Scheduling Surgery Residents

1
Scheduling Surgery Residents

• New rules limit work hours
• Scheduling problem
• Interesting context

2
Medical Education in the US

• Bachelor (4 years)
• Medical School (4 years)
• 42,974/year tuition at Northwestern
• Residency
• 3-7y, 5y for general surgery
• paid (first years 48,270.96 at Northwestern)
• Fellowship (subspecialties)

3
Residency

• Training of doctors
• Cheap labor
• Funded by Medicare
• If you have one less nurse, then you've saved
  40,000. If you have one less resident, you've
  saved 40,000, but you've lost 100,000 in
  reimbursement.
• Limited supply
• The Match and the Scramble
• Working conditions

4
Work Rules

• NY State Libby Zion law (1989)
• From accreditation body (ACGME, 2003)
• Work week 80 hrs (over averaged over 4wks)
• 1 on call night every 3 days
• 30 hr max shift
• 10 hr between shifts
• Routinely flouted
• Does not apply to fellows
• Controversy
• Reducing medical errors
• Getting necessary medical training

5
Scheduling Problem

• Hospitals (cheap labor) perspective
• How to cover various areas
• Rotations in Duke hospital, and
• Nearby hospitals
• Without violating the law

6
Formulation

• Seeking a schedule for a week
• MIP feasibility problem
• I set of residents
• J services to cover
• Includes other hospitals
• Includes time-off
• K set of 4 hr time slots
• xijk 1 if resident i covers service j at time k
• binary

7
Formulation

• zij1 if resident i does rotation j (binary)
• ?j zij 1 (at most one rotation in a week)
• ?k xijk 20zij (80 hrs/rotation limit)
• ?j xijk 1 (one thing at a time)
• ?ik xijk 1 (at least one available at each loc)
• 2xi,11,kxi,11,k1xi,11,k2 2xi,11,k-1 (breaks
  12hr)

8
Sample Result

• 1st year resident in trauma rotation
• Schedule
• Monday 6am to Tuesday 6am
• Tuesday 6pm to Wednesday 6am
• Thursday 10am to Friday 6am
• Saturday 6am to Sunday 2am
• 76 hours total

9
Criticism

• A year is scheduled at a time
• Educational component?
• Ensuring coverage not a compelling constraint
• Hospital could hire more
• Residents
• Doctors