Economic Order Quantity (EOQ) is given by:

Economic Order Quantity (EOQ) is given by:

• A. sqrt( (2 x cost to place an order x annual demand) / cost of holding one unit of inventory for one year)
• B. sqrt( (2 x cost to place an order) / annual demand)
• C. (2 x cost to place an order x annual demand) / cost of holding one unit of inventory for one year
• D. sqrt( (cost to place an order x annual demand) / (holding cost per year) )

Answer: (A)

The concept being tested is how to determine the order quantity that minimizes total inventory costs by balancing the costs of placing orders with the costs of holding stock. Each year you incur ordering costs based on how often you order, which is D divided by the order quantity Q, times the cost to place an order S, giving annual ordering cost = (D/Q) × S. You also incur holding costs on the stock you keep, and on average you carry half of the order size, so annual holding cost = (Q/2) × H, where H is the holding cost per unit per year. The total annual cost is the sum of these two parts. Minimizing this total leads to Q^2 = 2DS/H, so Q = sqrt(2DS/H). This matches the option that has the square root of two times the annual demand times the order cost, all divided by the holding cost per unit per year. The other choices omit or misplace factors (such as the 2, or the square root, or the H in the denominator), so they don’t give the correct balance.

The concept being tested is how to determine the order quantity that minimizes total inventory costs by balancing the costs of placing orders with the costs of holding stock. Each year you incur ordering costs based on how often you order, which is D divided by the order quantity Q, times the cost to place an order S, giving annual ordering cost = (D/Q) × S. You also incur holding costs on the stock you keep, and on average you carry half of the order size, so annual holding cost = (Q/2) × H, where H is the holding cost per unit per year. The total annual cost is the sum of these two parts. Minimizing this total leads to Q^2 = 2DS/H, so Q = sqrt(2DS/H). This matches the option that has the square root of two times the annual demand times the order cost, all divided by the holding cost per unit per year. The other choices omit or misplace factors (such as the 2, or the square root, or the H in the denominator), so they don’t give the correct balance.