© 2008 – Linda LaGanga and Stephen Lawrence© 2009 – Linda LaGanga and Stephen LawrenceMayo Clinic SE/OR 2009 1 Lean Options for Walk-In, Open Access, and

1© 2008 – Linda LaGanga and Stephen Lawrence© 2009 – Linda LaGanga and Stephen LawrenceMayo Clinic SE/OR 2009

Lean Options for Walk-In, Open Access, and

Traditional Appointment Scheduling in Outpatient

Health Care Clinics

© 2008 – Linda LaGanga and Stephen Lawrence

Linda R. LaGanga, Ph.D.Director of Quality Systems

Mental Health Center of Denver

Denver, CO USA

Stephen R. Lawrence, Ph.D.Leeds School of Business

University of Colorado

Boulder, CO USA

Mayo Clinic Conference on Systems Engineering & Operations

Research in Health CareRochester, Minnesota – August 17, 2009

Additional information available at: http://Leeds.colorado.edu/ApptSched


Disclosure: Linda LaGanga, Ph.D.Director of Quality Systems & Operational Excellence Mental Health Center of Denver

The Mental Health Center of Denver (MHCD) is a private, not-for-profit, 501 (c) (3), community mental health care organization providing comprehensive, recovery-focused services to more than 11,500 residents in the Denver metro area each year. Founded in 1989, MHCD is Colorado’s leading provider and key health care partner in the delivery of outcomes-based mental health services.


Agenda

1. Background on Appointment Scheduling

2. Lean Approaches

3. Response to Overbooking

4. Enhanced Models

5. Computational Results

6. Insights and Recommendations

7. Contributions and Future Directions


1. Background on Appointment Scheduling


Motivation Healthcare Capacity

Funding restrictions Demand exceeds supply Serve more people with limited resources

Manufacturing Scheduling Resource utilization Maximize throughput

Healthcare Scheduling as the point of access

Maximize appointment yield


2007 Consumer Reports survey of 39,000 patients and 335 primary care doctors (Hitti, 2007) Top patient complaint was about time spent

in the waiting room (24% of patients) Followed by 19% of patients who complained

that they couldn’t get an appointment within a week

Fifty-nine percent of doctors in the survey complained that patients did not follow prescribed treatment and 41% complained that patients waited too long to schedule appointments.


Literature: Appointment Scheduling and Yield Maximization LaGanga & Lawrence (2007)

Clinic overbooking to improve patient access and increase provider productivity. Decision Sciences, 38(2).

Qu, Rardin, Williams, & Willis (2007) Matching daily healthcare provider capacity to demand in

advanced access scheduling systems. European Journal of Operational Research, 183.

LaGanga & Lawrence (2009) Appointment Overbooking in Health Care Clinics to Improve Patient

Service and Clinic Performance, working paper, Leeds School of Business, University of Colorado, Boulder CO (in review)


Literature: Access to Healthcare Institute of Medicine (2001)

Crossing the quality chasm: A new health system for the 21st century.

Murray & Berwick (2003) Advanced access: Reducing waiting and delays in

primary care. Journal of the American Medical Association, 289(8).

Green, Savin, & Murray (2007) Providing timely access to care: What is the right

patient panel size? The Joint Commission Journal on Quality and Patient Safety, 33(4).


2. Lean Approaches

Rapid Improvement Capacity Expansion (RICE) TeamJanuary, 2008


Lean Approaches Reducing Waste

Underutilization Overtime No-shows Patient Wait time

Customer Service Choice Service Quality Outcomes


Lean Process Improvement in Healthcare Documented success in hospitals ThedaCare, Wisconsin Prairie Lakes, South Dakota Virginia Mason, Seattle University of Pittsburgh Medical Center Denver Health Medical Center

Influences Toyota Production System Ritz Carleton Disney

Hospitals to Outpatient Clinics run by hospitals Collaborating outpatient systems


Lean Process Improvement: One Year AfterRapid Improvement Capacity ExpansionRICE Results

Analysis of the1,726 intake appointments for the one year before and the full year after the lean project

27% increase in service capacity from 703 to 890 kept appointments) to intake new consumers

12% reduction in the no-show rate from 14% to 2% no-show

Capacity increase of 187 additional people who were able to access needed services, without increasing staff or other expenses for these services

93 fewer no-shows for intake appointments during the first full year of RICE improved operations.


Lean Process Improvement:RICE Project System TransformationAppointments Scheduled

and No-Show Rates

050

100150200250300350400450

Mon Tue Wed Thu Fri Mon Tue Wed Thu Fri

Ap

po

intm

en

ts

0%

5%

10%

15%

20%

Appointments

No-Show Rate

Year Before Lean Improvement

Year After Lean Improvement


How was this shift accomplished? Day of the week: shifted and added

Tuesdays and Thursdays Welcome call the day before Transportation and other information Time lag eliminated

Orientation to Intake Assessment Group intakes

Overbooking Flexible capacity


Recovery Marker Inventory


Lean Scheduling Challenge Choice versus Certainty Variability versus Predictability Sources of Uncertainty / Variability

No-shows Service duration Customer (patients’) Demand

Time is a significant factor Airline booking models?


3. Response to Overbooking


Reactions to Overbooking Article(LaGanga & Lawrence, 2007) Utility model to capture trade-offs

Serving additional patients Costs of patient wait time and provider overtime

Simulation model Compressed time between appointments More appointments without double-booking Allowed variable service times

Contacted by Newspapers Radio American Medical Association Practitioners


Sample Responses Campus reporter’s visit to student health

center “Not now and never will” Patient waits 15 – 20 minutes New administration, new interests

Morning News Radio “Overbooking leading to increased patient

satisfaction? That just doesn’t make any sense!” Public Radio Interviewer

Benefits of increased access at lower cost


Instant Message Response to News Radio“Overbooking at medical providers is unconscionable. Every

provider I have gone to has a policy of charging a hefty fee to those who miss appointments. Providers rarely, if ever, take into consideration the time and effort a patient must expend to attend an appointment. Extended wait times mean that many patients have to use PTO time or risk losing their jobs in order to obtain adequate medical care. An appointment should be considered a verbal contract. If the patient is a no-show then the provider should be allowed to charge for the visit. However, if the provider cannot see the patient within 30 minutes of the scheduled appointment then the patient should be commpensated [sic] for their time. Providers seem to forget who is ultimately paying the bills. When I get poor service at Macy's I have the option of shopping at Dillards. It is not so easy when it comes to medical care.”


21

Other Responses Practitioners

Dentists General medicine Child advocacy

How should we overbook? Other options

Lean Approaches Open Access (Advanced Access) Walk-ins


Which one of the following is true about Appointment Overbooking?1. Airline overbooking models are very suitable.

2. Overbooking can be accomplished without double-booking.

3. It is the best choice for increasing service capacity.

4. It is not beneficial when service times are variable.

5. The utility of overbooking depends mostly on the cost of patient wait time.


Which one of the following is true about Appointment Overbooking?1. Airline overbooking models are very suitable.

2. Overbooking can be accomplished without double-booking.

3. It is the best choice for increasing service capacity.

4. It is not beneficial when service times are variable.

5. The utility of overbooking depends mostly on the cost of patient wait time.


4. Enhanced Appointment Scheduling Model

0%

5%

10%

15%

20%

0 1 2 3 4 5 6 7 8 9 10 11 12

Number Waiting (k)

Pro

bab

ilit

y


Objectives of Research Optimize patient flow in health-care clinics

Traditionally scheduled (TS) clinic Some patients do not “show” for scheduled

appointments TS clinic wishes to increase scheduling flexibility

Some capacity allocated to “open access” (OA) appointments, OR

Some capacity allocated to “walk-in” traffic Balance needs of clinic, providers, and patients


Objectives of Research

Study impact of open access and walk-in traffic When is open access or walk-in traffic

beneficial? What mix of TS, OA, and WI traffic is

best? What are trade-offs of TS, OA, and WI

on clinic performance?


Assumptions A clinic session has N treatment slots

Each slot is d time units long (deterministic) A clinic session then is D=Nd time units in duration

One or multiple undifferentiated providers P Clients serviced by any available provider

Patients can arrive in one of three ways Binomial traditional appointments “show” with probability Poisson open access call-ins with mean (per day) Poisson walk-ins with mean (per appointment slot) Arrivals have equal service priority (undifferentiated)


Characteristics of Model Model flexibility

Appt show rates j can vary by treatment slot j (time of day)

Open access call-in rate can vary by day. Walk-in rate j can vary by treatment slot j Number of providers Pj can vary by slot j Any arrival distribution can be accommodated

Patient arrivals Patients are only seen at the start of a treatment slot

(early arrivals wait for next slot without cost) Patients are seen in order of arrival (FCFS)


Arrival of Scheduled Appointments Appointment arrivals are binomially distributed

sj patients scheduled for treatment slot j Probability of a patient showing is s aj ≤ sj actually arrive

in slot j

; , 1 j js aj kj j

j

sb a s

a

sj = 4, = 70%

0.00

0.10

0.20

0.30

0.40

0.50

0 1 2 3 4 5 6 7 8 9 10

Number of Patients

Den

sity

f(x

)

Binomial distribution has no

right tail


Arrival of Walk-In Patients Walk-ins arrive at some percentage of clinic

capacity Walk-in arrivals are Poisson distributed

Walk-ins arrive at rate per slot wj actually walk-in in slot j

;!

k

jj

ep w

w

0.00

0.10

0.20

0.30

0.40

0.50

0 1 2 3 4 5 6 7 8 9 10

Number of Patients

Den

sity

f(x)

= 1

Poisson distribution has a

long right tail


Arrival of Open Access Patients Open access (OA) calls arrive at a mean rate

equal to some fraction of clinic capacity (e.g., 50%)

Patients call for a same-day appointment Number of OA patients calling on a particular day

is Poisson distributed with mean “Turned away” if no open slots remain that day

Perhaps make an appointment on another day OA patients always show for appointments


Probability of k Clients Waiting

Elements of (rj) can be calculated as

1, ,0 1, , 1 1,0

k

j k j j k j i j k ii

10

,k

jk ij ki

b s p

jk = probability of k clients arriving for service at the start of appointment slot j

jk = probability of k clients waiting for service at start of appointment slot j

Probability of k new arrivals in

slot j

Binomial TS appointment

arrivals

New WI or OA arrivals

None waiting plus k arrivals

Waiting plus arrivals = k

Probability of k waiting at start of

slot j

32


Relative Benefits and Penalties = Benefit of seeing additional client = Penalty for client waiting = Penalty for clinic overtime Numéraire of , , and doesn’t matter

Ratios (relative importance) are important Allow linear, quadratic, and mixed (linear +

quadratic) costs


Linear & Quadratic Objectives

1, 1,1 1

ˆˆ 1ˆ

N k

jk N k N kj k k i k

U A k i kA

S

Linear Utility Function

Quadratic Utility Function

2 21, 1,

1 1

ˆˆ 2 1 1ˆ

N k

jk N k N kj k k i k

U A k i kA

S

Benefit from patients served

Patient waiting penalties during normal clinic ops

Patient waiting penalties during clinic overtime

Clinic overtime penalties


Heuristic Solution Methodology

1. Gradient search Increment/decrement appts scheduled in each slot Choose the single change with greatest utility Iterate until no further improvement found

2. Pairwise interchange Exchange appts scheduled in all slot pairs Choose the single swap with greatest utility Iterate until no further improvement found

3. Iterate (1) and (2) while utility improves4. Prior research: Optimality not guaranteed, but

almost always obtained


How does Open Access contribute to leaner scheduling?1. It provides a more reliable method of

overbooking.

2. It eliminates the uncertainty of demand for same-day appointments.

3. It guarantees that patients will be seen when they want.

4. It reduces uncertainty caused by no-shows.

5. It eliminates waste caused by unfilled appointments.


How does Open Access contribute to leaner scheduling?1. It provides a more reliable method of

overbooking.

2. It eliminates the uncertainty of demand for same-day appointments.

3. It guarantees that patients will be seen when they want.

4. It reduces uncertainty caused by no-shows.

5. It eliminates waste caused by unfilled appointments.


5. Computational Results

0

1

2

3

4

5

6

7

8

9

10

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Net

Util

ity p

er P

rovi

der

Open Access (OA) Traffic (% of capacity)

Walk-ins

Open Access

-6.190

1

2

3

4

5

6

7

8

9

10

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Net

Util

ity p

er P

rovi

der


Walk-ins

Open Access

-6.19


Computational Trials 44 sample problems solved Session size N = 12 Appointment show rate = 70% Number of providers P = {1, 2, 4, 8} OA call-in rate = {0%, 10%, …100%} capacity

With P = 4 and N = 12, then = 24 is 50% of capacity Walk-in rate = {0%, 10%, …100%} of capacity

With P = 4, then = 2 is 50% of capacity Quadratic costs

Parameters =1.0, =1.0, =1.5


50% Walk-Ins (= 0.5)N=12, P=1, =0.7, =1.0, =1.0, =1.5 (quadratic)

0

1

2

1 2 3 4 5 6 7 8 9 10 11 12

Num

ber

of A

ppoi

ntm

ents

Appointment Slot

0

1

2

1 2 3 4 5 6 7 8 9 10 11 12

Num

ber

of A

ppoi

ntm

ents

Appointment Slot


Patients Seen

10

11

12

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Pat

ien

ts S

een

per

Pro

vid

er

OA or WI Traffic (% of capacity)

Walk-ins

Open Access

2 Providers (P=2)10

11

12

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Pat

ien

ts S

een

per

Pro

vid

er


Walk-ins

Open Access

2 Providers (P=2)

N=12, P=1, =0.7, =1.0, =1.0, =1.0, =1.5


Patient Waiting Time

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Exp

ecte

d W

aitin

g T

ime

/ Pat

ien

t


Walk-ins

Open Access

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Exp

ecte

d W

aitin

g T

ime

/ Pat

ien

t


Walk-ins

Open Access

N=12, P=1, =0.7, =1.0, =1.0, =1.0, =1.5


Clinic Overtime

0.0

0.5

1.0

1.5

2.0

2.5

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Exp

ecte

d P

rovi

der

Ove

rtim

e (d

time

un

its)


Walk-ins

Open Access

0.0

0.5

1.0

1.5

2.0

2.5

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Exp

ecte

d P

rovi

der

Ove

rtim

e (d

time

un

its)


Walk-ins

Open Access

N=12, P=1, =0.7, =1.0, =1.0, =1.0, =1.5


Provider Utilization

60%

65%

70%

75%

80%

85%

90%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Exp

ecte

d P

rovi

der

Util

izat

ion


Walk-Ins

Open Acess

60%

65%

70%

75%

80%

85%

90%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Exp

ecte

d P

rovi

der

Util

izat

ion


Walk-Ins

Open Acess

N=12, P=1, =0.7, =1.0, =1.0, =1.0, =1.5


Net Utility

N=12, P=1, =0.7, =1.0, =1.0, =1.0, =1.5

0

1

2

3

4

5

6

7

8

9

10

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Net

Util

ity p

er P

rovi

der


Walk-ins

Open Access

-6.190

1

2

3

4

5

6

7

8

9

10

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Net

Util

ity p

er P

rovi

der


Walk-ins

Open Access

-6.19


% of Best Utility

N=12, P=1, =0.7, =1.0, =1.0, =1.0, =1.5

30%

40%

50%

60%

70%

80%

90%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Util

ity (%

of m

axim

um)


Walk-ins

Open Access

30%

40%

50%

60%

70%

80%

90%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Util

ity (%

of m

axim

um)


Walk-ins

Open Access


6. Insights and Recommendations


Managerial Implications TS appointments provide better clinic utility

than does WI traffic or OA call-ins Any WI or OA traffic causes some decline in utility

An all-WI or all-OA clinic performs worse than any clinic with some TS appointments Even a relatively small percentage of scheduled

appointments can significantly improve clinic utility Degree of improvement depends on number of providers

A mix of TS appointments with some OA or WI traffic does not greatly reduce clinic performance (utility)


Insights from the Model Loss of utility with WI traffic is due to the long

right-tail of Poisson distribution Excessive patient waiting & clinic overtime

Loss of utility with OA traffic is due to uncertainty about number of OA call-ins

TS appts reduce patient waiting and clinic overtime Binomial distribution has truncated right tail

Multiple providers improves clinic utility Portfolio effect – variance reduction


Managerial Caveats Results (to date) are for “reasonable” utility

parameters Sensitivity analysis currently under way

Attractiveness of WI and OA traffic may improve if they have a higher utility benefit than do scheduled appointments (WI > TS ; OA > TS ) Currently under investigation


7. Contributions & Future Directions


Contributions of Research Analytic yield management model for health care

clinics with OA traffic First to examine analytically examine combinations

of TS and OA Fast and effective near-optimal solutions Demonstrate the trade-offs of OA traffic

Scheduled appointments provide higher utility Even some appointments improve utility of an all

OA clinic


Future Work Determine sensitivity of results

Utility parameters, number of slots, show rates, linear costs

Show rates, walk-in rates, and providers vary by time of day

Extend model Different utility parameters for appointments and

walk-ins Walk-ins seen before appointments and vice versa Stochastic service times


Questions? Comments?Questions? Comments?Lean Options for Walk-In,

Open Access, and Traditional Appointment Scheduling in Outpatient

Health Care Clinics

© 2008 – Linda LaGanga and Stephen Lawrence

Linda R. LaGanga, Ph.D.Director of Quality Systems

Mental Health Center of Denver

Denver, CO USA

Stephen R. Lawrence, Ph.D.Leeds School of Business

University of Colorado

Boulder, CO USA

Mayo Clinic Conference on Systems Engineering & Operations

Research in Health CareRochester, Minnesota – August 17, 2009

Additional information available at: http://Leeds.colorado.edu/ApptSched

Documents

© 2008 – Linda LaGanga and Stephen Lawrence© 2009 – Linda LaGanga and Stephen LawrenceMayo Clinic SE/OR 2009 1 Lean Options for Walk-In, Open Access, and