Question 2 (2+2+3+3+3=13 points) – Newsvendor model with Normal demand Consider

Question

Question 2 (2+2+3+3+3=13 points) – Newsvendor model with Normal demand Consider a product satisfying assumptions of the newsvendor model. Demand ~ Normal[=1000, =200]. Purchase cost: $100 / unit. For every unit sold, there is a profit of $30 per unit. (Revenue = cost + profit = 100 + 30 = $130). Unsold units are disposed off at a loss of value: $20 per Unit (therefore V=$80).
a.) What is the mean demand?
b.) What is the newsvendor critical ratio?
c.) What is the optimal order quantity Q*? (Use Standard Normal Distribution Function Table 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? (Use Standard Normal Loss Function Table)
e.) If we order Q* as obtained in (c), what is the expected profit?

Explanation / Answer

a) Using the Normal Distribution Method, we can see that the mean demand is 1000.

b) The newsvendor Critical Ratio (PC) = ML (Marginal loss incurred by not selling a unit) divided by MP (Marginal profit incurred from selling a unit) + ML

= PC= 20/(20+30)

=20/50=0.4

c) Optimal Order Quantity = Mean+ZSL

SL = (Revenue - Cost)/ (Revenue - Salvage Value) = 30/50 = 0.6

Since the z-value for SL i.e. 0.6 is 0.255,

Opt. Order Quantity = 1000+0.255*200 = 1051 units

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