Question

Suppose that the demand for a particular t-shirt the UNC Student Stores sells is deterministic with 2 units per day. Each t-shirt costs $10 and the monthly charge of carrrying one t-shirt is 50 cents. If the fixed cost of placing an order (e.g. transportation cost etc.) regardless of the order size is $200 and the order arrives instantaneously, what is the optimal number of t-shirts the UNC Student Stores should order every time it places an order and how frequently should the orders be placed?

Answer 1

EOQ = 220.6052281 shirts rounded off to 221 shirts

The order should be placed after every 110 days.

Step-by-step explanation:

The EOQ or economic order quantity is the optimum order level or quantity which minimizes the inventory related costs. This is the order quantity where the cost of ordering and the cost of holding the inventory is the minimum. The formula for EOQ is,

EOQ = √(2 * AD * O) / H

Where,

• AD refers to annual demand
• O is ordering cost per order
• H is holding cost per unit per year

Annual demand for t shirts (assuming 365 days per year) = 2 * 365 = 730

Holding cost per unit per year = 0.5 * 12 = $6

EOQ = √(2 * 730 * 200) / 6

EOQ = 220.6052281 shirts rounded off to 221 shirts

To calculate how frequently the order should be placed,we will calculate the number of orders per year by dividing the total annual demand by the EOQ.

Number of orders per year = 730 / 220.61

Number of orders per year = 3.309 or 3.31 orders per year

Number of days per order = 365 / 3.309

Number of days per order = 110.305 days or 110 days