Question

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $12 each from its Asian supplier, TeddySports. Unfortunately, at the time of the order placement, demand is still uncertain: Teddy Bower forecasts that its demand is normally distributed with a mean of 2,300 and a standard deviation of 1,100. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity (and also doesn’t collect a tax benefit for the donation).
a) How many parkas should Teddy Bower buy from TeddySports to maximize expected profit?

For parts b) through d), assume Teddy Bower orders 3,000 parkas (Q=3,000). b) What is Teddy Bower’s CSL (in-stock probability)?

c) On average, how many customers does Teddy Bower expect to turn away because of shortage? And on average, how many parkas will Teddy Bower liquidate after each season?

d) What is Teddy Bower’s expected profit?

Answer 1

Answer:

a) 2179 parkas

b) 0.7389

c) 174 customers

d) 10,772

Explanation:

Given:

Bower's selling price =$22

Salvage value: $0

Cost price = $12

Mean distribution= 2300 parkas

S.d = 1100 parkas

a) Number of parkas Teddy Bower should buy from Teddysports to maximize profit:

Let's first calculate overage(Co) and underage (Cu) cost.

•Cu = Selling price - Cost price

= $22 - $12

= $10

Underage cost = $10

•Co = Cost price - Salvage value

= $12 - $0

= $12

Overage cost = $12

Let's now find the critical ratio with the formula:

$\frac{C_u}{C_u+C_o}$

$= \frac{10}{12+10}$

= 0.4545

From the Excel function NORMSINV, the corresponding z value is =

NORMSINV(0.4545)

z value = -0.11

For the number of parkas Teddy Brown should order, we have:

Quantity = Mean +(z*s.d)

= 2300+ (-0.11 * 1100)

= 2179 parkas

b) for z value corresponding to expected sales of 3000 parkas, we have:

z value = (expected demand -mean)/s.d

$\frac{3000-2300}{1100}$

= 0.64

From the Excel function NOEMSDIST, the corresponding probability =

NORMSDIST(0.64)

= 0.7389 = 73.89%

In stock probability = 0.7389

c) For L(0.64) using the standard normal loss function table, L(z) =

L (0.64) = 0.158

For expected lost sales, we have:

S.d * L(z)

= 1100* 0.158

= 173.8

= 174.

On average, there is expected to be a turn away of 174 customers due to shortage.

d)

Lets first calculate expected sales and left over inventory.

•Expected sales = Mean -expected lost sales

= 2,300 - 174

= 2,126

•Left over inventory expected=

Expected demand - Expected lost sales

= 3000 - 2126

= 874

For expected profit, we have:

$(C_u* Expected lost sales)-(C_o* Expected leftover inventory)$

=($10*2126)-($12*874)

= $10,772

Profit expected = $10,772