Question

Gucci finally opens an online shop to cater to their growing online demand. To ensure that it can deliver in time to its customers, Gucci keeps inventory of its most popular products in a fulfilment centre. When a replenishment is needed, it places an order from a local supplier who can deliver within a few hours. The cost of placing an order is $1000 per order. Gucci has an inventory holding cost of 30% per year. The company operates 360 days per year.

Gucci’s bestselling bag is the Bamboo, which retails for $125 per bag. The supplier charges Gucci a unit procurement cost of $30 for each Gucci bag it orders. Suppose that Gucci sells three Bamboo bags a day.

a) Suppose that Gucci decides to order exactly four times a year, how many Bamboo bags should it order each time to minimize inventory holding cost without ever running out?

Answer 1

To minimize inventory holding costs without running out, Gucci should order approximately 490 Bamboo bags every quarter (four times a year), using the Economic Order Quantity (EOQ) model.

Step-by-step explanation:

To determine how many Gucci Bamboo bags should be ordered each time to minimize inventory holding costs without running out, we employ the Economic Order Quantity (EOQ) model. Since Gucci sells three bags a day and operates 360 days per year, the annual demand (D) is 3 bags × 360 days = 1080 bags. Operating four times a year means ordering every quarter (90 days). The EOQ is given by the formula:

EOQ = √((2 × D × S) / H)

Where:

• D is the annual demand
• S is the cost of placing an order
• H is the annual holding cost per unit

Holding cost per unit can be calculated as the procurement cost × the holding cost rate: $30 × 30% = $9 per bag per year. Substituting the known values into the EOQ formula:

EOQ = √((2 × 1080 bags × $1000) / $9) = √((2160000) / 9) = √240000 = 490 bags (approx).

Since Gucci orders four times a year, it should order approximately 490 Bamboo bags each time to minimize inventory holding costs while ensuring it does not run out of stock.