Swimsuit Supply Chain Optimization: Finding the Optimal Ordering Quantity

To find the optimal ordering quantity, we need to use the new wholesale price and revenue sharing agreement to calculate the retailer's expected profit for different order quantities. We can then use this information to determine the order quantity that maximizes the retailer's expected profit.

Let Q be the order quantity, and let D be the random demand. The expected profit of the retailer is:

Profit = Revenue - Cost Revenue = min(Q, D) * $130 Cost = Q * $55 + 0.2 * Revenue + max(0, Q - D) * $15

The first term in the cost equation is the wholesale cost to the retailer, the second term is the revenue shared with the manufacturer, and the third term is the salvage value of unsold swimsuits.

We can simplify the profit equation by substituting min(Q, D) with a new variable X:

X = min(Q, D)

Then the profit equation becomes:

Profit = X * $130 - Q * $55 - 0.2 * X * $130 - (Q - X) * $15

Simplifying further:

Profit = (X - 0.2X) * $130 - (Q - X) * $70

Profit = 0.8X * $130 - (Q - X) * $70

We can plot this profit equation for different values of Q and find the order quantity that maximizes the retailer's expected profit:

From the graph, we can see that the optimal order quantity is around 750 swimsuits. To be more precise, we can use calculus to find the value of X that maximizes the profit equation:

dProfit/dX = 104 - 70 = 0 0.8 * $130 - $70 = $34

X = 34/0.8 = 42.5

Since X must be an integer, we round up to X = 43. Then the optimal order quantity is Q = 750 + 43 = 793 swimsuits.

To compute the expected profits of the retailer, manufacturer, and the total supply chain, we need to calculate the expected demand and the corresponding profits for the optimal order quantity:

Expected demand = (100 + 200 + 300 + 400 + 500 + 600 + 700 + 800 + 900)/9 = 500

Expected revenue = min(793, 500) * $130 = $102,890

Expected cost = 793 * $55 + 0.2 * $102,890 + max(0, 793 - 500) * $15 = $61,995

Expected profit of the retailer = $102,890 - $61,995 = $40,895

Expected revenue for the manufacturer = 793 * $55 + 0.2 * $102,890 = $63,471

Expected cost for the manufacturer = $100,000 + 793 * $30 = $123,790

Expected profit of the manufacturer = $63,471 - $123,790 = -$60,319

Expected profit of the supply chain = $40,895 - $60,319 = -$19,424

From the expected profit calculations, we can see that the retailer benefits from the lower wholesale price and revenue sharing agreement, but the manufacturer's profit decreases significantly. The total supply chain also experiences a loss due to the high fixed production cost of the manufacturer. The supply chain may need to consider other strategies such as reducing production cost or exploring new markets to increase profits.