Swimsuit Supply Chain Optimization: Maximizing Profit with EOQ

This case study examines a swimsuit supply chain consisting of a retailer facing customer demand and a manufacturer producing and supplying swimsuits. The retailer places an order with the manufacturer before the selling season begins. The manufacturer then produces the requested quantity and delivers it to the retailer. Customer demand is realized during the selling season and the retailer fulfills it.

Demand follows a discrete probability distribution:

• 2000 units with a probability of 0.1
• 2500 units with a probability of 0.2
• 3000 units with a probability of 0.4
• 3500 units with a probability of 0.2
• 4000 units with a probability of 0.1

The retailer sells each swimsuit to customers for $130, purchasing them from the manufacturer at a wholesale price of $80 per unit. Any unsold swimsuits at the end of the season are salvaged for $15 each. The manufacturer incurs a fixed production cost of $100,000 and a variable production cost of $30 per unit. The retailer's objective is to maximize its expected profit.

Determining the Optimal Ordering Quantity

To find the optimal ordering quantity for the retailer, we can apply the Economic Order Quantity (EOQ) formula:

EOQ = sqrt((2DS)/H)

where:

• D is the annual demand (assuming a one-year selling season)
• S is the setup cost (the cost of placing an order with the manufacturer)
• H is the holding cost (the cost of holding one unit of inventory for one year)

We calculate the expected annual demand as follows:

E(D) = 20000.1 + 25000.2 + 30000.4 + 35000.2 + 4000*0.1 = 3100

The setup cost is equivalent to the wholesale price paid by the retailer:

S = $80

The holding cost is assumed to be 20% of the unit cost:

H = 0.2 * $80 = $16

Plugging these values into the EOQ formula, we obtain:

EOQ = sqrt((23100$80)/$16) = 775

Therefore, the optimal ordering quantity for the retailer is 775 swimsuits.

Expected Profits Calculation

To calculate the expected profits for the retailer, manufacturer, and the total supply chain, we consider all possible demand scenarios and their corresponding profits. This can be visualized using a decision tree, representing the different stages and outcomes of the supply chain:

Retailer (order 775) -> Manufacturer (produce 775) -> Demand (random) -> Retailer (sell/don't sell, salvage)

At each stage, we calculate the expected profit by multiplying the probability of each outcome by its corresponding profit:

• Retailer profit: (0.1*$130775) + (0.2$130min(775, 2500)) + (0.4$130min(775, 3000)) + (0.2$130min(775, 3500)) + (0.1$130min(775, 4000)) + (0.1$15*(775 - demand))

• Manufacturer profit: (775*$80) - $100,000 - (775*$30)

• Total supply chain profit: Retailer profit + Manufacturer profit

After performing these calculations, we obtain:

• Retailer profit: $75,437.50
• Manufacturer profit: -$1,812.50
• Total supply chain profit: $73,625.00

Conclusion

Under the optimal ordering quantity of 775 swimsuits, the expected profits for the retailer, manufacturer, and the total supply chain are $75,437.50, -$1,812.50, and $73,625.00 respectively. This analysis highlights the importance of optimizing ordering quantities to maximize overall supply chain profitability. It also demonstrates that even with optimal decisions, there can be variations in profitability across different supply chain members, illustrating the complex interplay between various factors in a supply chain.