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Scheduling Surgery Residents

Scheduling Surgery Residents. New rules limit work hours Scheduling problem Interesting context. 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

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Scheduling Surgery Residents

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  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 • Hospital’s (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 • zij=1 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,k+xi,11,k+1+xi,11,k+2 ≥ 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

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