For a product that sells for $10 per unit in the open market, wholesale margins are 50% and retail margins are 33% (that is, the wholesalers buys the product for $5 per unit, then sells it to the retailer for $7.50 per unit, who sells it to end customers for $10). The manufacturing cost for the product is $2 per unit. HINT: For each stage in the supply chain calculate the values of Cs and Cx - assume cost of shortage is the margin and all of it lost if they don't have it in stock and cost of overstocking is the price paid for the product, that is, if you overstock and don't sell it, there is no salvage value from the product.
Likely demand for the product (demand history data)
|
Demand observed (X)
|
Frequency of observation
|
Probability
|
Cumulative probability that demand is less than X
|
|
12000
|
2
|
2/.08
|
0.08
|
|
15000
|
5
|
5/.20
|
0.28
|
|
30000
|
6
|
6/.24
|
0.52
|
|
46000
|
10
|
10/.40
|
0.92
|
|
50000
|
2
|
2/.08
|
1.00
|
|
Totals
|
25
|
1.00
|
|
- If retail demand for the product is as above, how much product will the retailer stock?
- How much product will the wholesaler stock?
- How much product will the manufacturer stock?
If this were a totally coordinated supply chain (for example, the same firm owned the manufacturing company, the distributor and the retailer like, say an Apple store), what would be the optimal stocking level?