It is 1 November, around AD 50 (the year is only for illustration). The sea is closing for winter, and a city of about a million people must live on what is in the warehouses until the ships return in spring. You are in charge of Rome's grain. Choose a crisis, give your orders, and see if the city makes it through the next 18 months.
Days of grain = grain in store ÷ what the whole city eats in a full day. It doesn't stretch with rationing.
Every day, grain ships reach port from Africa (60% of the grain; March to mid-November, short trips), Egypt (30%; one slow convoy, mid-June to October) and Sicily and elsewhere (10%). An average ship carries about 275 tons (250 tonnes). The chance of losing a ship rises outside the safe sailing season, and the sea is closed from 11 November to 9 March. Grain takes 3 days to get up the Tiber. The city eats about 1.4 lb (0.65 kg) of grain a person a day, roughly 260,000 tons (237,000 tonnes) a year for a million people.
Days of grain is the grain in store divided by what the whole city eats in a full day. It doesn't stretch with rationing: on a three-quarter ration, 30 days of grain last 40 days.
Warehouses. Grain that doesn't fit is sold on or never shipped, so the stock going into winter is whatever the last few summers left. Each run starts after 3 normal years. The dates (AD 50–52) are only for illustration.
Calibration. We tuned the warehouse space and the import surplus so a normal winter falls below 15 days about once in 25 years and runs dry about once in 45. Each run spans two winters, so about 6% of normal runs dip below 15 days. Rome recorded lows of 15 days or less three times between AD 41 and 70: 7–8 days (AD 41), 15 (AD 51) and 10 (AD 70). None ended in mass death.
Assumed numbers, stated plainly (no source gives them):