Advanced: Safety stocks and probability theory A company has determined that the EOQ for its only raw material is 2000 units every 30 days. The company knows with certainty that a four-day lead time is required for ordering. The following is the probability distribution of estimated usage of the raw material for the month:

Stockouts will cost the company £10 per unit, and the average monthly holding cost is £1 per unit.

(a) Determine the optimal safety stock.

(b) What is the probability of being out of stock?

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Usage (units) 1800 1900 2000 2100 2200 2300 2400 2500 Probability 0.06 0.14 0.30 0.16 0.13 0.10 0.07 0.04