Question

A lab orders a number of chemicals from the same supplier every 10 days. The lead time is six days. The assistant manager of the lab must determine how much of one of these chemicals to order. Check of stock reviewed that 5 jars of 30-milliliter (ml) are on hand. Daily usage of the chemical is appropriately normal with a mean of 11.5 ml per day and a standard deviation of 2.6 ml. The desired service level for this chemical is 95%.

a) How many jars of the chemical should he ordered?

b) What is the average amount of safety stock of the chemical?

Answer 1

Solution-

(A)

This is a fixed-order-interval system

Here, Target inventory = Expected demand + safety stock

= average demand*timespan + z*sqrt(Length of review period + lead time)*standard deviation of demand

= average demand*(Length of review period + lead time) + z*sqrt(Length of review period + lead time)*standard deviation of demand

= 11.5*(10+6)+1.65*sqrt(10+6)*2.6 - 150 = 51.16 ml

[z score = 1.65 for service level 95%]

order quantity = 51.16 ml

So number of jars to order = 51.16/30 = 2 (Approx)

b)

Safety stock = z*sqrt (Length of review period + lead time)*standard deviation of demand = 1.65*sqrt(10+6)*2.6 = 17.16

-average amount of safety stock of the chemical = 17.16 ml

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