Humanizing The Traffic Police Assignment Case Of Taipei

1. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
Humanizing the Traffic Police Assignment: Case of Taipei
Yi-San HUANG
Deputy Chief
Zhongzheng Second Police District, Taipei
City Police Department, TAIWAN
Tel: (886-2)2375-1875
Fax: (886-2)2375-1780
Email: goodgood31@yahoo.com.tw
Lawrence W. LAN
Chair Professor, Department of Marketing and
Logistics Management, Ta-Hwa Institute of
Technology, TAIWAN
Emeritus Professor, National Chiao Tung
University, TAIWAN
Tel: (886-3)592-7700 ext. 3210
Fax: (886-2)2337-5755
Email: lawrencelan@thit.edu.tw
Yu-Kai HUANG
Assistant Professor
Institute of Publishing and Culture Enterprise
Management, Nanhua University, TAIWAN
Tel: (886-5)272-1001 ext. 2521
Email: osilo.huang@gmail.com
Abstract. Most of the traffic police assignment practices in Taiwan are based on experiential
rules. Without an in-depth analysis, the prevailing practices may lead to overstaffing or unfair
duties loading among the police. To rectify the shortcomings, this paper develops a linear
programming (LP) model to solve the traffic police assignment problem. The core logic of the
proposed model is to adjust the current work shifts in a reasonable manner and then schedule
the available police manpower to various time intervals. For demonstration, the proposed LP
model is applied to Da-an Precinct in Taipei. The results showed that it can save up to 16% on
the existing deployable police force or 9% on the total police staff in the case precinct. Future
directions for traffic police assignment are elaborated.
Key words: linear programming; traffic police assignment
1. INTRODUCTION
Traffic police assignment is in essence a resource allocation problem—a problem of searching
for optimal deployment of limited resources. Traditionally, operations research has played an
important role in the optimal deployment of limited resources encompassing labors, assets,
materials, or capitals used to accomplish a single-goal or multi-goals. The best or optimal
solutions may mean maximizing profits, minimizing costs, or achieving the best possible
quality. Some recent researchers have endeavored to adopting goal programming for solving
single- or multi-objective resource allocation problems (e.g., Charnes and Collomb, 1972;
Flavell, 1976; Lee et al., 1979; Martel and Aouni, 1990; Tamiz et al., 1998; Romero, 2001;
Cheng and Tzeng, 2003). Moreover, fuzzy set theory combined with other algorithms like
two-phase approach, genetic annealing, hybrid genetic algorithm and ant colony optimization,
are also found to tackle multi-objective resource allocation problems (Konno and Ishii, 1995;
Ida and Gen, 1997; Abboud et al., 1998; Nishizaki and Sakawa, 1999; Sakawa et al., 1999,
2001; Chen and Tzeng, 2000; Wu, 2007; Lin and Gen, 2007; Chaharsooghi and Meimand
Kermani, 2008). In fact, the resource allocation problem-solving algorithms have a variety of
applications including product allocation (Hou and Chang, 2004), portfolio optimization
(Ehrgott et al., 2004), optimal scheduling for enterprises (Yan et al., 2005, 2007, 2008),
capital or project budgeting (Luss and Gupta, 1975), software testing (Dai et al., 2003), health

2. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
care resource allocation (Johannesson and Weinstein, 1993), processor allocation or job shop
scheduling (Ernst et al., 2001), and among others.
The optimal traffic police assignment problem involves with minimum manpower and
personnel assignment issues. Minimum manpower is to search for the minimum numbers of
police needed; whereas personnel assignment is to develop the efficiency of personnel
scheduling with limited police to achieve the maximal effectiveness of police dispatching to
duties in different time intervals along with different working shifts. In the past, several
researchers have developed methods to survey the police deployment or to determine the
optimal police district/patrol areas (e.g., Chaiken and Dormont, 1978; Kern, 1989; Taylor and
Huxley, 1989; D’Amico et al., 2002; Moonen, 2005; Curtin et al., 2005; Sharma and Ghosh,
2007). More recently, some others have dedicated to improve the efficiency of police crew
scheduling (e.g., Tseng, 2000; Tseng and Yang, 2001; Tseng et al., 2001, 2002; Tsay et al.,
2003; Yan et al., 2003). The aforementioned studies have pointed out that police duties are
quite different from ordinary business activities and thus police allocation and deployment
problems still deserve further exploration.
In most countries, keeping traffic moving and quick response to traffic incidents are the two
major duties for traffic police. In some countries, traffic police also take such duties as
reception/guard, traffic laws enforcement, and office work/stand-by. The fundamental of
traffic police assignment can be regarded as deploying available police staff into different
time intervals with reasonable shifts so as to complete all duties. Most of the traffic police
assignment practices in Taiwan, however, are based on previous experiences. Without an
in-depth analysis, the practical experiences may lead to unnecessary overstaffing or unfair
duties loading among the police. For instance, the current practices in Taipei City assigning
one or two lines of traffic police to investigate any single traffic collision can be problematic.
The current practices simply fail to answer the minimum number of traffic police needed.
Since the work shifts of traffic police are regulated and their duties are complex in nature,
assigning traffic police into various time intervals within reasonable work shifts is a
challenging issue. It is worthwhile to develop a scientific modeling approach to look into the
problem and to find out how we can improve the current practices.
In view of the stipulated limitations on the traffic police duties and work shifts, this study
aims to propose a linear programming model to search for an optimal allocation of traffic
police within reasonable work shifts. The traffic police duties are analyzed so that the
proposed model can be more in line with the real feasibility. The remaining parts of this paper
are organized as follows. Section 2 introduces the current practices of traffic police duties in
Taipei. Section 3 proposes the model formulation. Section 4 presents a case study of Taipei’s
Da-an Traffic Police Precinct. Conclusions and directions for future studies are addressed in
the final section.
2. THE PRACTICES
The Guideline of Police Duty in Taiwan roughly divides the police’s day-of-time duties into
three time slots: early-hours duty (00:00 a.m. - 06:00 a.m.), daytime duty (06:00 a.m. - 18:00
p.m.), and nighttime duty (18:00 p.m. - 24:00 p.m.). The Guideline applies to traffic police as
well. However, the number of police staff, the time slots, and the day-of-time duties may vary
from precinct to precinct, depending on geographical location. In metropolitan areas where
recurrent and non-recurrent traffic congestions usually emerge every working day, it requires

3. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
more traffic police than other geographical locations such as rural, mountainous, and offshore
areas. In Taiwan, traffic police generally take two major duties—traffic control/patrol and
collision investigation and other minor duties—reception, guard, traffic laws enforcement,
office documentation, and stand-by at office. Take Da-an Traffic Precinct in Taipei City as an
example, the current practices of each duty are explained as follows.
2.1 Traffic Control/Patrol
Traffic control/patrol is one of the main duties for traffic police in Taiwan. In order to keep
traffic moving smoothly, some traffic police are deployed standing at fixed points within the
precinct to monitor/control the traffic during peak hours, while others are dispatched to patrol
the potential roadway incidents during off-peaks. In Da-an Precinct, traffic police also require
investigating the level-of-service of main roads monthly. Normally, one person will be
deployed at each main intersection to monitor the traffic streams, while two to four people
will be dispatched to patrol along the main roadways to monitor the likely traffic incidents. It
should be noted that the number of traffic police charging for this duty in the morning peak
hours may not be the same as that in the evening peak hours because of the distinct traffic
patterns. Currently, ten policemen are deployed in the morning peak hours for traffic
control/patrol duty, whereas eleven policemen undertake the same duty in the evening peak
hours. The detailed sites and personnel are presented in Table 1.
Table 1 Traffic police deployment for traffic control/patrol in Da-an Precinct
Site (intersection/section)
Morning
peak hours
Evening
peak hours
Duty type
Intersection of Zhongxiao E.
Rd. and Fuxing S. Rd.
0 1 Traffic control
Intersection of Zhongxiao E.
Rd. and Dunhua S. Rd.
0 1 Traffic control
Intersection of Ren’ai Rd. and
Dunhua S. Rd.
0 1 Traffic control
Intersection of Xinyi Rd. and
Xinsheng N. Rd.
1 0 Traffic control
Intersection of Xinyi Rd. and
Dunhua S. Rd.
1 1 Traffic control
Intersection of Keelung Rd.
and Leye St.
1 1 Traffic control
Intersection of Heping E. Rd.
and Dunhua S. Rd.
1 1 Traffic control
Intersection of Keelung Rd.
and Xinhai Rd.
1 1 Traffic control
Ln. 175, Sec. 3, Xinhai Rd. 1 0 Traffic patrol
Section of Ren’ai Rd. 1 1 Traffic patrol
Section of Xinyi Rd. 1 1 Traffic patrol
Section of Zhongxiao E. Rd. 1 1 Traffic patrol
Section of Heping E. Rd. 1 0 Traffic patrol
Section of Xinhai Rd. 0 1 Traffic patrol
Total 10 11
Source: Taipei City Traffic Police Division (2009)
2.2 Collision Investigation
Collision investigation is another main duty for traffic police in Taiwan. Traffic police

4. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
investigate all types of traffic-related accident, which are further categorized into three classes
depending on the severity: fatal (A1), injured (A2) and property-damaged only (A3). Drivers
involved with a collision normally anticipate the traffic police arriving at the scene as soon as
possible. The traffic police are responsible for recording the relevant evidences at the scene,
which can serve as the liabilities for the involved parties. In Da-an Precinct, once an accident
is reported, two people are dispatched as the first line to process the collision investigation. If
the first line is not enough to investigate serious accidents or chain collisions, a second line
would be dispatched. In addition to the collision investigation, the police taking on this duty
normally require actively patrolling around their precinct.
The traffic collision information are collected and analyzed on a seasonal basis (March, June,
September and December) by the Taipei City Police Department (TCPD). In 2009, a total of
24,792 accidents have been investigated but only 14,947 cases have complete information
including the processing time. Table 2 shows the average investigation time for each class of
collision in different time intervals in Taipei City. Of the 14,947 cases, 2,900 cases occurred in
Da-an Precinct and the corresponding average investigation time is presented in Table 3. Note
that the investigation time for each collision is the sum of response time to the scene,
processing time at the scene, and the following administrative time afterward. It is noted that
the average investigation time of fatal accident is longer than that for investigating other
classes of accident.
Table 2 The average time for collision investigation in Taipei City (hr:min)
Collision Class
Early-hours
(00:00-06:00)
Morning
(06:00-12:00)
Afternoon
(12:00-18:00)
Nighttime
(18:00-24:00)
Average
investigation
time
03:06 02:26 02:34 02:51
Fatal
(A1)
No. of case 13 4 7 14
Average
investigation
time
02:11 01:38 01:48 02:12
Injury
(A2)
No. of case 711 621 708 1,662
Average
investigation
time
01:52 01:11 01:17 01:46
Property-
damaged
only (A3)
No. of case 904 3,087 3,772 3,444
Average
investigation
time
02:09 01:16 01:22 01:55
Overall
No. of case 1,628 3,712 4,487 5,120
Source: Taipei City Police Department (2009)

5. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
Table 3 The average time for collision investigation in Da-an Precinct (hr:min)
Collision Class
Early-hours
(00:00-06:00)
Morning
(06:00-12:00)
Afternoon
(12:00-18:00)
Nighttime
(18:00-24:00)
Average
investigation
time
03:09 03:51 03:13 02:41
Fatal
(A1)
No. of case 4 1 2 5
Average
investigation
time
02:05 01:40 02:10 01:51
Injury
(A2)
No. of case 175 151 149 272
Average
n
e
investigatio
tim
02:03 01:51 02:01 01:58
Property-
damaged only
(A3)
No. of case 346 448 556 791
Average
investigation
time
02:04 01:48 02:03 01:56
Overall
No. of case 525 600 707 1,068
Source: Taipei City Police Department (2009)
2.3 Reception/Guard
Police provide services to the general public as well as to their colleagues. Some must be
equipped with police outfit including guns, radios and cars when on duty. They take turns to
accept the public reports/inquiries. Traffic police take the same assignments as well. In Da-an
Precinct, the minimum number of traffic police in charge of reception/guard is one person per
two or four hours. During 07:00 a.m. - 23:00 p.m., an additional person is added to help this
duty because one person is considered too busy to handle the frequent reports/inquiries from
the public in this precinct.
2.4 Traffic Law Enforcement
Law enforcement conducted by traffic police in Taiwan can be roughly divided into two kinds:
regular enforcement and temporary enforcement. Traffic police exercise the regular
enforcement almost everyday, mainly for clamping down on traffic laws violation, such as
red-light runners, speeding, drunken drivers, double parking or road blocks (e.g., putting junk
to occupy parking spaces). Sometimes traffic police exercise temporary enforcement for
education purposes, such as enforcing the seat belt usage, educating the violated pedestrians.
During big events or special activities (e.g., demonstrations), traffic police and regular police
are required taking on temporary enforcement, too. In view of the growth of restaurants and
entertainments (night activities) in Da-an Precinct, an intensive enforcement on drunken
driving has been exercised regularly. The drunken driving enforcement is implemented by
four traffic police as a team. Other types of traffic law enforcement can be deployed with one
or two police.
2.5 Office Work/Stand-by
Traffic police handle the office documentation and stand by in office to tackle any potential
emergencies. Normally, one or two police are enough to do the office work and their working
time is from four hours to eight hours. The minimum number of stand-by police is one person
for each shift. In Da-an Precinct, the patrolling police are sometimes assigned to deal with the
emergencies or resident reports whenever the number of office stand-by police is insufficient.

6. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
3. THE MODEL
This study develops a linear programming (LP) model that optimally assigns the traffic police
to various time intervals and work shifts within a traffic precinct. The objective is to minimize
the number of traffic police while providing sufficient services to the public as well as
meeting all of the stipulations of the Guideline.
3.1 Basic Principles
Stipulated to the Guideline, some basic principles and/or limitations must be complied with as
follows:
1. Traffic police are on duties within a twelve-hour period rather than a continuous
eight-hour period to avoid overloaded.
2. Traffic police normally work eight hours a day and take two days off a week.
3. Each time interval of any duty is a multiple of even number; namely, two hours, four
hours or six hours. However, shifts can begin at even or odd o’clock. In this study, each
shift will begin at odd o’clock.
4. Cost for traffic police would not vary with personnel, working time intervals or types of
duty.
5. Duties in early hours (01:00 a.m. - 07:00 a.m.) are allowed to last for continuous four
hours at most, because of high energy consumption. Duties in other time intervals can be
scheduled more flexibly, lasting for two to six hours.
6. Each traffic police must finish a duty throughout a shift; namely, one person cannot be
assigned to two types of duty in one shift.
7. The personnel required for collision investigation is estimated from eq. (3).
Let represent the average number of various collisions in a precinct per day,
represent the number of investigators, and denote the average investigation time, wherein
t represents time intervals (early-hours, morning, afternoon or nighttime); a represents
accident type (A1, A2, or A3). Then the overall man-hours T for investigating the collisions
can be expressed as:
t
a
N a
P
t
a
T
∑ ×
×
=
a
t
t
a
a
t
a T
P
N
T
,
(1)
Because the duty time for each traffic police is given (in this study, eight hours), the
minimum number of police who investigate the daily collisions ( ) can be calculated as:
P
T
min
P
P
T
T
P =
min (2)
If the factor of regular training and vacation leaves in a year is further considered, the value
should be multiplied by a manpower adjustment factor (MAF), which is 1.58, according
to Tseng and Yang (2002). Then we have the modified value which is closer to the
personnel needed in practice, shown as follows.
min
P
min
*
P
MAF
P
P ×
= min
min
*
(3)
The value should be rounded up to an integer value if it is with decimal fraction.
min
*
P
3.2 An Initial Model
Let represent the number of traffic police assigned to time interval i, shift j (i = 1-12 and
ij
X

7. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
j = 1-8) and denote the minimum number of police needed for time interval i. The
problem is to determine the number of traffic police assigned to the shifts within the time
intervals each day so as to minimize the total personnel, subject to the necessary duties
described in Section 2 and the basic principles and limitations listed in Section 3.1. As above
mentioned, each shift will begin at odd o’clock in this study. The complete twelve time
intervals and eight shifts are displayed in Table 4.
i
P
Table 4 The initial model framework
Shift
Time
Interval 1 2 3 4 5 6 7 8
Minimum number
of police needed
01-03 X11 P1
03-05 X21 X22 P2
05-07 X31 X32 X33 P3
07-09 X41 X42 X43 X44 P4
09-11 X51 X52 X53 X54 X55 P5
11-13 X61 X62 X63 X64 X65 X66 P6
13-15 X72 X73 X74 X75 X76 X77 P7
15-17 X83 X84 X85 X86 X87 X88 P8
17-19 X94 X95 X96 X97 X98 P9
19-21 X105 X106 X107 X108 P10
21-23 X116 X117 X118 P11
23-01 X127 X128 P12
A complete LP for the initial model can be formulated as follows:
Minimize (4a)
8
,
,
2
,
1
, L
=
∑ j
i
Xij
Subject to
∑
=
=
≥
i
j
i
ij i
P
X
1
12
,
,
2
,
1 L (4b)
1
3
,
2
,
1 +
=
=
= j
i
j
X
X jj
ij (4c)
∑
+
+
=
=
=
2
3
3
,
2
,
1
2
i
i
jj
ij j
i
j
X
X (4d)
∑
+
+
=
=
=
4
1
7
,
6
,
5
,
4
3
i
i
jj
ij j
i
j
X
X (4e)
∑
+
+
=
=
=
3
1
8
3
i
i
jj
ij j
i
j
X
X (4f)
∑
+
+
=
=
<
2
1
8
,
7
,
6
,
5
,
4
3
i
i
jj
ij j
i
j
X
X (4g)
5
,
4
,
3
,
2
,
1
7
,
6
,
5
,
4 +
+
+
+
+
=
=
≤ j
j
j
j
j
i
j
X
X jj
ij (4h)
4
,
3
,
2
,
1
8 +
+
+
+
=
=
≤ j
j
j
j
i
j
X
X jj
ij (4i)
5
,
4
,
3
3
,
2
,
1 +
+
+
=
=
≤ j
j
j
i
j
X
X jj
ij (4j)
2
3
,
2
,
1
0 +
=
=
= j
i
j
Xij (4k)

8. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
Explanation of constraints:
1. Eq. (4b) represents the number of police on duty greater than or equal to the minimum
number of police needed.
2. Eq. (4c) represents the duties in early-hours (01:00 a.m. - 07:00 a.m.) scheduled in
continuous four hours.
3. Eq. (4d) and Eq. (4k) represent traffic police who begin at work in early-hours (shift 1,
shift 2 or shift 3) can work for four hours continuously, take a break for two or four hours,
and then work again. Or, they can work four hours, part of them take a break for two
hours and others take a break for four hours, and then work again.
4. Eq. (4e) through Eq. (4g) represent police starting at work in the day time (shift 4 through
shift 8). They can, within a twelve-hour period, take two or four hours off for the rest and
then work again till finishing their eight-hour daily jobs. They are not allowed to work
continuous eight-hours.
5. Eq. (4h) through Eq. (4j) represent the number of police assigned to each shift at the
beginning time interval greater than or equal to the number of working polices at the later
time intervals.
The initial model encompassing eight shifts seemed feasible in theory, but the optimal
solutions come out some unreasonable results (e.g., zero or one traffic police being assigned
to some certain time intervals), which are neither practical nor prevailing use in most traffic
police precincts in Taipei. In other words, the results of initial model may not be accepted by
the traffic police. Therefore, this study further combines a part of the shifts to be more in line
with the current practical operation. First, the starting time interval is modified to 07:00 a.m. -
09:00 a.m. because 07:00 a.m. is the beginning of morning peak hours in Taipei city for
workdays. It is also convenient for most traffic police to start at work to control traffic at
major intersections in the morning peak-hours. Next, in consideration of the characteristics of
Da-an Precinct, the number of police at the beginning of each shift is modified to no less than
three people, but no more than fifteen.
3.3 A Refined Model
Based on the above two modifications, five shifts are created, instead of eight shifts, and a
refined model is formulated. The complete twelve time intervals and five shifts are displayed
in Table 5.
Table 5 The refined model framework
Shift
Time
Interval 1 2 3 4 5
Minimum number of
police needed
07~09 X1 X5 P1
09~11 AX1 X5 P2
11~13 BX1 X2 P3
13~15 CX1 AX2 P4
15~17 DX1 BX2 X3 P5
17~19 EX1 CX2 AX3 P6
19~21 DX2 BX3 X4 P7
21~23 EX2 CX3 AX4 AX5 P8
23~01 DX3 BX5 P9
01~03 EX3 BX4 CX5 P10
03~05 X4 DX5 P11
05~07 X4 P12

9. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
Note: X1-X5 are the number of police on duty at various shifts. A-E represent the number of
police on duty altering flexibly after the beginning of each shift. P1-P12 denote the
minimum number of police needed at various time intervals.
A complete LP for the refined model can be formulated as follows.
Minimize (5a)
∑ = 5
,
4
,
3
,
2
,
1
i
Xi
Subject to
1
5
1 P
X
X ≥
+ (5b)
2
5
1 P
X
AX ≥
+ (5c)
3
2
1 P
X
BX ≥
+ (5d)
4
2
1 P
AX
CX ≥
+ (5e)
5
3
2
1 P
X
BX
DX ≥
+
+ (5f)
6
3
2
1 P
AX
CX
EX ≥
+
+ (5g)
7
4
3
2 P
X
BX
DX ≥
+
+ (5h)
8
5
4
3
2 P
AX
AX
CX
EX ≥
+
+
+ (5i)
9
5
3 P
BX
DX ≥
+ (5j)
10
5
4
3 P
CX
BX
EX ≥
+
+ (5k)
11
5
4 P
DX
X ≥
+ (5l)
12
4 P
X ≥ (5m)
( ) 3
,
2
,
1
3 =
=
+
+
+
+ i
X
X
E
D
C
B
A i
i (5n)
4
4
)
( X
X
B
A =
+ (5o)
( ) 5
5 2X
X
D
C
B
A =
+
+
+ (5p)
( ) 3
,
2
,
1
3 =
<
+
+ i
X
X
C
B
A i
i (5q)
D
C
B
A
k
i
X
kX i
i ,
,
,
5
,
3
,
2
,
1 =
=
≤ (5r)
3
,
2
,
1
=
≤ i
X
EX i
i (5s)
5
,
4
,
3
,
2
,
1
15 =
≤ i
Xi (5t)
5
,
4
,
3
,
2
,
1
3 =
≥ i
Xi (5u)
Explanation of constraints:
1. Eq. (5b) - Eq. (5m) represent the number of police on duty greater than or equal to the
minimum number of police needed.
2. Eq. (5n) represents the police starting at work in the day time (shift 1 - shift 3). Part of them
can choose, within continuous twelve hours, to take a two-hour break, while others take a
four-hour break, and they then work again till finishing the eight-hour daily duties.
3. Shift 4 assigns the police to work from 19:00 p.m. to 07:00 a.m. next day and Eq. (5o)
represents the police working in this shift taking a rest after on-duty for two or four hours.
Shift 5 assigns the police to work at two separated time intervals, from 07:00 a.m. to 11:00
a.m. and from 21:00 p.m. to 05:00 a.m. next day. Eq. (5p) represents the police who follow
shift 5 must work four hours in the morning and get through the remaining four-hour duty
at night after taking a twelve-hour rest. Likewise, within the eight-hour period at night,
some police can take a two-hour break, while others take a four-hour break, and they then
work again.
4. Eq. (5q) represents the police not allowed working eight hours continuously.
5. Eq. (5r) and Eq. (5s) represent the number of police assigned to each shift at the beginning

10. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
time interval greater than or equal to the number of police work at the later time intervals.
6. Eq. (5t) and Eq. (5u) represent the number of police working at the beginning of each shift
no less than three people but no more than fifteen.
4. CASE STUDY
A case study of traffic police assignment in Da-an Traffic Police Precinct, Taipei is
demonstrated. Currently, the total traffic police staff in this precinct is seventy-eight. Of them,
twenty-two staff have regular days-off, seven take turns on annual leave, one takes regular
training course, three transfer to other departments for duties support, and two senior officers
are responsible for assigning the personnel and managing the shifts. Therefore, only
forty-three police are available for deploying the duties assignment in this case study.
4.1 Minimum Traffic Police
To obtain practical results, an in-depth analysis on the collision investigation with
consideration of local traffic accident characteristics is first performed. According to Eq. (1)
and Eq. (2), the minimum police force needed for collision investigation at various time
intervals is calculated in Table 6. In Da-an Precinct, 982 light collisions were reported in 2009
but with no detailed investigation time information because the drivers have reconciled after
consulting with the arrived traffic police. Since the police have spent time to handle them, a
constant of twenty-five minutes will be used to represent the average investigation time for
such light collision case.
Table 6 Minimum police force needed for collision investigation in Da-an Precinct
Interval
( )
t
Collision
type
(a)
Average
number of
collisions
( )
t
a
N
Number of
default
investigators
( )
a
P
Average
investigation
time
( )
t
a
T
Average
person-hrs
per day
(T )
Minimum
police
force needed
( )
min
P
A1 0.03 2 3.15 0.19
A2 1.43 2 2.08 5.95
A3 2.83 2 2.05 11.60
Early hours
(00:00~
06:00)
Total - - - 17.74
3
A1 0.01 2 3.85 0.06
A2 1.24 2 1.67 4.14
A3 3.67 2 1.85 13.58
Morning
(06:00~
12:00)
Total - - - 17.78
3
A1 0.02 2 3.22 0.13
A2 1.22 2 2.17 5.29
A3 4.56 2 2.02 18.42
Afternoon
(12:00~
18:00)
Total - - - 23.85
4
A1 0.04 2 2.68 0.21
A2 2.23 2 1.85 8.25
A3 6.48 2 1.97 25.53
Nighttime
(18:00~
24:00)
Total - - - 34.00
5
The minimum police force needed in Da-an Precinct under normal circumstance is estimated
as follows:
1. At least ten and eleven police are assigned to control traffic and patrol in their precinct in
the daily two peak hours.

11. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
2. Collision investigation requires at least three to five policemen in each time interval,
according to Table 6.
3. Traffic enforcement on drunken driving, speeding, among others requires at least six or
seven police.
4. For other duties, such as reception/guard and office/stand-by, each duty demands one or
two people to take turns.
Accordingly, the minimum police force needed in each time interval is presented in Table 7.
This table only presents the number of police taking turns on various duties; it does not reveal
which time intervals to dispatch the personnel to work. The problem of deploying police into
each time interval depends upon the characteristics of precinct. For instance, the enforcement
of drunken driving in Da-an Precinct should be conducted at nighttime rather in the daytime.
In contrast, the enforcement of speeding in this precinct should be at non-peak hours or at
nighttime.
Table 7 The minimum traffic police force needed for different duties in different time intervals
in Da-an Precinct
Duty 7-9 9-11 11-13 13-15 15-17 17-19 19-21 21-23 23-1 1-3 3-5 5-7
Reception and
guard
2 2 2 2 2 2 2 2 1 1 1 1
Traffic control 6 0 0 0 0 7 0 0 0 0 0 0
Collision
investigation
4 4 4 4 4 4 6 6 6 6 3 3
Traffic patrol 4 4 2 2 2 4 2 0 0 0 0 0
Enforcement of
drunken driving
0 0 0 0 0 0 0 0 4 4 0 0
Enforcement of
speeding
2 2 2 2 2 2 0 0 0 0 0 0
Other enforcement 0 1 1 1 1 1 1 0 0 0 0 0
Office work 0 2 2 2 2 0 0 0 0 0 0 0
Total personnel 18 15 13 13 13 20 11 8 11 11 4 4
4.2 Optimal Traffic Police
Table 8 presents the model results solved by the computer software LINGO. From Table 8, it
is noted that the optimal numbers of police at 21:00 p.m. - 23:00 p.m., 03:00 a.m. - 05:00 a.m.
and 05:00 a.m. - 07:00 a.m. respectively require one more person than the minimum police
force calculated in Table 7. The optimal numbers of police at other periods are the same as the
minimum police force presented in Table 7. The figures in Table 7 should serve as the lower
bound of the police force needed; whereas the figures in Table 8 are regarded as the optimal
solution for Da-an Precinct. We note that some police resting for a while after on-duty for two
or four hours can be deployed to other duties such as stand-by to tackle potential emergencies.
Accordingly, the optimal number of traffic police is thirty-six in contrast to forty-three,
namely seven traffic police can be saved after implementing our refined LP model.

12. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
Table 8 The optimal numbers of traffic police in different time intervals/work shifts
Shift
Time
Interval 1 2 3 4 5
Total
Minimum police force
needed from Table 7
07-09 8 10 18 18
09-11 5 10 15 15
11-13 3 10 13 13
13-15 3 10 13 13
15-17 6 4 3 13 13
17-19 7 10 3 20 20
19-21 6 0 5 11 11
21-23 0 3 1 5 9 8
23-01 3 8 11 11
01-03 0 4 7 11 11
03-05 5 0 5 4
05-07 5 5 4
4.3 Comparison with the Current Practices
Table 9 presents the current traffic police duties assignment in Da-an Precinct, which is based
on experiential rules. Compared with Table 7 and Table 8, it is noted that the traffic police
charging for traffic control duty at the morning/evening peak hours are eleven/thirteen people
in practice, which are five to six people exceeding the minimum number of police actually
needed. The number of collision investigation at 07:00 a.m. - 11:00 a.m. and 15:00 p.m. -
19:00 p.m. are eight and six police in practice, which are also two to four people more than
the optimal number of police (four people) solved by the model. However, the optimal
number of collision investigators derived from the model is six people deployed at 19:00 p.m.
- 03:00 a.m., which is two police more than the current practice; moreover, three investigators
are allocated at 03:00 a.m. - 07:00 a.m. by the model, which is one police exceeding the
current practice. The above gaps indicate that the LP model can appropriately assign traffic
police to various duties in various time intervals; whereas the current practices adopted in
Da-an Precinct have over-assigned the traffic police force in peak hours.
Table 9 The current practice of traffic police duties assignment in Da-an Precinct
Duty 7-9 9-11 11-13 13-15 15-17 17-19 19-21 21-23 23-1 1-3 3-5 5-7
Reception and
guard
2 2 2 2 2 2 2 2 1 1 1 1
Traffic control 11 0 0 0 2 13 8 1 1 0 0 0
Collision
investigation
8 8 4 4 6 6 4 4 4 4 2 2
Traffic patrol 0 4 0 0 0 0 0 0 0 0 0 0
Enforcement of
drunken driving
0 0 0 0 0 0 0 0 4 4 0 0
Enforcement of
speeding
0 2 2 2 0 0 0 0 2 2 0 0
Other enforcement 0 6 0 0 0 0 0 0 0 0 0 0
Office 2 4 4 4 4 0 0 0 0 0 0 0
Total 23 26 12 12 14 21 14 7 12 11 3 3
The saving of police force derived from the proposed model mainly comes from the

13. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
over-deployment of traffic police in peak hours. It reflects a common phenomenon in Taipei
that most police departments have put too much manpower in peak hours and thus in turn
leading to a shortage of personnel in the ordinary time periods. The lacks of adequate
manpower in ordinary time periods oftentimes cause the delay of police arrival at the scene
upon a call-out for investigating an accident. It is imperative to keep balanced police force in
both peak hours and ordinary time periods.
The proposed LP model has demonstrated a satisfactory traffic police assignment to various
time intervals with reasonable working shifts, which not only fulfills all duties required but
also stipulates to the Guidelines. Through the in-depth understanding of traffic police duties
and the shifts regulation, not only the minimum numbers of police taking turns for various
shifts can be created, but the optimal allocation to various time intervals can also be obtained.
The results showed that the Da-an Traffic Police Precinct itself can save as high as seven
police manpower, representing a 16% (7/43) saving in terms of existing available police staff
or a 9% (7/78) saving in terms of total police staff in Da-an Traffic Police Precinct. It implies
that the traffic police assignment based on previous experiences do exhibit overstaffing
problems. As a consequence, if applying our model to the remaining precincts of Taipei City
or even applying to the traffic police precincts in Taiwan, it is believed that we can save
considerable number of traffic police staff while still completely fulfilling the current duties.
5. CONCLUSIONS
The office duty and traffic management duty for traffic police are rather rigid, which need to
be accomplished from beginning to end. However, other duties can be done with flexibility
from one shift to another or by more than one person. For example, personnel who are
responsible for collision investigation can also be assigned to patrol or to enforce traffic law
in their precinct when no traffic accidents occur. Traffic police who control traffic in daily
peak hours can be one or two people at some congested intersections. One police can be
assigned to control traffic at one intersection and the other police aids to control traffic by
patrolling. Allowing the vigilantes to assist traffic control at some intersections is another
practical solution so that the uniformed police can monitor traffic by patrolling along the main
roads. Furthermore, a group of police can be assigned to patrol around a small area to flexibly
control the traffic instead of standing at some fixed points. All the above tactics have been
adopted in the proposed LP model to be more flexibly assigning the traffic police aiming for
greater efficiency of manpower resource. The results showed that the Da-an Traffic Police
Precinct itself can save seven police manpower, representing 16% saving on existing available
police or 9% saving on total police manpower in the case study precinct.
In the future study, some constraints can be released in the model. For instance, those who
take on collision investigation duty could be assigned to patrol and/or enforce traffic law; but
not the other way around because collision investigation is a specialized subject acquiring a
license. In addition, different types of duty (e.g., traffic control and traffic patrol) can be
switched or swapped with each other, which will lead to different assignment results. The
minimum number of collision investigators, calculated by average number of various collision
types and average investigation time, could be smaller than actually needed, provided that the
factor of deviation is considered. It requires developing a more sophisticated assignment
model to cope with the deviations. Finally, other types of work shifts (e.g., three-hour shift,
special shifts on holidays) and schedules (scheduling a person across two days) could also be
attempted.

14. Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 8, 2011
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