Lean Options for Walk-In, Open Access, and Traditional Appointment Scheduling in Outpatient Health Care Clinics

Lean Options for Walk-In, Open Access, and Traditional Appointment Scheduling in Outpatient Health Care Clinics Mayo Clinic Conference on Systems Engineering & Operations Research in Health Care Rochester, Minnesota August 17, 2009 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 Additional information available at: http://leeds.colorado.edu/apptsched 1

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. 2

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 3

1. Background on Appointment Scheduling 4

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 5

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. 6

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) 7

Literature: Access to Healthcare Institute of Medicine (2001) Crossing the quality chasm: A new health system for the 21 st 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). 8

2. Lean Approaches Rapid Improvement Capacity Expansion (RICE) Team January, 2008 9

Lean Approaches Reducing Waste Underutilization Overtime No-shows Patient Wait time Customer Service Choice Service Quality Outcomes 10

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 11

Lean Process Improvement: One Year After Rapid Improvement Capacity Expansion RICE 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. 12

Appointments Lean Process Improvement: RICE Project System Transformation 450 400 350 300 250 200 150 100 50 0 Appointments Scheduled and No-Show Rates Mon Tue Wed Thu Fri Mon Tue Wed Thu Fri Year Before Lean Improvement Year After Lean Improvement 20% 15% 10% 5% 0% Appointments No-Show Rate 13

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 14

Recovery Marker Inventory 15

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? 16

3. Response to Overbooking 17

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 18

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 19

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. 20

Other Responses Practitioners Dentists General medicine Child advocacy How should we overbook? Other options Lean Approaches Open Access (Advanced Access) Walk-ins 21

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. 22

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. 23

4. Enhanced Appointment Scheduling Model 20% 15% Probability 10% 5% 0% 0 1 2 3 4 5 6 7 8 9 10 11 12 Number Waiting (k) 24

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 25

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? 26

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 σ Poisson open access call-ins with mean ϕ (per day) Poisson walk-ins with mean λ (per appointment slot) Arrivals have equal service priority (undifferentiated) 27

Characteristics of Model Model flexibility Appt show rates σ j can vary by treatment slot j (time of day) Open access call-in rate ϕ can vary by day. Walk-in rate λ j can vary by treatment slot j Number of providers P j 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) 28

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 ( ) j k ; s, = ( 1 ) b a j j s a sj σ σ σ j a j Density f(x) Binomial distribution has no right tail 0.50 0.40 0.30 0.20 0.10 0.00 0 1 2 3 4 5 6 7 8 9 10 Number of Patients s j = 4, σ = 70% 29

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 λ per slot w j actually walk-in in slot j ( ; λ ) p w j = k λ e w j λ! Density f(x) 0.50 0.40 0.30 0.20 0.10 Poisson distribution has a long right tail 0.00 0 1 2 3 4 5 6 7 8 9 10 Number of Patients λ = 1 30

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 ϕ Turned away if no open slots remain that day Perhaps make an appointment on another day OA patients always show for appointments 31

Probability of k Clients Waiting Probability of k Binomial TS New new arrivals in appointment WI or OA slot j 32 Elements of θ (r arrivals arrivals Probability of k j) can be calculated as None k waiting Waiting plus plus k arrivals arrivals = k waiting at start of slot j (, ) p ( ) α = b s σ λ jk ij k 1 i= 0 k = + θ θ α θ α j+ 1, k j,0 j+ 1, k j, i+ 1 j+ 1, k i i= 0 α jk = probability of k clients arriving for service at the start of appointment slot j θ jk = probability of k clients waiting for service at start of appointment slot j 32

Relative Benefits and Penalties π = Benefit of seeing additional client ω = Penalty for client waiting τ = Penalty for clinic overtime Numéraire of π, ω, and τ doesn t matter Ratios (relative importance) are important Allow linear, quadratic, and mixed (linear + quadratic) costs 33

Linear & Quadratic Objectives Linear Utility Function N k ˆ ω U A Patient k i 1 k Aˆ waiting Patient waiting ( S) = π ˆ θ + ( ) θ + 1, τ θ + 1, Benefit from penalties during patients served normal clinic ops Quadratic Utility Function jk N k N k j= 1 k k i= 1 k penalties during clinic overtime Clinic overtime penalties N k ˆ ( ) ˆ ω ( ) ( ) 2 2 U S = πa 2k 1 θ + i 1 θ τ k θ Aˆ jk N+ 1, k N+ 1, k j= 1 k k i= 1 k 34

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 improves 4. Prior research: Optimality not guaranteed, but almost always obtained 35

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. 36

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. 37

5. Computational Results 10 9 Net Utility per Provider 8 7 6 5 4 3 2 1 0 Walk-ins Open Access -6.19 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Open Access (OA) Traffic (% of capacity) 38

Computational Trials 44 sample problems solved Session size N = 12 Appointment show rate σ = 70% Number of providers P = {1, 2, 4, 8} OA call-in rate λ = {0%, 10%, 100%} capacity With P = 4 and N = 12, then ϕ = 24 is 50% of capacity Walk-in rate λ = {0%, 10%, 100%} of capacity With P = 4, then λ = 2 is 50% of capacity Quadratic costs Parameters π =1.0, ω =1.0, τ =1.5 39

50% Walk-Ins (λ = 0.5) 2 N=12, P=1, σ =0.7, π =1.0, ω =1.0, τ =1.5 (quadratic) Number of Appointments 1 0 1 2 3 4 5 6 7 8 9 10 11 12 Appointment Slot 40

Patients Seen 12 Patients Seen per Provider 11 10 Walk-ins Open Access 2 Providers (P=2) 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% OA or WI Traffic (% of capacity) N=12, P=1, σ =0.7, π =1.0, α =1.0, ω =1.0, τ =1.5 41

Patient Waiting Time 1.0 Expected Waiting Time / Patient 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Walk-ins Open Access 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% OA or WI Traffic (% of capacity) N=12, P=1, σ =0.7, π =1.0, α =1.0, ω =1.0, τ =1.5 42

Clinic Overtime Expected Provider Overtime (d time units) 2.5 2.0 1.5 1.0 0.5 Walk-ins Open Access 0.0 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% OA or WI Traffic (% of capacity) N=12, P=1, σ =0.7, π =1.0, α =1.0, ω =1.0, τ =1.5 43

Provider Utilization 90% Expected Provider Utilization 85% 80% 75% 70% 65% 60% Walk-Ins Open Acess 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% OA or WI Traffic (% of capacity) N=12, P=1, σ =0.7, π =1.0, α =1.0, ω =1.0, τ =1.5 44

Net Utility 10 9 Net Utility per Provider 8 7 6 5 4 3 2 Walk-ins Open Access 1 0-6.19 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Open Access (OA) Traffic (% of capacity) N=12, P=1, σ =0.7, π =1.0, α =1.0, ω =1.0, τ =1.5 45

% of Best Utility 100% 90% Utility (% of maximum) 80% 70% 60% 50% Walk-ins Open Access 40% 30% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% OA or WI Traffic (% of capacity) N=12, P=1, σ =0.7, π =1.0, α =1.0, ω =1.0, τ =1.5 46

6. Insights and Recommendations 47

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) 48

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 49

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 (π WI > π TS ; π OA > π TS ) Currently under investigation 50

7. Contributions & Future Directions 51

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 52

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 53

Questions? Comments? Lean Options for Walk-In, Open Access, and Traditional Appointment Scheduling in Outpatient Health Care Clinics Mayo Clinic Conference on Systems Engineering & Operations Research in Health Care Rochester, Minnesota August 17, 2009 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 Additional information available at: http://leeds.colorado.edu/apptsched 54