In EOQ analysis, which statement best describes the condition at the inventory optimum?

In EOQ analysis, which statement best describes the condition at the inventory optimum?

• A. The annual holding cost equals the annual ordering cost
• B. The annual holding cost equals the annual purchase cost
• C. The annual purchasing cost is minimized
• D. The total annual cost is minimized when the purchase price is minimized

Answer: (B)

In EOQ, the decision revolves around two main annual costs: the cost of holding inventory and the cost of placing orders. If D is annual demand, S is the cost per order, Q is the order size, and h is the annual holding cost per unit, then the annual holding cost is (Q/2) × h and the annual ordering cost is (D/Q) × S. The optimal order quantity occurs where these two costs are equal: (D/Q) × S = (Q/2) × h, which leads to Q* = sqrt(2DS/h). The purchase cost, which is D × price per unit, is typically fixed in the standard model (assuming a constant unit price) and does not depend on Q, so it isn’t minimized by choosing the optimal order quantity. Therefore, the condition at the inventory optimum is that the annual holding cost equals the annual ordering cost.

In EOQ, the decision revolves around two main annual costs: the cost of holding inventory and the cost of placing orders. If D is annual demand, S is the cost per order, Q is the order size, and h is the annual holding cost per unit, then the annual holding cost is (Q/2) × h and the annual ordering cost is (D/Q) × S. The optimal order quantity occurs where these two costs are equal: (D/Q) × S = (Q/2) × h, which leads to Q* = sqrt(2DS/h). The purchase cost, which is D × price per unit, is typically fixed in the standard model (assuming a constant unit price) and does not depend on Q, so it isn’t minimized by choosing the optimal order quantity. Therefore, the condition at the inventory optimum is that the annual holding cost equals the annual ordering cost.