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Pseudo Efficient Frontier of Outpatient Appointment Walk-ins in Taiwan

Pseudo Efficient Frontier of Outpatient Appointment Walk-ins in Taiwan. Fenghueih Huarng Dept. of Business Adm Southern Taiwan Univ. of Technology. Why Walk-in?. Patient ’ s habit (Taiwan starts pre-register since 1980.) Lack of good appointment system —

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Pseudo Efficient Frontier of Outpatient Appointment Walk-ins in Taiwan

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  1. Pseudo Efficient Frontier of Outpatient Appointment Walk-ins in Taiwan Fenghueih Huarng Dept. of Business Adm Southern Taiwan Univ. of Technology

  2. Why Walk-in? • Patient’s habit (Taiwan starts pre-register since 1980.) • Lack of good appointment system— ‧pre-register given only sequence number ( no appointed time) ‧late penalty for pre-register ( every 10th, more 3,etc.) • Different clinic nature ‧Fetter & Thompson (1996) — two air force hospitals. average 37% walk-in, pediatric 55~58% walk-in and call-in, urology 7~11%, dermatology 37.5% —clinic TV pediatric 15.2% walk-in, 42.7% call-in ‧Babes & Sarma (1991) — Algeria ‧Liu & Liu (1998) — Hong Kong

  3. Motivation • Lack of good pre-registration system • High percentage of walk-in • Time lag between registration & consultation ‧accumulation of walk-in patients before consultation ‧schedule late arrival of first pre-registered • Understand the impacts of walk-in arrival rate & pre-register ratio

  4. Simulation Setting • Register 8:00 Am ~ 11:30 (210min) Consult 8:30 Am ~ 12:00 Noon (210min) • # of patient per session (N): 20 ( m = 10.5 min), 60 ( m = 3.5 min) • Service-time distribution: exponentially, cv = 1 m uniformally , cv = 0.2 m , 0.5 m • No-show ratio is fixed to 0.1 • Pre-registration ratio: α = 0.3, 0.5, 0.7 • Walk-in arrival rate: λ=1.5, 2.0 (Homo Poisson) • Simulation runs 10000 times for evaluating criteria • Criteria: average waiting time per patient (TIQ) overtime per session mean inter-arrival time depends on (N,α)

  5. Benchmark ASR(even # given to appointment) • A1 = tlag + m • If a <= 0.5, Ai = Ai-1 + 2m , i = 2, …, aN • If a > 0.5. Ai = Ai-1 + 2m , i = 2, …, (1-a)N Ai = Ai-1 + m , i = (1-a)N+1, …, N Note: (1) Ai = arrival time of ith appointment (2) tlag = 30 minutes (3) the patient with least sequence # has highest priority (4) no penalty for pre-register ( punctuality assumption) (5) the best rule has been used in practice in Taiwan

  6. V-I ASR3(p, q, r, k)A1 = tlag + kfirst * p * mA(i+1) = Ai + q*m i = 1,2, …,k-1A(i+1) = Ai + r*m i = k,…,(aN-1) Equal Spacing ASR2(p, q)A1 = tlag + kfirst * p * mA(i+1)= Ai + q*m, i=1,2, …,aN-1 Kfirst = estimate accumulated walk-ins before 8:30AM = l * (1- a) * N * 30/210

  7. Setting of parameters p, q, r, k

  8. p ↑ PEF move upward & leftward Fig.1 cv=1.0,N=20,α=0.3,λ=1.5

  9. Fig.2 cv=0.2,N=60,α=0.7,λ=1.5

  10. Results(1) ASR2(p,q) is worse or not better than ASR3(p,q,r,k) Fig 3 N=20, cv=0.2, l = 1.5, a = 0.3~0.7

  11. Pseudo Efficient Frontiers

  12. pseudo efficient frontier Fig4. N=20,λ=1.5 Fig5. N=20,λ=2 Fig 6. N=60,λ=1.5 Fig 7. N=60,λ=2.

  13. Results (2)Compare Fig 4 ~Fig 7 cv ↓ →TIQ ↓，overtime ↓, slope is steeper（Same as previous literatures） (3) Compare Fig 4 ~Fig 7 α↑→TIQ ↓，overtime ↓ (4) Compare Fig 4& 5（compare Fig 6 & 7） λ↑→TIQ↑，overtime ↓ Fig 4. N=20,λ=1.5 Fig 5. N=20,λ=2

  14. (5) Compare Fig 4 & 6（Compare Fig 5 & 7） N=20, m =10.5minutes; N=60, m =3.5miute(* Different setting from previous literature) • Consider absolute time unit (in minute) N ↑→TIQ ↓，overtime is similar • Consider TIQ in terms of service time (m) => TIQ/m N ↑→TIQ/m ↑，overtime is similar Fig 4. N=20,λ=1.5 Fig 6. N=60,λ=1.5

  15. Conclusions • Walk-in practice need academic research • Investigate two types of ASR 1. equal spacing ASR2(p,q), 2. variable-interval ASR3(p,q,r,k) * ASR2 is a subset of ASR3 • Delay the first appointment • Pseudo efficient frontiers of ASR3 is better (or not worse) than PEF of ASR3 • Cv ↓ or α↑, TIQ↓ , overtime↓  PEF improved toward southwestern • λ↑ TIQ↑, overtime↓ trade-off • N↑ TIQ/m↑ system getting worse

  16. Future Research • Time lag ↑, more accumulation of walk-ins before consultation, the impact of delaying A2↑. • “time lag=0” fits for other country Appointment problem with walk-in(Fetter & Thompson,1996) and for Taiwan with electronical records. • Need to develop different ASR for moving PEF downward & leftward • Consider different walk-in arrival distribution (NHPP) • May consider different service distribution (Erlang, Gamma, Lognormal, …, etc). • May consider different types of patient (new vs. returned) • Robustness of ASR

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