Outpatient Appointment Scheduling with Different Arrival Rates of Walk-ins in Taiwan Fenghueih Huarng 1 & Ming-Te Chen 2 1. Dept. of Business Adm, Southern Taiwan Univ. of Technology 2. Dept. of Business Adm, National Chung Cheng Univ.

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

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

Simulation Setting Register 8:00 Am ~ 11:30 (210min) Consult 8:30 Am ~ 12:00 Noon (210min) # of patient per session (N): 20( =10.5 min), 40 ( =5.25 min), 60( =3.5 min) Service-time distribution: exponentially, cv =1 uniformally, cv = 0.2 No-show ratio: ρ= 0.1, 0.2 Pre-registration ratio: α = 0.3, 0.5, 0.7 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

Benchmark ASR (given even # to pre-register) If Note: (1) the patient with least sequence # has highest priority (2) no penalty for pre-register ( punctuality assumption) (3) the best rule has been used in practice in Taiwan

Benchmark rule results TIQ 23 min, for α=0.7 TIQ 52 min, for α=0.3 Leave 3~13 min before noon when α=0.3 Leave even 21 min after noon when α=0.7

Improve ASR(1) kfirst =expected # of walk-in before consultation na = # of pre-register tlag=time lag between register and consult cvαp

Improve ASR(4) — when cv α p

Benchmark vs. ASR (1) & (4)

Conclusions Walk-in practice need academic research Improving Benchmark ASR → ” closing time ” move toward noon. α is the most influential factor, α↑,TIQ↓, IDLE↓, Leave↓ walk-in arrival rate λ↑, TIQ↑, IDLE↓, Leave↓

Future Research Time lag ↑, more accumulation of walk-ins before consultation, the impact of delaying A 2 ↑. “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 different appointment ratio( α) May consider different arrival distribution for walk-ins. More ASRs should be tested and created.