Inventory control – EOQ: In the classical Economic Order Quantity model, EOQ occurs where ordering cost equals carrying (holding) cost. Is this statement true?

Introduction / Context:
The Economic Order Quantity (EOQ) model determines the order size that minimizes total annual inventory cost by balancing ordering costs against carrying (holding) costs for steady demand.

Given Data / Assumptions:

• Deterministic, constant annual demand D.
• Ordering cost per order S and annual holding cost per unit H.
• No shortages; instantaneous replenishment; constant prices.

Concept / Approach:
Total annual cost = Ordering cost + Holding cost = (D/Q)S + (Q/2)H. Differentiating with respect to Q and setting derivative to zero yields the optimal Q and implies equality of ordering and holding costs at the optimum.

Step-by-Step Solution:

Verification / Alternative check:
Substitute Q into both cost components to confirm equality; both evaluate to sqrt(DSH/2), proving the balancing condition.

Why Other Options Are Wrong:
“False” contradicts the first-order optimality condition in the basic EOQ model.

Common Pitfalls:
Applying the equality when quantity discounts, shortages, or variable demand invalidate the classical assumptions; in those cases, the condition may not hold.

Final Answer:
True