Home health nurse routing and scheduling

Transcription

1 Home health nurse routing and scheduling Ashlea Bennett and Alan Erera, Ph.D. April 25, 2008 Presentation overview Motivation: home health industry nursing shortage Problem description: dynamic single-clinician periodic scheduling Solution approach: scenario-based planning Results and future directions AB 4/14/2008 2

2 Home care facts Home care definition: health care services ordered by a physician, provided in the home Goal of home care: promote, maintain, or restore health and minimize effects of disability or illness Service providers of home care: skilled professionals such as nurses, therapists, and home health aides 7.6 million patients 20,000 agencies $47.5 billion spending Medicare represents 31% of spending AB 4/14/ Home care services Demand vs. supply Increasing demand: aging baby boomers and increased chronic diseases Supply shortage: By 2020, there will be 400,000 fewer nurses than needed Demand for home care services 20% gap Supply of home care services Conclusion: effective utilization of resources is key AB 4/14/2008 4

3 Visiting Nurse Hospice Atlanta Case study 2006 Operations: 10,000 patients 118,000 visits/yr 1,000 visits/day 200 clinicians 10,000 mi. 2 25% same day referrals 120 miles 90 miles Coverage area AB 4/14/ Operational environment Clinician teams 10 teams grouped by service type and zip code 12 to 15 clinicians per team Clinician service areas part of contract Pay per visit compensation program Visits Each patient receives 1 to 3 visits per week 30 to 60 minutes in length Episode of care (e.g., 4 weeks) Allowable visit day combinations AB 4/14/2008 6

4 Allowable visit day combinations f i Visit day combinations (consecutive visit days in italics) 1 {M, T, W, R, F} 2 {MW, MR, MF, TR, TF, WF, MT, TW, WR, RF} 3 {MTR, MTF, MWR, MWF, MRF, TWF, TRF, MTW, TWR, WRF} AB 4/14/ Home care clinician daily routes Legend Monday Tuesday Clinician s home 1-visit patient 2-visit patient 3-visit patient Daily route Wednesday Thursday Friday AB 4/14/2008 8

5 Operational approach Home care coordinators on-site at area hospitals Coordinate new patient admissions Decisions based on clinician availability in the patient s area Team scheduler plans initial visit schedules Admission visit Regular visits repeatable weekly schedules Idle time built into nurse schedules during afternoon for new patient visits AB 4/14/ Research objectives Home care coordinators on-site at area hospitals Team scheduler plans initial visit schedules Objective 1: Can we use automated scheduling procedures to build better schedules? Idle time built into nurse schedules during afternoon for new patient visits Objective 2: Can we use information about future patients to distribute the idle time for them? AB 4/14/

6 Research objectives Key objective: Build schedules that use nurses more effectively How to measure effectiveness? Minimize total driving time Maximize number of patients served Meet patient preferences Regular visit times and service providers Meet employee preferences Balanced workload AB 4/14/ Dynamic single-clinician periodic scheduling problem Patient parameters Planning horizon, T Visit frequency in visits/wk, f i Visit length, δ i Episode of care length, Δ i Set of allowable visit day combinations, V i Location, z i Distance from patient i to j, d ij Objective develop a solution technique that leads to daily visit schedules such that: Number of patients t served is maximized i Patient constraints are met (frequency, visit days) Visit times do not change from week to week Route duration constraints are met AB 4/14/

7 Solution technique characteristics Rolling horizon planning process used to dynamically update schedules Schedules created are periodic Predictive information regarding future patients is used AB 4/14/ Rolling horizon planning process T = planning period, for example, 4 weeks σ t = master schedule for periods t through t + T A A B A B C A B C B C C σ 5 σ 6 Objective: σ t-1 should be robust, such that new master schedule σ t can effectively incorporate visits for the changed patient set AB 4/14/

8 Schedules are periodic Day Slot M T W R F Admit Week Visit Week 1 Visit Week 2 Busy time Available time AB 4/14/ Schedules are periodic Day Slot M T W R F Admit Week Visit Week 1 Visit A Week 2 A A B 1-visit patient 2-visit patient 3-visit patient AB 4/14/

9 Schedules are periodic Day Slot M T W R F Admit Week Visit Week 1 Visit C Week 2 D C D 1-visit patient 2-visit patient 3-visit patient AB 4/14/ Schedules are periodic Day Slot M T W R F Admit Week Visit Week 1 C E C B Visit Week 2 1-visit patient 2-visit patient 3-visit patient AB 4/14/

10 Predictive information used 30 minute visit lengths Start in 15 min. increments A K B C 17 A B C 8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30 Driving time Busy time Available time AB 4/14/ Predictive information used Insertion costs for K A 16 Between A and B: 17 d AK + d KB d AB = =117 1 Between B and C: d BK +d KC d BC = =3 C 17 K B 2 A B C 8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30 Driving time Busy time Available time AB 4/14/

11 Predictive information used 30 minute visit lengths Start in 15 min. increments Cost = 1 A 16 K B 2 C 17 A K B C 8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30 Driving time Busy time Available time AB 4/14/ Predictive information used 30 minute visit lengths Start in 15 min. increments A 5 5 F 1 F 2 7 K B C 17 7 slots 6 slots A F 1 F 2 B C 8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30 Driving time Busy time Available time AB 4/14/

12 Predictive information used 30 minute visit lengths Start in 15 min. increments Cost = 3 A K B 2 C A B K C 8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30 Driving time Busy time Available time AB 4/14/ Predictive information used A 5 5 F 1 F 2 7 K 2 18 B C A F 1 F 2 B K C 8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 Driving time Busy time Available time 12:00 12:30 AB 4/14/

13 Solution approach: scenario-based planning Create a set of simulated future-patient scenarios from patient request distribution In each period, use rolling-horizon planning approach to create a master schedule for each scenario Includes visits for actual patients Includes visits for simulated patients Use a consensus function to select the best scenario master schedule Most common decisions regarding actual patients Adapt other scenario master schedules to the consensus scenario With respect to actual patients Execute the consensus master schedule for the actual patients until the next planning period AB 4/14/ Consensus function S I S = set of plans for all scenarios S σ S II S IV S III AB 4/14/

14 Consensus function f I (S) S I f I (S): Level I function finds the scenario plans in S accepting the most common number of new patients S σ S II S I S S IV S III AB 4/14/ Consensus function S S I f II (S I ) S I σ S II f II (S I ): Level II function finds the scenario plans in S I making the most common accept/reject decisions regarding new patients S II S I S IV S III AB 4/14/

15 Consensus function S S I σ S II f III(S II): Level III function finds the scenario plans in S II selecting the most common visit days for accepted new patients S III S II S IV S III f III (S II ) AB 4/14/ Consensus function S S I σ f IV(S III): Level IV function finds the scenario plans in S III selecting the most common visit times for accepted new patients S II S IV S III S IV f IV (S III ) S III AB 4/14/

16 Consensus function S I σ*: consensus plan If there is more than one scenario plan in S IV, select one arbitrarily S σ S II σ* S IV S IV S III 2/20/2008 σ* S IV S III S II S I S AB 4/14/ Experimentation Scenario-based vs. myopic planning 3 types of patient demand distributions Uniform Clustered Clustered + uniform combination Number of scenarios Low = 50 High = 100 Patient arrival rate Low High AB 4/14/

17 Preliminary results Scenario-based vs. myopic planning Acceptance rate = patients admitted/patients arrived Travel ratio = average amount of travel per patient visit (scenarios,arrival rate) (0.86) (0.74) (0.59) (H,H) (L,H) (H,L) (1.48) (L,L) Acceptance rate Myopic Travel ratio Patients equally likely to show up anywhere within gray region (2.77) (1.85) (8.09) (8.95) AB 4/14/ Preliminary results Scenario-based vs. myopic planning Acceptance rate = patients admitted/patients arrived Travel ratio = average amount of travel per patient visit (scenarios,arrival rate) (0.59) (H,H) (L,H) (0.074) (H,L) (L,L) (-0.55) (-0.19) Acceptance rate Myopic Travel ratio Patients equally likely to show up anywhere within gray regions; no patients in white region (3.45) (0.772) (2.35) (1.66) AB 4/14/

18 Preliminary results Scenario-based vs. myopic planning Acceptance rate = patients admitted/patients arrived Travel ratio = average amount of travel per patient visit (scenarios,arrival rate) (-0.132) (H,H) (L,H) (-0.21) (0.42) (H,L) (0.45) (L,L) Acceptance rate Myopic Travel ratio Patients 5 times more likely to show up in darker regions (-1.21) (1.02) (3.57) (2.81) AB 4/14/ Future work Improve dynamic single-clinician periodic scheduling approach Tradeoffs What can be gained by allowing visit days to change? What can be gained by allowing visit times to change? Multiple-clinician problem What can be gained by allowing the practitioner to change? Clinician zoning problem AB 4/14/

19 Questions? AB 4/14/