Advanced Medical Staff Scheduling & Hospitalist Duty Cycle Management
Born from helping a friend who was manually scheduling hospitalists at their hospital - we couldn't find any service that handled complex medical duty cycles and shift coverage, so we built one.
Adaptive Hospitalist Scheduling Algorithm
Shift Coverage Target: target = (n_hospitalists ÷ 2) ÷ 3
Where n_hospitalists is total staff count. Example: 22 hospitalists → 3.67 target per shift
Feedback Control System: Dynamic adjustment based on cumulative performance metrics
μ_current < μ_target → Apply ceil() function to increase shift coverage μ_current > μ_target → Apply floor() function to decrease shift coverage μ_current = μ_target → Apply ceil() (bias toward over-coverage )
Convergence Metrics: Dynamic adjustment maintains μ_actual near μ_theoretical
Adaptive algorithm: ceil() when below target , floor() when above target
Hospitalist Duty Cycle & Rotation Logic
Duty Cycle: Binary state machine with period T = 2 × k days
State: ON for k consecutive days , then OFF for k consecutive days . Example: k=9 → T=18 day cycle
Temporal Shift Assignment: Sequential rotation through shift set S = {AM, Noon, Night}
Ensures uniform distribution: ∀s ∈ S, |assignments(s)| ≈ |assignments|/3
Position Permutation: Cyclic group operation on position set P = {1,2,...,max_per_shift}
Prevents static team composition: σ(i) = (i mod max_per_shift) + 1
Hospitalist Resource Allocation & Load Balancing
Priority-Based Assignment: Multi-factor scoring system for optimal hospitalist selection
Score factors: total_shifts + exception_bonus + below_avg_bonus + shift_balance (lower score = higher priority )
Constraint Satisfaction: Enforces minimum shift coverage requirements and duty cycle constraints
Subject to: |hospitalists_per_shift| ≥ 1 , duty_cycle_state ∈ {ON, OFF} , exception_rules
0
Avg Hospitalists/Shift
Total shift assignments ÷ Total number of shifts (days × 3)
0
Shifts/Person/Yr
Total shifts ÷ Number of hospitalists (should be ~182.5 for 50% work cycle)
0%
Workload Imbalance
(1 - Min shifts ÷ Max shifts) × 100 (0% = perfect balance)
January 2025
Shows the cumulative percentage of days worked by each hospitalist throughout the year
Weekend work distribution with min/max totals
Hospitalist Schedule