Doctor Scheduling at Baystate Hospital

1
Doctor Scheduling at Baystate Hospital

• Rohan Khatau
• Claudio Stefan

2
Background

• Baystate Hospital in Springfield, MA compiles a
  quarterly schedule assigning doctors to specific
  shifts
• They have one person in charge of the schedule
  who follows a general guideline and fills it in
  manually
• Will acquire computer software at the end of this
  month
• Our Task scheduling for the month of June

3
Problem Details

• Assignment Problem with three types of doctors
• Clinicians
• Hospital Educators
• Dedicated Nocturnists
• Each set of doctors has its own specific shifts
  and constraints
• FTE (some work part time and some are full time)
• Clinicians can work day or night shifts
• Educators only work during the day
• Dedicated Nocturnists only work the overnight
  shift

4
Shifts

• For weekdays
• Eleven Clinician shifts, ten from 8am to 4pm and
  one from noon to 4pm
• Eight Hospital Educator shifts, all from 8am to
  4pm
• Two overnight shifts
• For weekends
• Ten clinician shifts (all from 8am to 4pm)
• Five Educator shifts
• Two overnight shifts

5
Some Important Rules and Constraints

• Maximum Number of shifts in a row is seven
• Maximum Number of overnights in a row is four
• Weekend Work is two weekends a month (only for
  Clinicians)
• If a physician worked overnight, the only shift
  he or she can work the following day is another
  overnight shift
• It is preferred that a physician works the same
  shift as much as possible during the seven day
  span
• All doctors are limited to one shift per day

6
Our Task

• Find a solution to this assignment problem using
  Integer programming
• See what we could do to improve the schedule
  using Baystates specific constraints
• See if academic scheduling methods are practical
  in a hospital environment

7
Methodology

• Integer program to solve the assignment problem
  (solved using ampl)
• Define Binary Variable
• Xi,j,k 1 if doctor i works shift j during
  day k 0 otherwise
• i indexes doctors (44 doctors in total)
• j indexes shifts (21 weekday shifts) (17
  weekend shifts)
• k days (30 total for June)

8
Methodology

• Constraints will make sure that only one doctor
  will be assigned to each shift on each day
• For the objective function, we added a bonus
  variable
• bonusi,j,k 7(Xi,j,kXi,j,k1 Xi,j,k2
  Xi,j,k3 Xi,j,k4 Xi,j,k5 Xi,j,k6)
• this will keep track of days in which the
  physicians worked the same shift and assign a
  large bonus for those respective days
• Objective Function
• max ? ? ? bonusi,j,k
• days shifts doctors

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Constraint Overview

• Seven Days in a Row
• ? (Xi,j,k Xi,j,k1 Xi,j,k2
  Xi,j,k6 i,j,k7) lt7
• shifts
• for all i and k
• Four Nights in a Row for Nocturnists
• ? (Xi,j,k Xi,j,k1 Xi,j,k2
  Xi,j,k3 Xi,j,k4) lt 4
• Night shifts
• for all i in Nocturnists, k in Days
• Cannot Work a Day Shift Following an Overnight
  Shift
• ? Xi,j,k ? Xi,j,k1 lt 1
• Night shifts Day shifts
• for all Clinicians on all days

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June 2009 Schedule (week 1)
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Sample Code (from .mod file)
var bonus1i in allDoctors, j in allShifts, k in
allDays gt 0 lt50 integer var Xi in
allDoctors, j in allShifts,k in allDays gt0 lt1
integer maximize objectiveDays sum i in
allDoctors,j in allShifts, k in bonusDays1
bonus1i,j,k subject to shiftAndDayConstraint
j in allShifts, k in weekDays sumi in
allDoctors Xi,j,k 1 subject to
shiftAndDayConstraint2 j in weekEndShifts, k in
weekEnds sumi in allDoctors Xi,j,k
1 subject to shiftAndDayConstraint3 j in
weekDayShifts, k in weekEnds sumi in
allDoctors Xi,j,k 0 subject to
shiftAndDayConstraint4 j in nightShifts, k in
allDays sumi in allDoctors Xi,j,k
1 subject to bonusConstraint1 i in allDoctors,
j in allShifts, k in bonusDays1 (bonus1i,j,k
7(Xi,j,kXi,j,k1Xi,j,k2Xi,j,k3 X
i,j,k4Xi,j,k5Xi,j,k6)) subject to
FTEConstraint i in allDoctors sumj in
allShifts,k in allDays Xi,j,klt FTEi
subject to nocturnistConstraint1 i in
nocturnists, k in allDays sumj in nightShifts
Xi,j,k lt 1 subject to nocturnistConstraint2
i in nocturnists sum j in dayShifts,k in
allDays Xi,j,k 0 subject to
CHMPnightConstraint i in CHMPs sum j in
nightShifts, k in allDays Xi,j,k lt
1 subject to CHMPshiftConstraint i in CHMPs
sum j in educatorShifts, k in allDays Xi,j,k
0 subject to HospEdNightConstraint i in
educators sum j in nightShifts, k in allDays
Xi,j,k0
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Sample Code
subject to HospEdshiftConstraint i in
educators sum j in chmpShifts, k in allDays
Xi,j,k0 subject to doctorAndDayConstraint i
in allDoctors, k in weekDays sum j in
allShifts Xi,j,k lt1 subject to
doctorAndDayConstraint2 i in allDoctors, k in
weekEnds sum j in weekEndShifts Xi,j,k
lt1 each doctor has to work at most one shift
every day subject to consecutvieDaysConstraint
i in allDoctors, k in consecutiveDays sum j
in allShifts (Xi,j,kXi,j,k1 Xi,j,k2Xi
,j,k3Xi,j,k4Xi,j,k5Xi,j,k6
Xi,j,k7)lt7 every doctor is only allowed to
work at most 7 seven days in a row you need the
last term because there should be a break between
the shifts subject to weekEndConstraint i in
CHMPsandEducators sum j in weekEndShifts, k in
weekEnds Xi,j,k lt4 doctors are allowed at
most one weekend of work subject to
RougemontDaysConstraint k in RougemontDays sum
j in nightShifts X"Rougemont",j,k
1 subject to EnriquezDaysConstraint k in
EnriquezDays sum j in nightShifts
X"Enriquez",j,k 1 subject to
FloresDaysConstraint k in FloresDays sum j in
nightShifts X"Flores",j,k 1 subject to
PalacioDaysConstraint k in PalacioDays sum j
in nightShifts X"Palacio",j,k
1 constraints for the nocturnists - what
specific days they are working on subject to
dayAfterOvernight i in CHMPs, k in
overnightDays (sum j in nightShifts Xi,j,k
sumj in dayShifts Xi,j,k1) lt 1 no
doctor will have a shifts following his overnight
visit
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The IP Solution

• Benefits
• Much more efficient than pencil and paper
  method
• Ensures that all constraints, if defined
  properly, are satisfied
• Enables one to identify inconsistent and
  redundant constraints
• One can write a simpler program and use it as a
  starting point for manual scheduling
• Shortcomings
• Less Flexible than the manual method
• Some Constraints are difficult to define and
  implement
• Output is difficult to interpret
• Need specialist to adjust and run the program

14
Thanks to

• the Baystate Hospital staff, especially Carmen
• Curry

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Questions?