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Business Administration QUESTION #9607
Question 1
A company's supply chain uses the Economic Order Quantity (EOQ) model. If annual demand doubles while holding cost per unit remains constant and ordering cost remains constant, how does the optimal order quantity change, and what inventory management principle does this illustrate?
  • EOQ doubles — demand and order quantity have a linear relationship in the EOQ model
  • EOQ increases by approximately 41% (square root of 2) — the EOQ model's square root relationship means that doubling demand increases optimal order quantity by the square root of 2, not by 2; this illustrates the principle of inventory risk pooling and the non-linear scaling of inventory with demand✔️
  • EOQ remains unchanged — the EOQ is only sensitive to changes in holding cost and ordering cost, not to demand changes
  • EOQ halves — higher demand requires more frequent smaller orders to reduce holding costs
Correct Answer Explanation
EOQ = √(2DS/H) where D=demand, S=ordering cost, H=holding cost. If D doubles: new EOQ = √(2×2D×S/H) = √2 × √(2DS/H) = √2 × original EOQ ≈ 1.414 × original EOQ. This square root relationship is fundamental — it means that as demand scales, inventory does not scale proportionally (sub-linear scaling), which is the mathematical basis for inventory risk pooling and the efficiency gains from demand aggregation in supply chain network design.