Question

Flower sellers Thomas and Roberto sell roses on the same block. Thomas and Roberto sell their flowers at $2.50 and throw away their flowers at a compost company which pays 25 cents for the old flowers. The demand for their flowers has a normal distribution (mean = 40 and sd= 15). In order to find optimal quantities they both use the newsvendor model. Thomas found a new wholesale distributor unbeknownst to Roberto. Roberto is envious of Thomas and wants to be able to estimate the purchase cost that Thomas is buying flowers at now. Roberto sees that Thomas brings 49 flowers to sell each morning. 2] Assume Roberto correctly assumes that Thomas uses the newsvendor model to compute her optimal order quantity where Q* is equal to 49.flowers what is Roberto’s estimate of c?

Answer 1

Cost of shortage Cs = price - cost = 2.5-c

Cost of overage Co = cost - salvage value = c-0.25

service level = Cs / Cs+Co = 2.5-c / 2.5-c+c-0.25 = 2.5-c /2.25

Optimum order size is defined as

Q = mean + z xstandard deviation

where z is a measure of in stock service level

49 = 40+zx15

z = 9/15 = 0.6

service level for z =0.6 is 0.7257

Now, 0.7257 = 2.5-c/2.25

c = 2.5 -2.25*7257 = 0.8671