Linear Programming Tools for Scheduling Trainees in Healthcare

Transcription

1 Linear Programming Tools for Scheduling Trainees in Healthcare William Pozehl Rishindra Reddy MD F. Jacob Seagull PhD Mark Daskin PhD Amy Cohn PhD Janice Davis Nate Janes Yicong Zhang

2 Presentation Outline Background Motivation Model Formulation Model Implementation Conclusions and Future Work 2

3 Presentation Outline Background Motivation Model Formulation Model Implementation Conclusions and Future Work 3

4 Healthcare Training Basics Attending Fellowship Residency Internship Medical School PGY4 PGY3 PGY2 PGY1 M4 M3 M2 M1 Undergraduate Program 4

5 Healthcare Training at Michigan 1,199 trainees 25 residencies 105 training programs 80 fellowships 5

6 Importance of Scheduling 6

7 Who does the Scheduling? Program dependent Chief Resident Faculty (Program Director) Senior Administrative Staff 7

8 Presentation Outline Background Motivation Model Formulation Model Implementation Conclusions and Future Work 8

9 Challenges in Scheduling Time-intensive process Numerous stakeholders Complex rules and legal requirements Conflicting goals Varying strategies and interdependencies Good enough mentality 9

10 Resident Education Requirements Each program has unique educational requirements (operative and disease exposure) PGY1 PGY1 PGY2 PGY2 PGY3 PGY3 PGY4 PGY5 PGY4 PGY6 PGY5 PGY7 1 1 MAIZE MAIZE MAIZE MAIZE RED GOLD BLUE BLUE MAIZE 2 2 BLUE BLUE BLUE VA BLUE RED 3 3 WHITE WHITE WHITE BLUE HAND ENT A WHITE GOLD BLUE 4 4 MAIZE/BLUE/WHITE MAIZE/BLUE/WHITE BLUE C 5 5 ACS ACS A HAND SJMH SJMH SJMH RED WHITE 6 6 DSP ACS D ACS BLUE 7 7 TBE PLA DSP OP E DAY CSLT GOLD SJMH ACS 8 8 GI SURG SICU ANES FLOAT OMFS M 9 9 VA GS-VASC STX RED DSP DAY CSLT SICU I STX NIGHT CSLT HAND VASC SVA ORTHO FLOAT NIGHT CSLT THS ELECTIVE C SVA GOLD STX VA CT TBE SICU VASC STX/SVA FOOTE VA GS RED HAND PED VA SURG GS-VASC SICU VA GS-VASC SURG ONC VA GS VA GS-VASC VA GS-VASC General Plastic Surgery Surgery (6 residents (4 residents + 12 fellows per level per per level year) per year) 10

11 Service Coverage Requirements Each service requires a resident complement comprised of varying skillsets and disciplines 1 ST YEAR GENERAL SURG 1 ST YEAR PLASTIC SURG 1 ST YEAR VASCULAR SURG WHITE SICU STX 11

12 Traditional Scheduling Approach 1. Build rotation templates 2. Adjust for coverage and educational needs 3. Renegotiate after reaching a dead-end JULY AUG SEPT OCT NOV DEC JAN FEB MAR APRIL MAY JUNE VA VA BLUE MAIZE WHITE PLA ACS SVA SICU BLUE WHITE DSP PLA STX SVA VA CT DSP G&V G&V VA BLUE PLA MAIZE WHITE ACS BLUE SICU BLUE SICU BLUE DSP PLA STX SVA STX VA CT G&V VA VA VA CT PLA BLUE MAIZE DSP WHITE ACS SICU BLUE MAIZE DSP WHITE PLA SVA STX SVA G&V G&V VA MAIZE SVA VA CT BLUE MAIZE SVA WHITE ACS SICU BLUE DSP STX PLA DSP STX G&V 12

13 Project Goal Design a linear program which automates creation of a block schedule that satisfies the needs of the residents and services. 13

14 Presentation Outline Background Motivation Model Formulation Model Implementation Conclusions and Future Work 14

15 Linear Programming Basics A technique to solve complicated story problems Four basic parts Sets and parameters Decision variables Objective function Constraints min 2x 1 + x 2 subject to x 1 + x 2 5 2x 1 + 3x 2 11 x 1, x 2 0 Optimal Solution: (1, 4) Objective Value = 6 15

16 Sets R: residents C: resident categories S: services M: months 16

17 Parameters a rc 0, 1 : indicates if resident r fits category c L csm : lower bound on number of residents fitting category c in service s during month m U csm : upper bound on number of residents fitting category c in service s during month m λ rs : lower bound on number of months resident r must spend on service s μ rs : upper bound on number of months resident r must spend on service s 17

18 Decision Variables x rsm 0, 1 : whether resident r is assigned to service s in month m r R, s S, m M The base model does not have an objective function. 18

19 Constraints 1. Every resident gets assigned to one service every month x rsm s S = 1, r R, m M 2. Every resident satisfies their educational requirements λ rs x rsm m M μ rs, r R, s S 3. Every service satisfies their service coverage needs L csm. r R a rc x rsm U csm, c C, s S, m M 19

20 Constraints 1. Every resident gets assigned to one service every month x Smith,Maize,July Is Dr. Smith assigned to the Maize service in July? If yes, x Smith,Maize,July = 1. If no, x Smith,Maize,July = 0. x Smith,Blue,July x Smith,White,July Is Dr. Smith assigned to the Blue service in July? Is Dr. Smith assigned to the White service in July? x Smith,Maize,July + x Smith,Blue,July + x Smith,White,July = 1 20

21 Constraints 1. Every resident gets assigned to one service every month x Smith,Maize,July + x Smith,Blue,July + x Smith,White,July = 1 x Smith,Maize,Aug + x Smith,Blue,Aug + x Smith,White,Aug = 1. x Smith,Maize,June + x Smith,Blue,June + x Smith,White,June = 1 x Jones,Maize,July + x Jones,Blue,July + x Jones,White,July = 1. x Jones,Maize,June + x Jones,Blue,June + x Jones,White,June = 1 x rsm = 1, r R, m M s S 21

22 Constraints 2. Every resident satisfies their educational requirements x Smith,Maize,July Is Dr. Smith assigned to the Maize service in July? If yes, x Smith,Maize,July = 1. If no, x Smith,Maize,July = 0. x Smith,Maize,Aug. x Smith,Maize,June Is Dr. Smith assigned to the Maize service in August? Is Dr. Smith assigned to the Maize service in June? 1 x Smith,Maize,July + x Smith,Maize,Aug x Smith,Maize,June 2 22

23 Constraints 2. Every resident satisfies their educational requirements 1 x Smith,Maize,July + x Smith,Maize,Aug x Smith,Maize,June 2 1 x Smith,Blue,July + x Smith,Blue,Aug x Smith,Blue,June 2 1 x Smith,White,July + x Smith,White,Aug x Smith,White,June 2 1 x Jones,Maize,July + x Jones,Maize,Aug x Jones,Maize,June 2. 1 x Jones,Blue,July + x Jones,Blue,Aug x Jones,Blue,June 2 λ rs m M x rsm μ rs, r R, s S 23

24 Constraints 3. Every service satisfies their service coverage needs x Smith,Maize,July Is Dr. Smith assigned to the Maize service in July? If yes, x Smith,Maize,July = 1. If no, x Smith,Maize,July = 0. a Smith,GS a Smith,PGY1 a Smith,GS_PGY1 Is Dr. Smith a General Surgery resident? If yes, a Smith,GS = 1.If no, a Smith,GS = 0. Is Dr. Smith a PGY1 resident? If yes, a Smith,PGY1 = 1. If no, a Smith,PGY1 = 0. Is Dr. Smith a General Surgery PGY1 resident? If yes, a Smith,GS_PGY1 = 1. If no, a Smith,GS_PGY1 = 0. 24

25 Constraints 3. Every service satisfies their service coverage needs 3 a Smith,GS x Smith,Maize,July + a Jones,GS x Jones,Maize,July + a Chan,GS x Chan,Maize,July a Gupta,GS x Gupta,Maize,July 4 1 a Smith,PGY1 x Smith,Maize,July + a Jones,PGY1 x Jones,Maize,July + a Chan,PGY1 x Chan,Maize,July a Gupta,PGY1 x Gupta,Maize,July 2 L csm r R a rc x rsm U csm, c C, s S, m M 25

26 Expanded Model Distributed Educational Requirements Distributed Coverage Needs Extended Rotations Service Sequencing Service Spacing Resident Pairing 26

27 Presentation Outline Background Motivation Model Formulation Model Implementation Conclusions and Future Work 27

28 Implementation Process 28

29 Presentation Outline Background Motivation Model Formulation Model Implementation Conclusions and Future Work 29

30 Recap Scheduling issues affect hospital workflow, training quality, and patient safety Scheduling residency programs at UMHS is highly interdependent, complex, and poorly executed We can address these scheduling needs using a linear programming formulation 30

31 Future Work Define metrics for schedule optimality Minimize deviation from desired resident complement by service Maximize satisfied requests for educational customization Apply model to improve scheduling for other training programs 31

32 Related Applications Pediatric Medicine rotation schedule C.S. Mott Emergency Department shift schedule Chemotherapy infusion patient schedule Physician clinic/or schedule Master surgical schedule problem Nurse staff scheduling 32

33 Acknowledgements Center for Healthcare Engineering and Patient Safety University of Michigan Department of Surgery The Seth Bonder Foundation The Doctors Company Foundation 33

34 Questions [? ] and Comments [! ] Billy Pozehl pozewil@umich.edu Dr. Rishi Reddy reddyrm@med.umich.edu Prof. Jake Seagull jseagull@med.umich.edu Prof. Amy Cohn amycohn@med.umich.edu Prof. Mark Daskin msdaskin@umich.edu Janice Davis janiced@med.umich.edu 34