daily demand of500 units and a standard deviation of S0. The lead time foy s saf

Question

daily demand of500 units and a standard deviation of S0. The lead time foy s safety component is 9 days. If a service level of 95% is desi comp stock for this component is approximately for the red, then the A) 150 units B) 247 units C) 336 units D) 740 units E) 810 units onut vendor has concluded that the demand for donuts is Normally Distributed with a mean of 28. A d 32 and a standard deviation of 7.85. The vendor purchases the rom a local bakery at $3.25 per dozen and sells them for $8.50 per dozen. Any donuts that are not sold a $2.00 per dozen. (ROUND YOUR INTERMEDIATE CALCULATIONS TO FOUR DECIMAL PLACES) (ROUND YOUR FINAL ANSWER TO THE NEAREST WHOLE NUMBER) What is the optimal quantity of donuts that the vendor should order? A) 24 B) 28 C) 32 D) 39 E) 34

Explanation / Answer

Given Lead time = 5 days

Service level = 95%

At Service level 95% Z = 1.644

Standard deviation = 50

Safety stock = 1.644*50*(9)(1/2)

Safety stock = 247units

B) 247 units

28)

Underage cost Cu = Revenue – purchase cost = 8.5-3.25 = 5.25

Overage cost Co = purchase cost – Salvage cost = 3.25-2 = 1.25

Service level = Cu/(Cu+Co) = 5.25/(5.25+1.25) = 0.8077

At service level 0.8077 Z = 0.8695

Order quantity Q = Mean + z*standard deviation = 32+0.8695*7.85 = 39

D) 39

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