong to its

associate local government, the fi re service items and standard operation

procedure are all consistent in Taiwan area, but the allocate of the fi re re-

source for each fi re bureau is diff erent due to the diff erent fi nancial con-

ditions in each local government. The new fi re manpower is assigned by

the central government consistently and there is no consistent standard

to be followed. Comparing to other major cities worldwide, the average

fi re manpower per population of 10,000 in Taiwan, 3.92, is signifi cantly

lower than others, it reveals that the job load of fi re manpower in Taiwan

is signifi cant heavy. Table 1 indicates the comparison of fi re manpower

among Taiwan and other major cities worldwide [1-2].

Based upon the economic viewpoint, a better and reasonable fi re

manpower allocation approach is mainly focused on to fi nd out a critical

point on the relationship among the fi re manpower, the disaster rescues,

and the emergency medical services to avoid the waste of social cost by too

much manpower and facilities input, as well as keep suff icient fi re man-

power and facilities for providing the basic safety assurance. Therefore,

facing the increasing disaster rescue cases, the constrained governmental

budget, and the lower level of fi re manpower in Taiwan, how to reasonable

allocate fi re manpower to minimize the gap of other advanced countries

is an important lesson.

In 1978, Hatry pointed out that eff iciency; eff ectiveness and pro-

ductivity are three major parts of performance [3]. Fortuin (1988) placed

the organizational goal in two categories: eff iciency and eff ectiveness [4].

The eff iciency is defi ned as the ratio between input and output [5], and the

eff ectiveness is defi ned as the achieving level of the expected production

output by a production system [6-7]. In fact, eff iciency and eff ectiveness

represent diff erent levels of performance, and there is no guarantee that

both of them can be achieved simultaneously. However, an eff icient orga-

nization must handle both of them well, and use the most eff icient way to

pursue maximum eff ectiveness [8].

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HUMAN RESOURCE ALLOCATION MODEL 189

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) [9-14]. Among these methods, the DEA is the most suit-

able way to measure the performance eff iciency of nonprofi t organizations

Table 1A comparison of fi re manpower allocations among Taiwan and other

major cities worldwide in 2006

Average

population of Firefi ghters

Country Control Population 1 fi refi ghter per 10,000

City Area (km2) (10,000) Firefi ghters assigned populations

USANew York 892 800 14950 535.1 18.7

USAChicago 595 337 4774 705.9 18.97

Canada

Toronto 97 65 1283 506.6 19.74

UKLondon 1587 750 7600 986.8 10.13

Germany

Hamburg 755 171 2554 669.5 14.91

AustralianSydney 5000 420 6000 700 14.29

South Africa

Johannesburg 1356 561 1145 4899.6 2.04

JapanTokyo 612 1200 17906 670.2 14.92

ChinaBeijing 16800 1200 6480 2006.2 5.4

South KoreaSeoul 606 1047 4963 2109.6 4.74

SP

Singapore 648 320 1467 2181.3 4.58

Taiwan Major

Area 35879 2259 8849 2568.8 3.92

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because of its multi-indication character. The performance eff iciencies of

fi re organizations have to be reasonably measured by multiple inputs and

outputs, and the function relationship between inputs and outputs are un-

known in advance [15]. In this research, DEA is selected as the measuring

method of performance eff iciencies for fi re organizations because of its

characteristic of multi-indication, and thus the relative eff iciency of each

fi re bureau can be determined by comparing the quantitative data of in-

puts and outputs [16].

The Data Envelopment Analysis (DEA) was proposed from Charnes,

Cooper and Rhodes in 1978. Originally, the DEA is applied to measure

the performance eff iciency of the public or nonprofi t organization [17],

but later is applied to many benefi cial organizations. The model of DEA

is shown by the ratio of output/input and has the same meaning of the

so-called TFP [18]. The DEA is based on the concepts of Pareto Optimal-

ity and Frontier to calculate the relative eff iciencies of the whole decision

making units (DMUs) in order to determine their performances, especially

for the similar decision making units [19-20]. In fact, the DEA uses the

separated programming via the fractional programming and then trans-

fers the process to linear programming in order to fi nd out the values of

the relative eff iciencies for the whole decision making units (DMUs) and

to determine the ineff icient DMUs [17]. This study is trying to measure the

relative eff iciency for each fi re bureau under the double duties of disas-

ter prevention and the security of peoples’ life and property. Besides, not

only can the DEA strengthen the justice on the judgment of performance

eff iciency for each fi re organization and provide an excellent referenced

guideline for the resource allocation of each fi re organization [21], but it

also can off er the new thinking to measure the performance eff iciencies of

fi re organizations.

American “Municipal Fire Service Workbook” points out that to eval-

uate the fi re prevention, the rescue eff iciency, and the performance of the

fi re bureau is to provide a method to evaluate the fi re mission execution

and help the municipal administrators or chief executives of fi re depart-

ments to estimate their own fi re system [22]. There are 25 fi re bureaus

in the Taiwan in every county and city administrative area including

remote/separate area. This research excludes three fi re bureaus in the

remote/separate areas; therefore, only 22 fi re bureaus are left. This study

aims to assess the performance eff iciencies of fi re bureaus by using

22 fi re bureaus of Taiwan as an example. Based upon Taiwan’s policy,

the manpower of the fi re bureau is arranged relative to the population

and the size of the area [23]. According to the Fire Engine, Equipment

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and Manpower Allocation Standards for the Municipality, County and

City [24], if the population is over 50,000, the number of fi re engines is

determined by one engine per 10,000; if the population is between 30,000

and 50,000, the number of fi re engines is determined by one engine per

15,000; if the population is below 30,000, two fi re engines are assigned to

this area. And thus, the manpower of each fi re bureau is determined in

accordance with the number of fi re engines. Every county and city have

to follow this regulation to input its proper manpower and equipment.

The current allocation of fi re protection resources merely considers the

location and its associated response time [25-27]. The resource allocation

for each fi re bureau has no rules to be followed, and the current alloca-

tion depends on the resource distributor; the diff ering characteristics of

the city and country, the governmental budget subsidiaries and the scale

of fi re branch are not considered. Therefore, the current method often

causes a biased assessment of performances. This study tries to consider

the aspects of control area, loadings on fi re duties and government bud-

get in order to establish a reasonable method to assess the performances

of fi re bureaus.

A Two-Staged Design Approach is adopted in The DEA is con-

ducted in the fi rst-stage of this study. The second stage, according to the

future estimated trend of output to select a proper strategy. If the output

trend is steady or decreasing, the suggested strategy is Omit Resource

Approach (ORA), where the solutions of ORA are recommended from

the contribution index of each input item [28]; however, considering the

resource elimination only functions as a temporary solution. In fact, to

establish a reasonable resource allocation standard is the total solution.

This paper tries to propose a better resource allocation approach, Total

Eff iciency-Based Scale Approach- TEBSA. TEBSA not only performs a

reasonable and better allocation scale to help the decision makers, but

also provides a referenced guideline for executing the decision-making

process.

2. Selections of model, input and output items

This study mainly investigates the performance eff iciency for each

fi re bureau; the production function of each DMU is not assumed, and

thus DEA can be chosen as the assessing measure of performance eff i-

ciency. In fact, the DEA includes two diff erent models: CCR (Charnes,

Cooper and Rhodes) model and BCC (Banker, Charnes and Cooper) model

[17; 19]. Both of them have two options-input orientation and output

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orientation. Because a fi re bureau tries to minimize its input usage of

resources to maintain current performance, this study adopts the input-

oriented model of CCR model to conduct the eff iciency analysis for each

fi re bureau. In 1989, Golan and Roll thought that the selection of input

Table 2The defi nitions of input and output items

No. Input/Output Items Defi nitions

01 Input Number of on-duty The average on-duty personnel personnel per month of the fi re

organization during the evaluation period (person)

02 Input Fire budget The total budget of current account and capital account of the fi re organization during the evaluation period (thousand dollars)

03 Input Number of fi re The number of various fi re engines engines in the fi re organization

during the evaluation period (vehicle)

04 Input Number of fi re The number of fi re branch in branch the fi re organization during the

evaluation period (branch)

05 Input Number of fi re The number of fi re hydrants hydrants listed in the fi re organization

during the evaluation period (hydrant)

01 Output Number of fi re cases The number of fi re cases in the fi re organization control area during the evaluation period (case)

02 Output Number of emergency The number of emergency rescues cases rescues cases in the fi re

organization during the evaluation period (case)

03 Output Number of listed fi re The number of listed fi re protected places protected places in the fi re

organization during the evaluation period (house)

04 Output Population of control The total population of the fi re area organization control area during

the evaluation period (person)

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and output items was very important while executing DEA [29]. 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 off icers and

then to analyze the organization and management objectives, literature

reviews, and experiences [30].

Therefore, fi ve input items (the number of on-duty personnel, the

fi re budget, the number of fi re engines, the number of fi re branch and

the number of fi re hydrants) and four output items (the number of fi re

cases, the number of emergency rescues cases, the number of listed fi re

protected places and the population of control area) were selected as vari-

ables in this article for assessing the eff iciency. The number of on-duty

personnel, the number of fi re engines, and the number of fi re hydrants

are regarded as the fi re protection resources in a fi re bureau [31]. Besides,

the fi re budget and the number of fi re branch are regarded as the factors

for estimating the response time of the fi re bureau. The defi nition of each

variable is given in Table 2, and the input and output values for each

DMU are listed in Appendix 1. Table 3 describes the correlation coeff i-

ciencies 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. The Backward elimination [30] is then ap-

plied 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 conducting the

backward elimination, the previous selected items cannot be deducted

from this study.

Table 3Correlation coeff icients between input and output items

Name

of Item Input 1 Input 2 Input 3 Input 4 Input 5 Output 1 Output 2 Output 3 Output 4

Input 1 1 0.986 0.927 0.771 0.935 0.630 0.914 0.914 0.865

Input 2 0.986 1 0.947 0.793 0.954 0.645 0.928 0.916 0.886

Input 3 0.927 0.947 1 0.866 0.955 0.751 0.969 0.894 0.965

Input 4 0.771 0.793 0.866 1 0.855 0.770 0.880 0.814 0.908

Input 5 0.935 0.954 0.955 0.855 1 0.683 0.955 0.921 0.935

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3. Empirical analysis

The Frontier software was applied to investigate 22 Fire Bureaus in

Taiwan by using the input and output data in 2007 to perform the eff iciency

analysis and potential improvement analysis. The eff iciency analysis is de-

scribed below.

The production eff iciency includes the technical eff iciency and the

scale eff iciency, and thus the production eff iciency, the technical eff iciency,

the scale eff iciency and the return to scale of each fi re bureau in Taiwan

are listed in Appendix 2. For example, the production eff iciency of Yunlin

County fi re bureau is 0.7522, its technical eff iciency is 0.7966 and its scale

eff iciency is 0.9443. It reveals that the production ineff iciency of Yunlin

County fi re bureau mainly comes from its technical factor because its

technical eff iciency (0.7966) is smaller than the scale eff iciency (0.9443).

The entire analysis results of DEA for those 22 fi re bureaus in Taiwan are

described as follows.

The production eff iciencies of 9 fi re bureaus among 22 fi re bureaus

are equal to one, there are 14 fi re bureaus whose technical eff iciencies are

equal to one, the scale eff iciencies of 9 fi re bureaus among 22 fi re bureaus

are equal to one, and there are three fi re bureaus which have been cat-

egorized into the decreasing return to scale (DRS). Those three DRS fi re

bureaus are recommended to decrease their scale for eff iciency improve-

ment. In addition, nine fi re bureaus are in the category of constant return

to scale (CRS); it means that these 9 fi re bureaus have already reached the

optimal production scale. The 10 fi re bureaus left are in the category of

increasing return to scale (IRS) meaning that those 10 IRS branches are

recommended to amplify their scales for eff iciency improvement. The de-

tailed information of DRS, CRS and IRS for those 22 fi re bureaus is listed

in Appendix 2.

4. The resource scale strategy – Total Eff iciency-Based Scale Approach (TEBSA)

By the potentially improved goal and improved level of fi re bureaus in

each county and city, there is no need to input resources to the relative in-

eff icient units because these units need to appropriately reduce resources

more than to add. From the empirical analysis, the average eff iciency of

the entire fi re bureaus is 0.9076 and it means that there are about 10%

of the input resources being ineff ective. The reason of causing production

ineff iciency is from the average technical eff iciency, 0.9508 and the average

scale eff iciency is 0.9522. Lan et al. (2007) proposed the Omit Resource

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Approach (ORA) to reduce resources according to the DEA report data

when the future output trend is steady or decreasing [32]. This approach

can be applied as a way for improving the production ineff iciency if the

future output tendency is steady or decreasing. In addition, when the

reduction is conducted, which input resource should the administrators

accurately and reasonably reduce fi rst? Based on the contribution index

data analysis of the DEA report, the administrators should start from the

resource with a greater contribution index because the output value of

each fi re bureau cannot change arbitrarily. Now, we take Miaoli county as

an example, its existing input values, “the number of on-duty personnel,

the fi re budget, the number of fi re engines, the number of fi re branches

and the number of fi re hydrants” are 226, 320080, 94, 19, and 3254 sepa-

rately, the computed contribution indexes of input items are 3.9%, 78%, 0,

0, and 18.1%, and the objective values of each input resource are 160.15,

226822.8, 63.16, 9.63, and 2305.93. Based on the ORA to start the eff iciency

improvement, the Miaoli County fi re bureau should improve its “fi re

budget” from the input aspect fi rst to reach its objective value, 226822.8,

because the improved contribution index of this item is 78%; secondly,

“the number of fi re hydrants” for reaching its objective value, 2305.93 with

a improved contribution index, 18.1% which is next to the contribution of

“fi re budget”. The objective values of each fi re organization and contribu-

tion indexes of various variables are listed in Appendix 3.

In addition, ORA strategy is to properly balance the uneven work

loading of the relative ineff icient units if the administrators can reduce

the input resources of those units when the future output trend is steady

or decreasing. In fact, it often not assigned the required manpower in the

yearly budget of the county and city fi re bureaus, because some reasons as

the governmental budget, the inattentive fi re manpower and the fi re miss-

ing getting more and more arduous. In order to resolve how reasonably

and accurately adjust the current resources to the more satisfi ed scale, this

study presents the Total Eff iciency-Based Scale Approach (TEBSA) to off er

a referenced guideline for the resource distributors of fi re organization

when the resource allocation planning executes.

The empirical analysis shows that 59.1% of total fi re bureaus are pro-

duction ineff iciency, and causing the ineff iciency of fi re bureaus is from

the technical ineff iciency in 37.4% and the scale ineff iciency in 59.1%. This

means if the administrators want to enhance the eff iciencies of the entire

fi re bureaus, they must start with the scale allocation and omni-directional

eff iciency improvement of the fi re bureaus. The TEBSA of the research is

to balance the work loading between the relatively eff icient bureaus and

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other fi re bureaus. If the administrators can increase input resources of

the relative eff icient bureaus, then they can eff ectively reduce the work-

load of these units. Practically, the outputs of fi re bureaus, such as rescue

services and fi re protected places, are increasing year by year; therefore,

the local government inevitably must increase the fi re manpower to serve

the general public. How should the administrators reasonably and accu-

rately distribute resources to bureaus which really need? According to

this, the proposed TEBSA strategy is properly to off er a reasonable and

quantitative reference guideline for the fi re resource distributors when the

fi re manpower allocation executes. The executing steps of TEBSA are de-

scribed as following.

At fi rst, list the entire DMUs according to their performance eff iciency

from the highest to the lowest one to form the initial data set. Defi ne the

smallest allocation unit as 1 fi refi ghter in the resource allocation and set

the upper-and-lower bound of the index value at this stage. The principle

of setting the upper-and-lower bound is adopting the maximum and mini-

mum values respectively of the original average population proportion for

one fi refi ghter assigned by the current DMUs. Now, take the upper bound

of the index value as the index value of the initial input.

Step 1. Set the input index value as the benchmark, and if the value of

the original average population proportion of DMUs for one

fi refi ghter assigned are over the benchmark and they are also

categorized as eff icient DMUs; then these DMUs are defi ned as

the current candidate units of manpower input. For these cur-

rent candidate units, decrease the value of the average popu-

lation proportion to the index value of current input and the

value of the average population proportion in the rest non-can-

didate units stays the same. Continue this step until reaching

the lower bound of the index value, and in the meantime, the

index value that maximizing the total eff iciencies will be found

and become the suggested solution at this stage. Then, accord-

ing to results of the suggested solution, re-list the initial data

sets for the next stage from all eff icient and ineff icient units

evaluated and move into the next stage.

Step 2. Re-calculate the eff iciency value of all units to become the new

candidate eff icient DMUs and compute the total performance

of all units under the current conditions. Adjust index value

downward by the ratio of 500 people and compute the new

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performance eff iciency value of each DMU based on the new

index value, and then return to step 1.

Step 3. At stage two, taking the suggested solution, the index value of

stage one as the starting point for computation, then repeating

step 1 and 2. At step 2, adjusting the index value downward

and upward range to be ±100 people until the index values

have been searched in stage one. Meanwhile, fi nding the index

value that can maximize the total eff iciencies and set it as the

suggested solution of this stage, then based on this solution,

re-computing the initial data set for the next stage from all ef-

fi cient and ineff icient units.

Step 4. At stage three, taking the suggested solution of stage two as

the starting point for computation, then repeating step 1 and

2. At step 2, adjusting the index value downward and up-

ward range to be ±10 people until the index values have been

searched in stage two. Meanwhile, fi nd the index value that

can maximized the total eff iciencies and set it as the suggested

solution of this stage, then based on this solution, re-compute

the initial data set for the next stage from all eff icient and inef-

fi cient units.

Step 5. At stage four, taking the suggested solution of stage three as

the starting point for computation, then repeating step 1 and

2. At step 2, adjusting the index value downward and up-

ward range to be ±1 person until the index values have been

searched in stage three. Meanwhile, fi nd the index value that

can maximize the total eff iciencies and set it as the suggested

solution of this stage. The solution here is also the fi nal solu-

tion of TEBSA.

5. Explanations of resource scale strategy

The population of Taiwan is getting continuously positive growth,

and according to Bryan (1979), when the population is growing, the cost

lost of fi re cases, related costs of fi re control and total system will increase

as well [33]. Therefore, every fi re bureau of Taiwan needs to supplement

resources. Taking the supplementation of fi re manpower as an example,

how can the entire fi re bureaus of Taiwan in 2007 minimize the dispar-

ity of every major city worldwide by the average population proportion

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with one fi refi ghter assigned? Also, under diff erent average population

proportion with one fi refi ghter assigned by each county and city, how

much average population proportion does each county and city fi re bu-

reau need to assign one fi refi ghter and how can the fi re bureaus reach

the best total eff iciency and the reasonable allocation scale? According

to DEA analysis report and TEBSA, the detailed description is shown as

below.

At fi rst, orderly list of the entire DMUs according to their performance

eff iciency from the highest to the lowest one to the sources form the ini-

tial data set and defi ne the smallest allocation unit as one fi refi ghter. The

total numbers of current fi refi ghters nationwide are 8,797 under a ratio of

1:2569 for the total national population. In the four counties and cities as

Taichung City, Taipei County, Taichung County and Changhua County

among the current 22 DMUs, their original average population propor-

tions are over 3,000 people with a fi re manpower assigned, and the total

populations of these four counties and cities are 7,618,723 which occupy

about 30% of the total Taiwan population. The research uses the average

population proportion about 1:3000 to calculate fi rstly and the purpose

is going to examine the fi re resource ratio as 1:2569 for the current total

fi refi ghters to the total population nationwide where it is appropriate

or not.

The research begins with setting a benchmark by the proportion

value, index value, of 3,000 people with one fi refi ghter assigned. If the

original average population proportion of each county and city with

a fi refi ghter assigned is over this index value, and also these DMUs

are evaluated as candidate units of the current manpower input and

the value of the average population proportion in the rest non-candi-

date units remains the same. The fi refi ghters of the candidate units in

the current manpower input are assigned by the ratio as 1:3000 and if

the numbers of fi refi ghters is an integer after the calculation, then we

directly uses this integer, otherwise, we round the value into an integer.

At this moment, re-calculate the performance eff iciencies of DMUs’ with

the newly inputted fi refi ghter numbers to determine the candidate units

of the manpower input at the next stage, then by an arithmetic popula-

tion proportion with 500 people, orderly decreasing the proportion until

lower than the minimum bound, i.e. starting from 2500, 2000, and 1500,

and determine the suggested index value with the maximum total ef-

fi ciency of the fi rst stage. At this stage, the research uses the population

proportion 1:2,000 as the allocation basis, where this proportion contrib-

uted the maximal total eff iciency of 2142.72. In addition, the research

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uses the population proportion 1:1500 as the allocation basis where this

proportion contributed the next maximal total eff iciency of 2133.61.

Moreover, the research uses the population proportion 1:2500 as the al-

location basis, where this proportion contributed the third maximal total

eff iciency of 2106.03. Thus, the search range is reduced to between 1,500

and 2,500 at the next stage.

In stage one, the maximal total eff iciency is achieved by a population

proportion 1:2000 and set this proportion as benchmark index value in this

stage. By this benchmark index value, DMUs which are categorized as re-

lated eff icient units and their original average population proportions are

over the benchmark index value and regarded as the candidate units to

add the manpower, then we adjusted the above-mentioned benchmark in-

dex vale by ±100 people, i.e. (2100, 1900); (2200, 1800); (2300, 1700); (2400,

1600), in order to get the total eff iciency vale of each index value within

the range (1500~2500). At this stage, the research uses the population

proportion 1:1900 as the allocation basis which contributed the maximal

total eff iciency of 2155.25. In addition, the population proportion 1:1800

as the allocation basis which contributed the next maximal total eff iciency

of 2145.08. Moreover, the total eff iciency of 2142.72 by population propor-

tion 1:2000, shown in the fi rst stage functions as the third maximal total

eff iciency. Thus, the search range is reduced to between 1,800 and 2,000 at

the next stage.

The maximal total eff iciency is achieved by a population proportion

1:1900 in the previous stage and set this proportion as benchmark in-

dex value in this stage. Based upon this benchmark index value, DMUs

which are categorized as relative eff icient units and their original average

population proportions are over the benchmark index value and they are

regarded as the candidate units to add the manpower. Then we adjust the

above-mentioned benchmark index vale by ±10 people, i.e. (1910, 1890);

(1920, 1880); (1930, 1870); (1940, 1860); (1950, 1850); (1960, 1840); (1970,

1830); (1980, 1820); (1990, 1810), in order to get the total eff iciency vale of

each index value within the range (1800~2000). At this stage, the research

uses the population proportion 1:1990 as the allocation basis which con-

tributed the maximal total eff iciency of 2166.46. In addition, the popula-

tion proportion 1:1980 as the allocation basis which contributed the next

maximal total eff iciency of 2165.28. Thus, the fi nal search range is reduced

to between 1,980 and 2,000 at the next stage.

The maximal total eff iciency is achieved by a population proportion

1:1990 in the previous stage and set this proportion as benchmark index

value in this stage. Based upon this benchmark index value, DMUs which

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are categorized as relative eff icient units and their original average popu-

lation proportions are over the benchmark index value are regarded as

the candidate units to add the manpower, and then we adjust the above-

mentioned benchmark index vale by ±1 people, i.e. (1991, 1989); (1992,

1988); (1993, 1987); (1994, 1986); (1995, 1985); (1996, 1984); (1997, 1983);

(1998, 1982); (1999, 1981), in order to get the total eff iciency vale of each in-

dex value within the range (1980~2000). At this stage, the population pro-

portion 1:1981 contributes the maximal entire total eff iciency of 2167.72.

Therefore, the suggested population proportion 1:1981 is determined by

applying the proposed TEBSA and the detailed information are shown in

Appendix 4.

While a DMU owns the smaller output of production, the input of

its manpower should be less. On the other hand, when a DMU owns

the higher output of production, the input of its manpower should be

larger in order to properly handle the arduous and complicate fi re duties.

According to the above discussion on the computational results, the pop-

ulation proportion to one fi refi ghter assigned (1:1981) is the suggested

proportion for handling the current situation in Taiwan. The proportion

has a discrepancy of 2936 fi refi ghters, as compared to the current num-

ber of fi refi ghters nationwide, and is larger than the number of currently

permitted fi refi ghters, which is 1779. As shown, the discrepancy of man-

power support has reached the budgeted quota according to the exist-

ing laws and regulations, and it satisfi es the manpower demand forecast

and the supplements of the manpower quota. To achieve the equilibrium

of the total productivity and completion of the fi refi ghting purpose, the

actual demand for nationwide fi re organization is computed as 11733

fi refi ghters, and suggested population proportion (1:1981) can make

the ration of 10000 persons from 3.92 to 5.2, and closes the gap as com-

pared with other countries. This study made adjustment on the future

manpower allocation based on the eff iciency rate obtained from output

variables, and conducted 5-year medium to long term manpower allo-

cation, budget planning, and procurement of fi re engines based on the

scale discrepancy. It also provided adjustment on the reasonable work-

ing hours for fi refi ghters after the manpower compensation is completed.

The method could be used as a reference to improve the eff iciency of fi re

bureau when the manpower allocation plan is conducted. The manpower

under the current governmental organization, the estimated manpower

of the government, current manpower, and the suggested manpower are

as shown in Appendix 5.

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6. Conclusions and suggestions

Performance evaluation has become one of the key topics in

management sciences both in public and private organizations, as better

performance is a guarantee of good management [34]. In order to achieve

organizational goals and/or mission statements, improve organizational

eff iciency, and increase motivation, performance evaluation has become

one of the key strategies. If the resources were not allocated reasonably, it

would infl uence the eff ectiveness, eff iciency and productivity within the

organization. The proposed TEBSA will be able to solve the diff icult and

complicated problems encountered in the organization.

Regarding the resource strategy, it is suggested that decision makers

use ORA and TEBSA to allocate resources when the future output trend

is considered. ORA and TEBSA provide decision makers with the guide-

lines for resource adjustment, based on the performance from the DMUs.

When there is a decreasing or steady output trend in the future, the ORA

strategy suggests that those relatively ineff icient DMUs should reduce the

input resources, so resource allocation can be improved. In contrast, when

the future output trend is estimated to be rising, decision makers are re-

quired to increase resources. The proposed TEBSA strategy assists deci-

sion makers to perform a reasonable resource allocation and maximize

overall eff iciencies in eff icient DMUs.

Due to the nature that the fi re service is responsible for the pub-

lic safety, the scale of fi re resources should be taken into consideration

critically. If the input resources of relatively ineff icient departments are

reduced sharply over a short period, public safety will be impacted. Due

to the sharply increasing population rate in Taiwan, there will be heavier

workload for fi re service; decision makers should consider the appropri-

ate scale of fi re resource for each fi re department while performing the

ORA strategy. The proposed performance-based and quantitative fi re

resource allocation method - TEBSA strategy - will play an important role

in the allocation of future fi re protection resources. TEBSA strategy pro-

vides the fi re services a guideline to utilize and allocate their constrained

resources more eff ectively in their jurisdictions. Under the limited fi re

manpower and equipment, the TEBSA strategy helps improve the ef-

fectiveness of emergency response and social resources; it also reduces

the waste of social resources. It is suggested that the fi re departments use

the DEA model, ORA and TEBSA approaches to perform a reasonable

resource allocation. It is proposed that similar methods to be applied to

future comparative studies.

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202 C. H. LAN, L. L. CHUANG, AND Y. F. CHENA

ppen

dix

1Th

e va

lues

of i

nput

and

out

put i

tem

s fo

r eac

h D

MU

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ut1

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ity

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App

endi

x 2

The

prod

uctio

n eff

ici

ency

, the

tech

nica

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icie

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the

scal

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ici

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, and

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retu

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sca

le o

f eac

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reau

Pro

du

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eff i

cien

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eff i

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1

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204 C. H. LAN, L. L. CHUANG, AND Y. F. CHENA

ppen

dix

3Th

e ta

rget

val

ues

and

impr

oved

rang

es o

f inp

ut a

nd o

utpu

t ite

ms

for e

ach

fi re

bure

au. N

ote

that

, (%

) mea

ns

the

cont

ribu

tion

inde

xes

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e B

ure

au

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pu

t 1

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ut

2

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ut

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ut

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tpu

t 1

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ity

1119.5

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ober

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3449.1

3

211.4

3

27291.8

3

5049

898300

(2

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Yil

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156

24314

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15

4162

286

14106

3115

461586

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Hu

ali

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120.6

5

188082.7

53.4

6

7.5

8

1870.9

7

126.2

7

14713

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Tait

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146

304216

63

16

1854

226

9732

1876

238943

(0

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Dow

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at 0

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18

Oct

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201

4


App

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x 4

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tal e

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aft

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P

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A

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A

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peo

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p

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E

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ass

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Ori

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1 fi

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Taip

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ity

1783.4

9

95.4

4%

14

67 (

+o

) 95.4

4%

1467 (

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1467 (

+o

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Kao

hsi

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ity

2331.2

5

100%

648 (

+o

) 100%

648 (

+o

) 100%

756 (

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100%

Kee

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ity

2188.4

2

100%

17

9 (

+o

) 100%

179 (

+o

) 100%

196 (

+17)

100%

Hsi

nch

u C

ity

2111.8

5

100%

185 (

+o

) 100%

185 (

+o

) 100%

196 (

+11)

100%

Taic

hu

ng

Cit

y

3002.2

6

100%

345 (

+1)

100%

414 (

+69)

100%

517 (

+103)

100%

Ch

iay

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ity

1386.2

3

95.1

3%

196 (

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) 95.1

3%

196 (

+o

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196 (

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3%

Tain

an

Cit

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2539.8

84.2

3%

298 (

+o

) 87.1

%

298 (

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) 100%

379 (

+81)

99.1

4%

Taip

ei C

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nty

4048.4

1

100%

1246 (

+323)

100%

1495 (

+249)

100%

1869 (

+37

4)

100%

Tao

yu

an

Co

un

ty

2773.3

3

95.9

5%

678 (

+o

) 96.8

5%

678 (

+o

) 100%

941 (

+263)

98.9

9%

Hsi

nch

u C

ou

nty

1858.6

7

68.8

2%

257 (

+o

) 69.2

2%

257 (

+o

) 73.5

0%

257 (

+o

) 86.4

5%

Mia

oli

Co

un

ty

2477.6

3

70.8

6%

226 (

+o

) 78.2

7%

226 (

+o

) 89.8

3%

226 (

+o

) 100%

Taic

hu

ng

Co

un

ty

3833.6

1

95.4

1%

400 (

+0)

100%

614 (

+214)

94.7

9%

614 (

+0)

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Nan

tou

Co

un

ty

1898.1

2

100%

283 (

+o

) 100%

283 (

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283 (

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) 100%

Ch

an

gh

ua

C

ou

nty

3178.3

2

100%

439 (

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527 (

+88)

100%

658 (

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100%

Dow

nloa

ded

by [

Uni

vers

ity o

f Y

ork]

at 0

8:11

18

Oct

ober

201

4


Yu

nli

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ou

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2350.4

2

75.2

2%

312 (

+o

) 77.3

9%

312 (

+o

) 87.8

5%

312 (

+o

) 100%

Ch

iay

i C

ou

nty

1596.2

8

69.4

9%

349 (

+o

) 69.4

9%

349 (

+o

) 69.4

9%

349 (

+o

) 76.4

2%

Tain

an

Co

un

ty

2658.8

84.3

0%

416 (

+o

) 87.5

9%

416 (

+o

) 100%

554 (

+138)

96.0

8%

Kao

hsi

un

g

C

ou

nty

2701.8

2

91.9

9%

460 (

+o

) 96.7

1%

460 (

+o

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622 (

+162)

97.7

6%

Pin

gtu

ng

Co

un

ty

2824.8

4

83.4

1%

318 (

+o

) 91.7

0%

318 (

+o

) 100%

450 (

+132)

92.7

5%

Yil

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Co

un

ty

2958.8

9

100%

156 (

+10)

100%

185 (

+29)

100%

231 (

+46)

100%

Hu

ali

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ou

nty

2445.7

6

86.5

1%

142 (

+o

) 100%

142 (

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100%

174 (

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Tait

un

g C

ou

nty

1636.6

100%

146 (

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146 (

+o

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146 (

+o

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To

tal

Eff

icie

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--

1996.7

6

--

2044.8

9

--

2106.0

3

--

2142.7

2

Dow

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ded

by [

Uni

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at 0

8:11

18

Oct

ober

201

4


App

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x 4-

2Th

e to

tal e

ff ic

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y ch

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aft

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loca

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com

plet

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at e

ach

stag

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A

dju

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500

A

dju

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900

A

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A

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p

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Us

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Taip

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ity

1745 (

+278)

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1467 (

+0)

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1467 (

+0)

100%

1467 (

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Kao

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un

g C

ity

1008 (

+252)

100%

796 (

+40)

100%

840 (

+44)

100%

760 (

+4)

100%

Kee

lun

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ity

262 (

+66)

100%

207 (

+11)

100%

218 (

+11)

100%

197 (

+1)

100%

Hsi

nch

u C

ity

261 (

+65)

100%

206 (

+10)

100%

218 (

+12)

100%

197 (

+1)

100%

Taic

hu

ng

Cit

y

689 (

+172)

100%

544 (

+27)

100%

574 (

+30)

100%

519 (

+2)

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Ch

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ity

196 (

+0)

99.7

3%

196 (

+0)

95.1

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196 (

+0)

95.1

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196 (

+0)

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3%

Tain

an

Cit

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379 (

+0)

100%

379 (

+0)

100%

379 (

+0)

100%

379 (

+0)

100%

Taip

ei C

ou

nty

2492 (

+623)

100%

1967 (

+98)

100%

2076 (

+109)

100%

1878 (

+9)

100%

Tao

yu

an

Co

un

ty

941 (

+0)

100%

941 (

+0)

100%

941 (

+0)

100%

941 (

+0)

100%

Hsi

nch

u C

ou

nty

257 (

+0)

94.9

7%

257 (

+0)

93.4

9%

257 (

+0)

93.9

8%

257 (

+0)

93.0

7%

Mia

oli

Co

un

ty

374 (

+148)

83.1

7%

295 (

+69)

94.9

9%

312 (

+17)

90.1

7%

282 (

+56)

99.3

7%

Taic

hu

ng

Co

un

ty

1023 (

+409)

89.9

3%

808 (

+194)

96.3

5%

852 (

+44)

93.9

9%

771 (

+157)

99.6

2%

Nan

tou

Co

un

ty

359 (

+76)

100%

283 (

+0)

100%

299 (

+16)

100%

283 (

+0)

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Dow

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ded

by [

Uni

vers

ity o

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at 0

8:11

18

Oct

ober

201

4


Ch

an

gh

ua

C

ou

nty

878 (

+220)

100%

693 (

+35)

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732 (

+39)

100%

662 (

+4)

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Yu

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ou

nty

489 (

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85.6

1%

386 (

+74)

95.3

8%

408 (

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91.8

0%

369 (

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7)

99.4

7%

Ch

iay

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ou

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349 (

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80.3

0%

349 (

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80.0

1%

349 (

+0)

80.1

1%

349 (

+0)

79.9

0%

Tain

an

Co

un

ty

554 (

+0)

100%

554 (

+0)

100%

554 (

+0)

100%

554 (

+0)

100%

Kao

hsi

un

g

C

ou

nty

622 (

+0)

100%

622 (

+0)

100%

622 (

+0)

100%

622 (

+0)

100%

Pin

gtu

ng

Co

un

ty

450 (

+0)

99.9

0%

450 (

+0)

99.9

0%

450 (

+0)

99.9

%

450 (

+0)

99.9

0%

Yil

an

Co

un

ty

308 (

+77)

100%

243 (

+12)

100%

257 (

+14)

100%

232 (

+1)

100%

Hu

ali

en C

ou

nty

232 (

+58)

100%

183 (

+9)

100%

193 (

+10)

100%

175 (

+1)

100%

Tait

un

g C

ou

nty

160 (

+14)

100%

146 (

+0)

100%

146 (

+0)

100%

146 (

+0)

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To

tal

Eff

icie

ncy

–

2133.6

1

–

2155.2

5

–

2145.0

8

–

2166.4

6

Dow

nloa

ded

by [

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vers

ity o

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at 0

8:11

18

Oct

ober

201

4


App

endi

x 4-

3Th

e to

tal e

ff ic

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y ch

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aft

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loca

tion

com

plet

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at e

ach

stag

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A

dju

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980

A

dju

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992

A

dju

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981

p

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1 fi

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1 fi

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Us

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Taip

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ity

1467 (

+0)

100%

1467 (

+0)

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1467 (

+0)

100%

1467 (

+0)

100%

Kao

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un

g C

ity

763 (

+7)

100%

759 (

+3)

100%

762 (

+6)

100%

763 (

+7)

100%

Kee

lun

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ity

198 (

+2)

100%

197 (

+1)

100%

198 (

+2)

100%

198 (

+2)

100%

Hsi

nch

u C

ity

198 (

+2)

100%

197 (

+1)

100%

198 (

+2)

100%

198 (

+2)

100%

Taic

hu

ng

Cit

y

522 (

+5)

100%

519 (

+2)

100%

521 (

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100%

522 (

+5)

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Ch

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ity

196 (

+0)

95.1

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196 (

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95.1

3%

196 (

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196 (

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Tain

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379 (

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382 (

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383 (

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Taip

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1888 (

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1876 (

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1885 (

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100%

1887 (

+18)

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Tao

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Co

un

ty

941 (

+0)

100%

941 (

+0)

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949 (

+8)

99.8

8%

950 (

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0%

Hsi

nch

u C

ou

nty

257 (

+0)

93.1

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257 (

+0)

93.0

7%

257 (

+0)

93.3

8%

257 (

+0)

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4%

Mia

oli

Co

un

ty

283 (

+57)

99.0

2%

282 (

+56)

99.3

7%

282 (

+56)

99.5

1%

282 (

+5

6)

99.5

2%

Taic

hu

ng

Co

un

ty

775 (

+161)

99.1

8%

770 (

+156)

99.7

3%

771 (

+157)

100%

771 (

+157)

100%

Nan

tou

Co

un

ty

283 (

+0)

100%

283 (

+0)

100%

283 (

+0)

100%

283 (

+0)

100%

Ch

an

gh

uaC

ou

nty

665 (

+7)

100%

661 (

+3)

100%

664 (

+6)

100%

665 (

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100%

Dow

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ded

by [

Uni

vers

ity o

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ork]

at 0

8:11

18

Oct

ober

201

4


Yu

nli

n C

ou

nty

371 (

+59)

98.9

6%

369 (

+57)

99.4

7%

369 (

+57)

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6%

369 (

+57)

99.8

4%

Ch

iay

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ou

nty

349 (

+0)

79.9

2%

349 (

+0)

79.9

0%

349 (

+0)

80.2

5%

349 (

+0)

80.3

0%

Tain

an

Co

un

ty

554 (

+0)

100%

554 (

+0)

100%

558 (

+4)

99.8

3%

559 (

+5)

99.8

3%

Kao

hsi

un

g C

ou

nty

622 (

+0)

100%

622 (

+0)

100%

627 (

+5)

99.9

6%

628 (

+6)

99.8

9%

Pin

gtu

ng

Co

un

ty

450 (

+0)

99.9

0%

450 (

+0)

99.9

0%

450 (

+0)

100%

450 (

+0)

100%

Yil

an

Co

un

ty

234 (

+3)

100%

232 (

+0)

100%

233 (

+2)

100%

234 (

+3)

100%

Hu

ali

en C

ou

nty

176 (

+2)

100%

175 (

+1)

100%

176 (

+2)

100%

176 (

+2)

100%

Tait

un

g C

ou

nty

146 (

+0)

100%

146 (

+0)

100%

146 (

+0)

100%

146 (

+0)

100%

To

tal

Eff

icie

ncy

–

2165.2

8

–

2166.5

7

–

2167.6

5

–

2167.7

2

Dow

nloa

ded

by [

Uni

vers

ity o

f Y

ork]

at 0

8:11

18

Oct

ober

201

4


App

endi

x 5

List

s of

man

pow

er u

nder

the

curr

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over

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rgan

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the

budg

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f the

gov

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curr

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anpo

wer

, and

the

sugg

este

d m

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Su

gg

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d m

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po

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Man

po

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un

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fo

r p

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ula

tio

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th

e cu

rren

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ud

get

ed

p

rop

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to

D

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etw

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of

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Us

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man

po

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Taip

ei C

ity

1761

1570

1467

1467

0

Kao

hsi

un

g C

ity

713

668

648

763

11

5

Kee

lun

g C

ity

269

204

179

198

19

Hsi

nch

u C

ity

262

237

185

198

13

Taic

hu

ng

Cit

y

554

453

344

522

17

8

Ch

iay

i C

ity

201

201

196

196

0

Tain

an

Cit

y

468

307

298

383

85

Taip

ei C

ou

nty

1657

1224

923

1887

96

4

Tao

yu

an

Co

un

ty

1044

850

678

950

27

2

Hsi

nch

u C

ou

nty

329

329

257

257

0

Mia

oli

Co

un

ty

389

237

226

282

56

Taic

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420

294

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450

450

414

665

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338

338

312

369

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Ch

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Received January, 2010

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Documents

Optimal human resource allocation model: A case study of Taiwan fire service