A balanced rota can still fail: a two-person scheduling example

A rota can give everyone the same number of assignments and still leave a shift uncovered. The problem often starts with a reasonable shortcut: assign the next shift to the person with the lowest current workload. Here is a small, fictional example that exposes the limitation. Person Morning Afternoon Maximum assignments Ada Available 1 Ben Unavailable Both shifts need one person. At the start, Ada and Ben have equal workloads. If a greedy tie-break assigns Ada to the morning, the afternoon is left without an eligible person: Ben is unavailable, and Ada has reached her limit. Yet a complete sc
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