Question

You just got hired into a t-shirt company as their CEO. The company sells 10,000 shirts a year. The company buys these shirts in batches of 1,000 right now from the supplier.

The supplier charges $100 per order placed, and the holding cost is $1 per t-shirt per year. If you were to recommend the optimal inventory order size, how much money (setup cost + inventory cost) can you save the company each year?

Answer 1

Using the Economic Order Quantity model, we can calculate the optimal inventory order size for the t-shirt company to be approximately 1,414 shirts. By adopting this order size, the company reduces the number of orders placed and holds less inventory, thus saving on setup and inventory costs.

Step-by-step explanation:

To determine the optimal inventory order size for the t-shirt company, we will employ the Economic Order Quantity (EOQ) model, which minimizes the total cost of ordering and holding inventory. The annual demand is 10,000 shirts, the ordering cost is $100 per order, and the holding cost is $1 per t-shirt per year. The EOQ formula is √((2DS)/H), where D is the annual demand, S is the setup (ordering) cost, and H is the holding cost per unit.

The current ordering batch size is 1,000 shirts, which means the company places 10 orders per year (10,000 shirts / 1,000 shirts per order). Using the EOQ formula, we calculate the optimal order size as follows: EOQ = √((2*10,000*$100)/$1) = √(2,000,000) = 1,414.21. The optimal order size is approximately 1,414 shirts per order.

If they adopt the EOQ instead of the current 1,000 shirts per batch, they would order approximately 7.07 times per year (10,000 / 1,414). By calculating the total costs with the EOQ, we find that the company saves on the overall costs from reduced ordering and holding expenses.