1 The Impact of Walk-In Ratio on Outpatient Department Fenghueih Huarng Dept. of Business Adm, Southern Taiwan Univ. of Technology

2 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%

3 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

4 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 mean inter-arrival time depends on (N,α) λ =1.5λ =2.0λ =1.0 N \ α

5 Benchmark ASR (given even # to pre-register) If  s = mean service time tlag = 30 minutes (8:00AM ~ 8:30AM) α ： appointment rate

Table 1. Simulation results using Benchmark ASR. *As IDLE is less than 1.0 minute per session, TIQ/IDLE is set to TIQ.

7 Figure 1: TIQ/IDLE Using Benchmark ASR (N-cv-λ). Figure 2: Closing Time After Noon Using Benchmark ASR (N-cv-λ).

8 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 ).

9 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 ≧ Overtime ↑ as α ≦ 0.8, Overtime ↓ as α ≧ TIQ/IDLE ↓(except one case)

10 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)

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

12 Figure 5. TIQ/IDLE of new ASRs with P = 3.0 and different values of Q. Figure6. Closing Time After Noon Using New ASRs with P=3.0.

13 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.

14 Figure 9: TIQ/IDLE Using New ASRs (N-cv-λ). Figure 10: Closing Time After Noon Using New ASRs (N-cv-λ).

15 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 ).

16 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).