Consider a product satisfying assumptions of the newsvendor model. Demand ~ Norm

Question

Consider a product satisfying assumptions of the newsvendor model. Demand ~ Normal[=1000, =200]. Purchase cost: C=$100 / unit. For every unit sold, there is a profit of $40 per unit (Revenue= R= cost + profit = 100 + 40 = $140). Unsold units are disposed off at a loss of value: $10 per Unit (therefore V=$90).

a.) What is the mean demand?

b.) What is the newsvendor critical ratio?

c.) What is the optimal order quantity Q*? (Round up to the nearest integer if you get a non-integer.)

d.) If we order Q* as obtained in (c), what is the expected lost sales?

e.) If we order Q* as obtained in (c), what is the expected profit?

Explanation / Answer

It is mentioned that demand follows normal distribution with mean 1000 and standard deviation 200.

Expected Lost sales = .2*40 = 8

Expected Profit = .8*10 = 8

a.) What is the mean demand? Mean demand is 1000 units b.) What is the newsvendor critical ratio? Critical ratio = Marginal Loss / (Marginal Loss+Maginal Profit) = 10/(40+10)=.2 c.) What is the optimal order quantity Q*? (Round up to the nearest integer if you get a non-integer.) Optimal Q is for Prob.( demand>=Q) = critical ratio=.2 Standard Normal Z = (X-1000)/200 value of Z for critical ratio is 0.84162 Therefore Optimal order quantity Q = 1000 +(.84162*200)=1168 Using NORMDIST the value obtained is 1169 for comulative probability of 0.800945

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