1 the impact of walk-in ratio on outpatient department fenghueih huarng dept. of business adm,...
TRANSCRIPT
1
The Impact of Walk-In Ratio on Outpatient Department
Fenghueih Huarng Dept. of Business Adm, Southern Taiwan Univ. of Technology
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Why Walk-in? Patient’s habit
Lack of good appointment system
Different clinic nature
‧Fetter & Thompson (1966) pediatric 15~60% (walk-in rate) urology 7~11% dermatology 37.5%
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Motivation Lack of good appointment system High percentage of walk-in Time lag between registration & consultation Understand the impacts of walk-in ratio
(walk-in ratio is more controllable than N, cv, λ)
N ： clinic size cv ： coefficient of variation of physician’s consultation time λ ： arrival rate of walk-in
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Simulation Setting Register 8:00 Am ~ 11:30 Consult 8:30 Am ~ 12:00 Noon (210min) # of patient per session (N)： 20( =10.5 min), 60( =3.5 min) Service-time distribution： exponentially, cv =1 uniformally , cv = 0.2 No-show ratio： ρ= 0 (fixed) Appointment ratio： α = 0.1,0.2,0.3,0.4,….,0.9,1.0 Walk-in arrival rate： λ=1.5, 2.0
ss
s
s
mean inter-arrival time depends on (N,α)
λ =1.5 λ =2.0 λ =1.0
N \ α 0.3 0.5 0.7 0.3 0.5 0.7 0.3 0.5 0.7
20 10 14 23.33 7.5 10.5 17.5 15 21 35
60 3.33 4.67 7.78 2.5 3.5 5.84 5 7 11.67
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Benchmark ASR (given even # to pre-register)
If
If
s = mean service timetlag = 30 minutes (8:00AM ~ 8:30AM) α ： appointment rate
2 sA tlag
2 2 2
0.52 ...........k k sA A
2 2 2
1
0.52 ...........................
k k s
i i s
A A
A A
: 2 ~k N
: 2 ~ (1 )k N
: 2(1 ) 1 ~i N N
CV=0.2 CV=1.0 CV=0.2 CV=1.0
N λ α TIQ IDLE TIQ/IDLE leave TIQ IDLE TIQ/IDLE leave N λ α TIQ IDLE TIQ/IDLE leave TIQ IDLE TIQ/IDLE leave
20 1.5 0.1 65.31 0.24 65.3100* 239.91 65.90 1.88 35.0532 241.40 60 1.5 0.1 66.30 0.00 66.3000* 240.06 66.30 0.02 66.3000* 240.24
0.2 63.20 0.14 63.2000* 239.81 63.94 1.72 37.1744 241.48 0.2 63.90 0.00 63.9000* 240.02 63.86 0.03 63.8600* 240.10
μ s= 0.3 56.69 0.22 56.6900* 239.76 57.87 2.41 24.0124 242.00 μ s= 0.3 57.57 0.00 57.5700* 240.08 57.61 0.07 57.6100* 240.40
10.5 0.4 46.20 0.49 46.2000* 239.96 48.35 6.19 7.8110 245.73 3.5 0.4 46.80 0.00 46.8000* 239.98 46.96 0.77 46.9600* 240.69
0.5 31.97 4.96 6.4456 244.24 36.41 21.25 1.7134 260.37 0.5 31.99 2.22 14.4099 242.16 33.38 11.20 2.9804 251.17
0.6 20.30 7.47 2.7175 246.80 27.62 26.17 1.0554 265.46 0.6 18.23 3.36 5.4256 243.27 21.92 15.08 1.4536 254.76
0.7 13.67 10.63 1.2860 249.75 23.15 30.19 0.7668 269.35 0.7 10.29 6.05 1.7008 245.98 15.98 18.15 0.8804 258.11
0.8 10.71 12.11 0.8844 251.35 21.49 32.03 0.6709 271.13 0.8 8.35 10.13 0.8243 249.88 14.48 21.40 0.6766 260.89
0.9 7.67 9.25 0.8292 248.82 20.43 31.63 0.6459 271.04 0.9 7.15 9.53 0.7503 249.26 14.37 21.68 0.6628 261.55
1 3.92 6.31 0.6212 246.41 18.59 30.08 0.6180 270.71 1 2.54 3.92 0.6480 243.96 12.24 19.11 0.6405 259.33
2 0.1 79.89 0.01 79.8900* 239.99 79.72 0.24 79.7200* 239.90 2 0.1 81.80 0.00 81.8000* 240.08 81.87 0.00 81.8700* 240.30
0.2 75.87 0.01 75.8700* 239.99 75.80 0.33 75.8000* 240.04 0.2 77.75 0.00 77.7500* 240.08 77.82 0.00 77.8200* 240.30
0.3 67.59 0.02 67.5900* 239.98 67.76 0.75 67.7600* 240.34 0.3 69.50 0.00 69.5000* 240.08 69.57 0.00 69.5700* 240.30
0.4 55.48 0.06 55.4800* 240.08 56.43 4.12 13.6966 244.01 0.4 57.04 0.00 57.0400* 240.08 57.15 0.49 57.1500* 240.79
0.5 38.97 3.87 10.0698 243.79 41.95 19.67 2.1327 259.18 0.5 40.44 2.11 19.1659 242.19 41.35 10.94 3.7797 251.25
0.6 24.70 5.25 4.7048 245.26 31.15 24.07 1.2941 264.07 0.6 24.65 2.87 8.5889 242.95 27.57 14.29 1.9293 254.59
0.7 15.28 7.24 2.1105 247.17 24.62 27.54 0.8940 267.51 0.7 13.37 3.52 3.7983 243.59 18.57 16.38 1.1337 256.67
0.8 10.59 9.18 1.1536 249.05 21.66 30.26 0.7158 269.94 0.8 7.84 5.80 1.3517 245.84 14.63 18.79 0.7786 259.03
0.9 7.58 8.42 0.9002 248.30 20.64 30.85 0.6690 270.86 0.9 6.47 7.46 0.8673 247.44 13.94 20.42 0.6827 260.54
1 3.92 6.31 0.6212 246.41 18.59 30.08 0.6180 270.71 1 2.54 3.92 0.6480 243.96 12.24 19.11 0.6405 259.33
Table 1. Simulation results using Benchmark ASR.
*As IDLE is less than 1.0 minute per session, TIQ/IDLE is set to TIQ.
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Figure 1: TIQ/IDLE Using Benchmark ASR (N-cv-λ).
Benchmark ASR
0
10
20
30
40
50
60
70
80
90
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
TIQ
/IDLE
20-10-15 20-10-20 20-02-15 20-02-20
60-10-15 60-10-20 60-02-15 60-02-20
Benchmark ASR
0
5
10
15
20
25
30
35
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
Ove
rtim
e
20-10-15 20-10-20 20-02-15 20-02-20
60-10-15 60-10-20 60-02-15 60-02-20
Figure 2: Closing Time After Noon Using Benchmark ASR (N-cv-λ).
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Benchmark ASR
0
10
20
30
40
50
60
70
80
90
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
TIQ
20-10-15 20-10-20 20-02-15 20-02-20
60-10-15 60-10-20 60-02-15 60-02-20
Benchmark ASR
0
5
10
15
20
25
30
35
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
IDLE
20-10-15 20-10-20 20-02-15 20-02-20
60-10-15 60-10-20 60-02-15 60-02-20
Figure 3: TIQ (Time in queue per patient ) Using Benchmark ASR (N-cv-λ).
Figure 4: IDLE (idle time per session) Using Benchmark ASR (N-cv-λ).
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N↑--- TIQ↑asα small, TIQ↓asα large --- IDLE ↓ --- Overtime ↓ --- TIQ/IDLE ↑ (For most cases)
cv↑--- TIQ↑ --- IDLE↑ --- Overtime↑ --- TIQ/IDLE ↓ (For most cases)
λ↑--- TIQ↑ --- IDLE ↓ --- Overtime ↓ --- TIQ/IDLE ↑
α↑--- TIQ ↓ --- IDLE ↑ as α 0.8 , IDLE ↓ as α 0.8 ≦ ≧ --- Overtime ↑ as α 0.8 , Overtime ↓ as α 0.8≦ ≧ --- TIQ/IDLE ↓(except one case)
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Evaluation criteria 1st criterion： TIQ/IDLE TIQ： Time in queue per patient IDLE： idle time per session
(1)From table 1： TIQ/IDLE is more easier to use than TIQ or IDLE (2)As α=1.0,cv=0.5,ρ=0.0 (Ho & Lau,1992), TIQ/IDLE→0.65 for
2nd criterion： Overtime(=Leave-Noon)
Benchmark
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
N
TIQ
/ID
LE
Benchmark
N
11
ASR2(delay first appointment & equal spacing)
N=20, cv=1.0, λ=1.5 • Fixing p=3.0 with q= 0.7, 0.9, 1.0, 1.1, 1.3 → Fig.5 & Fig.6 → ASR2 (p=3.0, q=0.9) ASR2 (p=3.0, q=1.0) → TIQ/IDLE 2 , as α 0.7≦ ≧ • Fixing q=1.0 with p=1, 2, 3, 4, 5 → Fig.7 & Fig.8 → ASR2 (p=2.0, q=1.0) ASR2 (p=3.0, q=1.0) ASR2 (p=4.0, q=1.0) → TIQ/IDLE 3 , as α 0.7≦ ≧ For all eight operating conditions ASR2 (p=3, q=1) outperform
2
2 2 2 .............. 2,......,
(1 ) 30 / 210
=estimated # of walk-in before consultation
s
k k s
A tlag kfirst p
A A q k N
kfirst N
12
20-10-15
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1appointment rate
TIQ
/IDLE
Benchmark ASR2(p30q07) ASR2(p30q09)
ASR2(p30q10) ASR2(p30q11) ASR2(p30q13)
Figure 5. TIQ/IDLE of new ASRs with P = 3.0 and different values of Q.
20-10-15
-5
05
10
1520
25
3035
40
45
5055
60
6570
75
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1appointment rate
Ove
rtim
e
Benchmark ASR2(p30q07) ASR2(p30q09)
ASR2(p30q10) ASR2(p30q11) ASR2(p30q13)
Figure6. Closing Time After Noon Using New ASRs with P=3.0.
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20-10-15
0
5
10
15
20
25
30
35
40
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
TIQ
/IDLE
Benchmark ASR2(p10q10) ASR2(p20q10)
ASR2(p30q10) ASR2(p40q10) ASR2(p50q10)
20-10-15
0
5
10
15
20
25
30
35
40
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
Ove
rtim
e
Benchmark ASR2(p10q10) ASR2(p20q10)
ASR2(p30q10) ASR2(p40q10) ASR2(p50q10)
Figure8. Closing Time After Noon Using New ASRs with Q=1.0.
Figure7. TIQ/IDLE of New ASRs with Q=1.0 and different values of P.
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ASR2(p=3.0,q=1.0)
0
10
20
30
40
50
60
70
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
TIQ
/IDLE
20-10-15 20-10-20 20-02-15 20-02-20
60-10-15 60-10-20 60-02-15 60-02-20
ASR2(p=3.0,q=1.0)
0
5
10
15
20
25
30
35
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
Ove
rtim
e
20-10-15 20-10-20 20-02-15 20-02-20
60-10-15 60-10-20 60-02-15 60-02-20
Figure 9: TIQ/IDLE Using New ASRs (N-cv-λ).
Figure 10: Closing Time After Noon Using New ASRs (N-cv-λ).
15
ASR2(p=3.0,q=1.0)
0
10
20
30
40
50
60
70
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
TIQ
20-10-15 20-10-20 20-02-15 20-02-20
60-10-15 60-10-20 60-02-15 60-02-20
ASR2(p=3.0,q=1.0)
0
5
10
15
20
25
30
35
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Appointment rate
IDLE
20-10-15 20-10-20 20-02-15 20-02-20
60-10-15 60-10-20 60-02-15 60-02-20
Figure11: TIQ (Time in queue per patient ) Using New ASRs (N-cv-λ).
Figure 12: IDLE (idle time per session) Using New ASRs (N-cv-λ).
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Conclusions A trade-off relationship between TIQ/IDLE and
Overtime when comparing different ASRs.
ASR2(p=3, q=1) perform more robust than
Benchmark ASR (1) much smaller range of TIQ/IDLE (2) similar range of overtime
ASR2 (p=3, q=1) had TIQ/IDLE < 3 as α 0.7≧ Overtime < 31 for all α TIQ < 31 as α 0.7≧ Hospitals should have higher appointment rate to
benefit both patients and physicians(hospitals).