Question

In the classical economic order quantity (EOQ) model, let \( Q \) and \( C \) denote the optimal order quantity and the corresponding minimum total annual cost (the sum of the inventory holding and ordering costs). If the order quantity is estimated incorrectly as \( Q' = 2Q \), then the corresponding total annual cost \( C' \) is

• A. \( C' = 1.25C \)
• B. \( C' = 1.5C \)
• C. \( C' = 1.75C \)
• D. \( C' = 2C \)

Hint:

If the order quantity is doubled in the EOQ model, the total cost increases by 25% due to the interaction between the ordering and holding costs.

Answer 1

The Correct Option is A

In the Economic Order Quantity (EOQ) model, the total annual cost \( C \) is the sum of the ordering cost and the holding cost. The optimal order quantity \( Q \) minimizes the total cost. The total cost for the EOQ model is given by the formula: \[ C = \frac{D}{Q} \cdot S + \frac{Q}{2} \cdot H \] where:
- \( D \) is the demand,
- \( Q \) is the order quantity,
- \( S \) is the ordering cost per order,
- \( H \) is the holding cost per unit per year.
If the order quantity is incorrectly estimated as \( Q' = 2Q \), the new total cost \( C' \) becomes: \[ C' = \frac{D}{Q'} \cdot S + \frac{Q'}{2} \cdot H = \frac{D}{2Q} \cdot S + \frac{2Q}{2} \cdot H \] \[ C' = \frac{1}{2} \cdot \frac{D}{Q} \cdot S + Q \cdot H \] Substitute the original total cost formula \( C = \frac{D}{Q} \cdot S + \frac{Q}{2} \cdot H \) into the above equation: \[ C' = \frac{1}{2} \cdot C + C = 1.25C. \] Thus, the new total cost \( C' \) is \( 1.25 \) times the original total cost \( C \). Therefore, the correct answer is (A).