Assignment:
Q: In the next week, Ryan Ltd. will sell cashmere jerseys during the local market in Madeira (OH). Ryan will sell the jerseys at $80. Suppose the following table shows the probability of jerseys sales quantities.
|
Probability
|
0.05
|
0.1
|
0.3
|
0.2
|
0.2
|
0.15
|
|
Demand
|
100
|
200
|
300
|
400
|
500
|
600
|
The manufacturer of the jerseys, Scott Ltd., sells the jerseys at $40 each. Based on the contract, Scott will buy back any left over. The buy-back price is still negotiable. Scott has calculated that his optimal production order size is 400 units, therefore he would like to set the buy-back price so that Ryan orders exactly 400 units.
1. Compute the buy-back price b such that Ryan orders 400 units.
Since Scott will buy back any leftover, the salvage value for Ryan is the buy-back price. You do not know the buy-back price (b), therefore Ryan's critical ratio is a function of b.
You need to solve the exercise the other way around: Ryan will order 400 units if his Critical Ratio will be in a certain range of values...: what range of values is it? Find it. Once you know the range (e.g. 100 < Critical Ratio <= 200), solve the 2 inequalities for b to find the range of values for b.
2. The unit production cost of Scott (the Manufacturer) is $20. What buy-back price should the supply chain partners choose in order to maximize the whole supply chain profit (= coordinated supply chain)?
When you consider the whole supply chain, the transfer of money between the two actors (buy-back price; purchasing cost) is ignored. Therefore, the relevant financial flows are: the price that Ryan gets from the sale and the cost that Scott pays for manufacturing the jerseys. Notice that the salvage value is zero here.