Staff a distribution centre for one week - 7 days × 3 shifts - against a demand profile. Every missing worker costs service, every extra one costs money.
Outline = demand. Solid = what you rostered. Red gap = a shift you left short.
Wages fall and penalty rises as you cut staff. The cheapest week is where the two stop trading evenly - not where coverage hits 100%.
Shift scheduling matches paid capacity to a time-varying demand profile. Demand for pickers rises and falls across the day and the week, but every rostered worker is paid whether the work shows up or not - the roster is a bet on the demand curve.
Each cell of the week is its own little decision: the cost of one more worker (the casual rate for that shift and day) versus the cost of a gap (the service-failure penalty). Wages versus penalty decides every cell, one worker at a time.
Full coverage is NOT always optimal. When the penalty for an empty slot is cheaper than the shift that would fill it, the rational roster deliberately leaves it empty - cutting cost without cutting anything that pays for itself.
