Robust Optimization for Integrated Healthcare Scheduling

Supervisor: Dr. Burak Gokgur

Overview

Integrated hospital scheduling sits at the intersection of surgical capacity planning and nurse rostering — two problems that are traditionally solved in isolation, even though they share the same bottlenecks (OR time, recovery beds, nurse hours). Solving them jointly under uncertainty is what makes the problem interesting.

Approach

I formulated a Mixed-Integer Linear Program with budgeted uncertainty (Bertsimas & Sim, 2004) over both surgical demand and nurse availability. The budget parameter lets the hospital administrator trade conservatism for optimality explicitly.

• Decision variables: surgery-to-day-to-OR assignment, nurse-to-shift assignment.
• Constraints: coupled workload caps, skill-mix requirements, maximum consecutive shifts.
• Objective: weighted surgical throughput minus overtime penalties.

Implemented in Python with Gurobi, tested on synthetic instances calibrated against published hospital data.

Outcome

The robust model prevented staff workload violations during stochastic demand spikes without materially degrading surgical throughput on nominal days — the main trade-off a risk-averse planner wants to see.