Shift Scheduling in Pediatric Emergency Medicine

Transcription

1 Shift Scheduling in Pediatric Emergency Medicine Presenter : Young-Chae Hong M.S.E. Co-Authors : Amy Cohn, Ph.D. & Ed O'Brien M.D. University of Michigan INFOMS at San Francisco 11 / 10 / 2014

2 Collaborators Amy Cohn, Ph.D Edmond O'Brien, M.D Zachary VerSchure Jennifer Zank, M.D Gabriel Zayas-Caban, Ph.D William Pozehl, B.S.E. Daniel Hazlett, B.S.E. Peter Mayoros Nina Scheinberg Hannah Schapiro Aaron Cohen 2

3 Content Background Motivation Formulations Weighted Sum method Metric constraints method esult Future esearch Pareto method 3

4 esident esponsibilities in the U-M Pediatric Emergency Department 3-7 year medical training program esponsibilities differ by residency year Balancing patient care and educational requirements In hospital Caring for patients Teaching medical students Learning from attending physicians Out of hospital Community clinics Conferences Other educational requirements 4

5 Pediatric ED: Scheduling Considerations All shifts assigned to a resident Appropriate coverage e.g. certain shifts require a senior resident ACGME rules (similar to ABET for engineering) e.g. 10 hour break rule Several different residency programs Pediatrics (PED) Family practice (FP) Emergency medicine (EM) And others 5

6 Motivation Scheduling residents Complicated requirements (UM Pediatric ED) 25 governing rules and preferences Educational goals Patient care egularization / Safety Chief resident built monthly schedule by hand Time consuming process: hours / month Transfer every year: no scheduling experience in July Guess and check: errors / tedious correction process Mixed Integer Programming 6

7 Motivation Practical Significance Poor-quality schedule esidents: decreased interest in learning Patients: adverse health events (Smith-Coggins, et. al. (1994) : "elationship of day versus night sleep to physician performance and mood." Annals of Emergency Medicine) Goals Solves for feasible schedule quickly Create a good quality schedule with no violations Quality Time 7

8 Formulation: Problem Size Sets : set of residents residents D: set of days in the schedule 35 days S: set of shifts 8 shifts Decision Variables Binary: x rds {0, 1} 1 if resident r works shift s on day d 0 otherwise esidents Name Smith Sanchez Chen Shah 27 th 1 st 31 st 7a-4p Shah 9a-6p Joe Shah 10a-7p 12p-9p Chen Chen 4p-1a Smith Sanchez 5p-2a Sanchez 8p-5a Sanchez Smith Smith 11p-8a Chen Joe 8

9 Objectives: Shift Fairness Total / night shift equity Equal opportunities for training Improved morale and learning ability esident Name Night Shifts / Total Shifts Smith Jones Chen Joe Joe 0 / 7 1 / 7 1 / 7 5 / 7 / Total Shifts 0 / 7 1 / 7 1 / 7 5 / 7 Fairness Total shift equity (TSE): ( t ij, t ij = D i D j, i > j) Night shift equity (NSE): ( n ij, n ij = N i N j, i > j) 9

10 Objectives: Undesired Shift Bad sleep patterns and post-clinic shifts Improves resident quality of life Increases patient safety Monday Tuesday Sleep Pattern Monday Tuesday Wednesday NIGHIT 1AM 10AM Wake-up NIGHIT Continuity Clinics 7AM 2PM Day 1PM 10PM Sleepy Day 4PM 1AM NIGHIT NIGHIT Bad sleep pattern Post-Clinic shift Minimum bad sleep patterns (BSP): ( count ) 10

11 Objectives: Undesired Shift Bad sleep patterns and post-clinic shifts Improves resident quality of life Increases patient safety Monday Tuesday Sleep Pattern Monday Tuesday Wednesday NIGHIT 1AM 10AM Wake-up NIGHIT Continuity Clinics 7AM 2PM Day 1PM 10PM Sleepy Day 4PM 1AM NIGHIT NIGHIT Bad sleep pattern Post-Clinic shift Minimum post-clinic shifts (PCC): ( count ) 11

12 Formulation: Constraints Constraints (rules/requirements) One resident assigned to each shift in the month r all x rds = 1, Meets shift requests d, s x rds = 0, r, d, s {day off, conferences, continuity clinic} Ensure resident type appropriate for shift r PED s P x rsd 1, d, P = 7a,9a, {4p,5p}, {8p,11p} Intern-forbidden shifts r {interns} d x rsd = 0, s {7a, 11p} And others 12

13 Multi-Criteria Problem Multi-Criteria schedule Metrics for UM Pediatric Emergency Department Total shift equity (TSE) Night shift equity (NSE) Minimum bad sleep patterns (BSP) Minimum post-clinic shifts (PCC) Weights? Preferences? Trade-off? Multi-objective Mathematical Programming 13

14 Weighted Sum Method Min w 1 TSE + w 2 NSE + w 3 BSP + w 4 PCC s. t. "rules/requirements" x rds {0,1} Quantifying preferences (w i ) is difficult Weights are subjective and difficult to quantify esulting schedule does not match their intentions Various measurement units Equity (σ, Max diff ij, diff ij, ) 14

15 Optimized esidency Scheduling Assistant (OSA): Metrics Formulation Feasibility problem Constraint on metrics Min w 1 TSE + w 2 NSE + w 3 BSP + w 4 PCC s. t. "rules/requirements" x rds {0,1} Benefits of a feasibility problem More flexible Faster to solve: < 2 sec. Given: 35 days / 20 PEDs / 8 shifts 15

16 Optimized esidency Scheduling Assistant (OSA): Metrics Formulation Feasibility problem Constraint on metrics Benefits of a feasibility problem More flexible Min w 1 TSE + w 2 NSE + w 3 BSP + w 4 PCC s. t. "rules/requirements" x rds {0,1} lb TSE (TSE) ub TSE lb NSE NSE ub NSE lb BSP BSP ub BSP lb PCC PCC ub PCC Faster to solve: < 2 sec. Given: 35 days / 20 PEDs / 8 shifts 16

17 Optimized esidency Scheduling Assistant (OSA) : Interactive Improvement Example output of metrics Value (Lower bound, Upper bound) esident Name Number of Shifts Number of Night Shifts Number of Post CC Interactive approach engaging chief resident Iteratively adjust bounds on metric constraints Quickly build high quality schedule Number of Bad Sleep Templates Smith 8 (7,9) 2 (0,10) 0 (0,1) 1 (0,1) Sanchez 8 (7,10) 1 (0,10) 0 (0,1) 1 (0,1) Chen 8 (7,9) 5 (0,10) 1 (0,1) 1 (0,1) Shah 14 (13,15) 3 (0,10) 1 (0,1) 1 (0,1) 17

18 Optimized esidency Scheduling Assistant (OSA) : Interactive Improvement Interactive Feedback Chief resident identifies undesirable qualitative characteristics f 2 (x) (w 1, w 2 ) Metrics f 1 (x) f 2 (x) f 3 (x) Value Value Value f 1 (x) 18

19 OSA Methodology Lb Equity Ub Lb BSPs Ub Lb PostCC Ub (Squeezing) Lb Equity Ub Lb BSPs Ub Lb PostCC Ub TSE CC BSPs Sched. A Sched. B Sched. C

20 Standard Deviation per esident per Day Count per esident per Month OSA: esults Our metrics-based scheduling tool: educes time to create schedules 20 hours /month 1 hour /month Solves a multi-criteria scheduling problem (Without OSA) (Without OSA) (With OSA) (With OSA) Total Shift Disparity Night Shift Disparity 0.0 Bad Sleep Patterns Post-Clinic Shifts 20

21 OSA: Limitations Myopic Solution Non-Pareto solution could be selected by a chief residents Never see the whole picture (the set of Pareto solutions) The most preferred solution is most preferred with respect to their satisfaction f 2 (x) Pareto solutions Solutions 21 f 1 (x)

22 Next Step Pareto Solutions Generate the Pareto solutions of the problem (all of them or a sufficient representation) Select the most preferred one among them f 2 (x) z I = z 1 I, z 2 I z N = (z 1 N, z 2 N ) Efficient Schedules f 1 (x) 22

23 Pareto: Bi-Objective Problem Notation H : Solution Space, the set of feasible solutions P : Pareto Set z i = f i (x) : ith integer objective function, Z Dominance ( ) : x x if and only if z i z i where at least one inequality is strict Bi-Objective Problem min f x = (f 1 x, f 2 x ) s. t. x H 23

24 Pareto: Bi-Objective Problem Pareto Square egion Ideal Point: z 1 = min f 1(x) and z x H 2 = min f 2(x) x H Nadir Point: z 1 = min f x H f 2 x =z 1(x) and z 2 = 2 f 2 (x) min f x H f 1 x =z 2(x) 1 min f 1(x) x H z 1 24 z 1 f 1 (x)

25 Pareto: Bi-Objective Problem Pareto Square egion Ideal Point: z 1 = min f 1(x) and z x H 2 = min f 2(x) x H Nadir Point: z 1 = min f x H f 2 x =z 1(x) and z 2 = 2 f 2 (x) min f x H f 1 x =z 2(x) 1 min f 2(x) x H z 2 25 z 1 f 1 (x)

26 Pareto: Bi-Objective Problem Pareto Square egion Ideal Point: z 1 = min f 1(x) and z x H 2 = min f 2(x) x H Nadir Point: z 1 = min f x H f 2 x =z 1(x) and z 2 = 2 f 2 (x) min f x H f 1 x =z 2(x) 1 z = z 1, z 2 26 z 1 f 1 (x)

27 Pareto: Bi-Objective Problem Pareto Square egion Ideal Point: z 1 = min f 1(x) and z x H 2 = min f 2(x) x H Nadir Point: z 1 = min f x H f 2 x =z 1(x) and z 2 = 2 z 2 f 2 (x) min f x H f 1 x =z 2(x) 1 z = z 1, z 2 27 z 1 f 1 (x)

28 Pareto: Bi-Objective Problem Pareto Square egion Ideal Point: z 1 = min f 1(x) and z x H 2 = min f 2(x) x H Nadir Point: z 1 = min f x H f 2 x =z 1(x) and z 2 = 2 z 2 f 2 (x) min f x H f 1 x =z 2(x) 1 z = z 1, z 2 28 f 1 (x)

29 Pareto: Bi-Objective Problem Pareto Square egion Ideal Point: z 1 = min f 1(x) and z x H 2 = min f 2(x) x H Nadir Point: z 1 = min f x H f 2 x =z 1(x) and z 2 = 2 f 2 (x) z = ( z z 1, z 2 ) 2 min f x H f 1 x =z 2(x) 1 z = z 1, z 2 29 z 1 f 1 (x)

30 Pareto: Bi-Objective Problem Pareto Squeezing Algorithm For integer metrics X 1 and X 2, X 1 + X 2 N 1 + N 2 1 X 1 N 1 X 2 N 2 f 2 (x) 30 z 1 f 1 (x)

31 Pareto: Bi-Objective Problem Pareto Squeezing Algorithm For integer metrics X 1 and X 2, X 1 + X 2 N 1 + N 2 1 X 1 N 1 X 2 N 2 f 2 (x) δ = z 1 1 min f 2 (x) s. t. x 1 δ Δ = 1 31 z 1 f 1 (x)

32 Pareto: Bi-Objective Problem Pareto Squeezing Algorithm For integer metrics X 1 and X 2, X 1 + X 2 N 1 + N 2 1 X 1 N 1 X 2 N 2 f 2 (x) δ = z 1 1 minf 1 x x 2 = min f 2(x) s. t. x 1 δ Δ = 1 32 (squeezing) z 1 f 1 (x)

33 Pareto: Bi-Objective Problem Pareto Squeezing Algorithm For integer metrics X 1 and X 2, X 1 + X 2 N 1 + N 2 1 X 1 N 1 X 2 N 2 f 2 (x) δ = z min f 2 (x) s. t. x 1 δ Δ = 1 Δ = 1 33 z 1 1 z 1 f 1 (x)

34 Pareto: Bi-Objective Problem Pareto Squeezing Algorithm For integer metrics X 1 and X 2, X 1 + X 2 N 1 + N 2 1 X 1 N 1 X 2 N 2 f 2 (x) δ = z minf 1 x x 2 = min f 2(x) s. t. x 1 δ Δ = 1 Δ = 1 (squeezing) 34 z 1 1 z 1 f 1 (x)

35 Pareto: Bi-Objective Problem Pareto Squeezing Algorithm For integer metrics X 1 and X 2, X 1 + X 2 N 1 + N 2 1 X 1 N 1 X 2 N 2 f 2 (x) Δ = 1 Δ = 1 Δ = 1 z 1 3 z z 1 1 z 1 f 1 (x)

36 Pareto: Tri-Objective Problem Pareto Cone Given fixed z level, bi-objective problem z Given z = z, f 2 (x) z = ( z 1, z 2 ) (x, y, z ) z = z 1, z 2 x f 1 (x) ( x, y z, z ) (x z, y, z ) y 36

37 Acknowledgements Thank you to CHEPS, TDC Foundation, the Bonder Foundation, and Dr. Brian Jordan, Dr. Micah Long, Dr. Jenny Zank and Dr. Ed O'Brien for making this research possible. 37

38 CHEPS and the HEPS Master s Program CHEPS: The Center for Healthcare Engineering and Patient Safety HEPS: Industrial and Operations Engineering (IOE) Master s Concentration in Healthcare Engineering and Patient Safety offered by CHEPS CHEPS and HEPS offer unique multidisciplinary teams from engineering, medicine, public health, nursing, and more collaborating with healthcare professionals to better provide and care for patients For more information, contact Amy Cohn at amycohn@umich.edu or visit the CHEPS website at:

39 Thank You! 39

40 Feedback and Questions Young-Chae Hong Prof. Amy Cohn Department of Industrial and Operations Engineering University of Michigan 40