Inventory control (EOQ model): If the annual demand for an item is trebled (multiplied by 3) and the ordering/setup cost is reduced to one third (S/3), while the holding cost per unit per year remains unchanged, how does the Economic Order Quantity (EOQ) change?

Introduction:
The Economic Order Quantity (EOQ) model is a foundational result in operations and supply chain management. It balances the trade-off between ordering costs (or setup costs) and inventory holding costs to minimize total annual cost. This problem tests your understanding of how EOQ scales when demand and ordering cost change simultaneously.

Given Data / Assumptions:

• Classical EOQ applies with constant, deterministic demand and instantaneous replenishment.
• Original parameters: demand D, ordering cost S, holding cost H.
• Changes: D becomes 3D (trebled), S becomes S/3 (one third), H is unchanged.
• No quantity discounts, no stockouts, and lead time effects are ignored.

Concept / Approach:
The EOQ formula is EOQ = sqrt(2 * D * S / H). The key insight is that EOQ depends on the square root of the product D * S. If two adjustments offset each other so that D * S remains the same, then EOQ remains identical. We will substitute the changed values and compare to the original EOQ.

Step-by-Step Solution:
Start with the standard formula: EOQ = sqrt(2 * D * S / H).Apply the changes: D' = 3D and S' = S / 3.Compute the new EOQ: EOQ' = sqrt(2 * (3D) * (S/3) / H).Algebraic simplification: EOQ' = sqrt(2 * D * S / H).Conclusion: EOQ' equals the original EOQ; therefore, EOQ remains unchanged.

Verification / Alternative check:
Use proportional (sensitivity) reasoning. Since EOQ ∝ (D * S)^(1/2) * H^(−1/2), the combined change factor for D * S is (3) * (1/3) = 1. Thus (D * S)^(1/2) is multiplied by 1^(1/2) = 1, and EOQ is unaffected. This confirms the algebraic result without numbers.

Why Other Options Are Wrong:

• is trebled. EOQ would triple only if D * S increased by a factor of 9 (since EOQ scales with the square root), which it does not.
• decreases by a factor of 3. This would require D * S to drop by a factor of 9; not the case here.
• decreases by a factor of 1/3. Would imply D * S decreased to 1/9 of its value; incorrect.
• increases by a factor of √3. Would require D * S to triple; instead, it is unchanged.

Common Pitfalls:
Students often forget the square-root relationship and attempt linear reasoning (e.g., “demand tripled, so EOQ triples”). Always inspect how parameters enter the EOQ formula—EOQ scales with the square root of the product D * S and inversely with the square root of H.

Final Answer:
remains unchanged.