Tyranolicious, a manufacturer of gourmet organic dinosaur treats, wishes to bett
ID: 450224 • Letter: T
Question
Tyranolicious, a manufacturer of gourmet organic dinosaur treats, wishes to better manage its ordering process. Because of the nature of its business, Tyranolicious guarantees its product is no more than a day old, and donates the remains of the day’s inventory to the local animal shelter. The ingredients for a pound of Tyranos cost $3, and are worth 10 cents (as a tax write-off) when donated. Each pound of Tyranos sells for $10. The average demand is 50 and the standard deviation of demand is 10.
a. How much ingredients (in pounds) should Tyranolicious order for each day?
b. If Tyranolicious decides that it wishes to have a 95% customer service level, what is the new stocking level?
c. What is the implied shortage cost at this 95% customer service level? Does this value seem reasonable to you? Why or why not?
Explanation / Answer
The cost of underestimating demand is $7 and cost of overestimating demand is $2.90 Cu = $10 - $3 = $7 Co = $3 - $0.10 = $2.90 P Cu / Cu + Co P 7/7 + 2.90 P 0.7071 Z Value at above probability = 0.54485 Per day order = Mean + Z Value * SD = 50 + 10*0.54485 = 55.448 Tyranolicious should order 55 ingredients each day. At 95% service level, Z Value = 1.645 = 50 + 10 * 1.645 = 50 + 16.44 = 66 P Cu / Cu + Co or, 0.95 = Cu / Cu + 2.90 or, 0.95 * (Cu + 2.90) = Cu or, 0.05 Cu = 2.755 or, Shortage Cost (Cu) = 2.755 / 0.05 = 55.10 This value is unreasonable as cost of product is $3 and selling price is $10. So to incur shortage loss of $55.10 is absurd.
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