A baker must decide the right number of breads to bake at the beginning of the d
ID: 349161 • Letter: A
Question
A baker must decide the right number of breads to bake at the beginning of the day. He can sell the bread for $1.50 while his ingredients and labor costs are $0.75 in total. If he is unable to sell a bread loaf at the end of the day, he can give it to a discount store for $0.25. The deli manager has run statistics on historical demand and determined the weekly demand was normally distributed with mean of 2,000 and standard deviation of 150 units. The store is open 24 hrs a day, 7 days a week for business and no apparent seasonal/cyclic pattern can be found.
Explanation / Answer
This problem will be solved using Newsvendor model
As per Newsvendor model ,
Sale price of bread = P = $1.50
Cost of bread = C = $0.75
Salvage price = S = $0.25
Thus,
Cost of underage = Cu = P – C = $1.50 - $0.75 = $0.75
Cost of overage = Co = C – S = $0.50 - $0.25 = $0.25
Therefore , Critical Ratio = Cu / Cu + Co = 0.75 / ( 0.75 + 0.25) = 0.75/1 = 0.75
Critical ratio is the probability of the optimum order quantity .
Thus probability of the optimum order quantity = 0.75
Corresponding Z value for probability of 0.75 = 0.6745
Therefore optimum order quantity for the stores manager
= Mean weekly demand + Z value x Standard deviation of weekly demand
= 2000 + 0.6745x 150
= 2000 + 101.17
= 2101.17 ( 2101 rounded to nearest whole number )
OPTIMUM ORDER QUANTITY FOR THE STORES MANAGER = 2101
OPTIMUM ORDER QUANTITY FOR THE STORES MANAGER = 2101
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