Why Manual Scheduling of Resident Rosters Fails: "Schedule Gridlock" and the Case for Combinatorial Optimization

Staff scheduling is pervasive in healthcare and has profound ramifications for safety, efficiency, and morale. Resident block scheduling is particularly demanding, requiring simultaneous satisfaction of regulatory requirements, evolving clinical eligibility, programmatic priorities, and individual preferences. Despite the availability of mature and superior optimization methods, such schedules are commonly produced by hand.

We modeled the clinical base year deployment at one anesthesiology residency and solved it using the CP-SAT solver from Google's OR-Tools, under a weighted objective function over elective and vacation preferences. We retrospectively compared solver-generated schedules against the schedule manually produced and deployed for academic year 2022-2023 (AY22-23) on preference satisfaction, distribution of strenuous rotations, and timing of formative rotations. We then prospectively deployed the system for three subsequent academic years (AY23-24 to AY25-26), characterized the structure of the solution space by enumeration, and assessed large language model (LLM) assistance for input specification.

Our framework produced valid schedules in a median of 39 seconds (interquartile range [IQR], 22-67 seconds). Compared with the manually constructed AY22-23 schedule, which required 10 to 20 hours and violated several constraints, solver-generated schedules granted a median of 1.5 more "top priority" elective requests per resident (95% confidence interval [CI], 0.5-2.0; P < .001) and, by construction, precluded triplets of consecutive strenuous rotations-which occurred in an average of 8% of three-block windows under manual scheduling (bootstrapped 95% CI, 7-10). The solver-generated schedule deployed all 26 residents to a formative rotation within the required window (vs 23 of 26 in the manual schedule). Across 3 years of prospective use, new and evolving requirements-ranging from a delayed-visa contingency to a phased surgical intensive care unit (SICU) rotation structure-were accommodated by configuration-file changes alone in most cases; only two reusable constraint primitives required additions to the solver code. LLM-assisted configuration of AY26-27 was feasible but depended on active human review. Approximately 4.4 × 1018 valid schedules exist per resident, yet 76% (95% CI, 73-79) of a resident's assignments admitted no valid alternatives. We term this property "schedule gridlock."

An expressive constraint-specification language kept combinatorial optimization ergonomic across 3 years of evolving program requirements. Schedule gridlock-local rigidity in spite of global flexibility-helps explain why automated generation of schedules is so much more effective. The barrier to wider adoption has not been solver efficacy, which is well-established, but the burden of encoding and maintaining institutional requirements in a form amenable to optimization. This study addresses that burden.