The Impact of Walk-In Ratio on Outpatient Department

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

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

6. 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≧0.8 --- Overtime ↑ as α≦0.8 , Overtime ↓ as α≧0.8 --- TIQ/IDLE ↓(except one case)

10. Evaluation criteria • 1st criterion：TIQ/IDLETIQ：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. Figure7. TIQ/IDLE of New ASRs with Q=1.0 and different values of P. Figure8. Closing Time After Noon Using New ASRs with Q=1.0.

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).