Quantum Optimization of Physician Scheduling For Maximal Healthcare Capacity

Abstract

Physician scheduling is a critical challenge in healthcare systems, demanding a balance between operational efficiency, fairness, and individual preferences. This thesis investigates the use of quantum computing, specifically the Quantum Approximate Optimization Algorithm (QAOA), as a novel approach to solving the Physician Scheduling Problem (PSP), a known combinatorial optimization task. Classical methods, Mixed Integer Linear Programming (MILP) with Gurobi and Satisfiability Modulo Theories (SMT) with Z3, are implemented as benchmarks and used to establish feasible, constraint-satisfying solutions. The PSP is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which serves as input to the QAOA algorithm. This is then executed on both quantum simulators and IBM’s real quantum hardware. A modular scheduling framework is developed to encode fairness, availability, preferences, and contractual work extent into the objective functions, enabling both short- and long-term optimization scenarios. Comparative evaluations reveal that while classical solvers consistently yield feasible schedules, QAOA demonstrates potential for competitive solution quality despite current hardware limitations.