Swimsuit Supply Chain Optimization: Retailer and Manufacturer Profit Maximization

To find the optimal ordering quantity, we need to first calculate the expected demand for the season. Using the provided demand distribution, we can calculate the expected demand as:

Expected demand = (0.2 x 100) + (0.3 x 200) + (0.3 x 300) + (0.2 x 400) = 260

Next, we can calculate the optimal ordering quantity using the newsvendor formula:

Optimal ordering quantity = (zα + zβ)σ/λ where zα is the z-score for the desired service level (we'll assume a service level of 95%, so zα = 1.645), zβ is the z-score for the salvage value (we'll assume a salvage value of $15, so zβ = -0.524), σ is the standard deviation of demand (calculated as [400-260]^2 x 0.2 + [300-260]^2 x 0.3 + [200-260]^2 x 0.3 + [100-260]^2 x 0.2 = 3600), and λ is the unit contribution margin (calculated as $130 - $80 = $50).

Plugging in the values, we get:

Optimal ordering quantity = (1.645 + (-0.524)) x sqrt(3600)/50 = 47.75, rounded up to 48

Therefore, the retailer should order 48 swimsuits from the manufacturer.

To calculate the expected profits, we can use the following table:

| | Retailer | Manufacturer | Total supply chain ||----------------|----------|--------------|--------------------|| Revenue | $6,240 | $3,840 | $10,080 || Cost of goods | $3,840 | $2,640 | $6,480 || Salvage value | $720 | $240 | $960 || Profit | $3,120 | $440 | $3,560 |

Note that the manufacturer's profit is simply the revenue from the sale of swimsuits ($80 x 48 = $3,840) minus the variable production costs ($30 x 48 = $1,440) minus the cost of buying back unsold swimsuits ($60 x max(0, 48-260) = $0, since the retailer will sell all 48 swimsuits).

The retailer's profit is the revenue from the sale of swimsuits ($130 x min(48, 260) = $6,240) minus the cost of goods sold ($80 x 48 = $3,840) plus the salvage value of any unsold swimsuits ($15 x max(0, 48-260) = $720).

The total supply chain profit is the sum of the retailer and manufacturer profits plus any salvage value of unsold swimsuits ($15 x max(0, 260-48) = $240).

Therefore, the expected profits for the retailer, manufacturer, and total supply chain are:

Retailer: $3,120 Manufacturer: $440 Total supply chain: $3,560