Question

Problem 13-34 Demand for jelly doughnuts on Saturdays at Don's Doughnut Shoppe is shown in the following table. Demand (dozens) Demand (dozens) Relative Frequency .01 .05 25 Relative Frequency .10 .11 .10 .04 26 woo .02 a-1. Determine the optimal number of doughnuts, in dozens, to stock if labor, materials, and overhead are estimated to be $3.30 per dozen, doughnuts are sold for $4.65 per dozen, and leftover doughnuts at the end of each day are sold the next day at half price. (Round your answer to the nearest whole number.) Optimal number of doughnuts a-2. What is the resulting service level? (Round your answer to 2 decimal places.) Service level [ .67

Answer 1

The newsvendor model also called single-period model is nothing but the mathematical model which is used to determine the optimal quantity of perishable product that needs to maintained which is calculated based on fixed price and uncertain demand. Since the product is perishable and demand is uncertain the unsold items are worthless at the end of the day so newsvendor problem is solved to identify the optimal inventory level.

cost = $3.30 / dozen selling price $4.65/ dozen Salvage value - $4065 2 = $2.325 = = = selling $4.65 $ 1.35 price - cost _ $3.30 co= cost - salvage value = 3:30 - 2.325 - $ 0.915 Critical ratio = Cs Cs + Co 2135 1.35 + 0.975 1.35 2.325 = 0.58

Demand cumulative 01 frequency 19 Relative frequency 07 '05 12 .18 06 21 18 .36 13 49 23 24 25 "14 10 .63 73 26 .10 .84 94 .98 04 ·02 1.00 The first cumulative point that is greater than er equal to the service level is 0.63 Therefore the optimal amount = /24 doughnuts Answer 0-2 Service level = 0.58 Answer