Question

In the Basic Economic Order Quantity (EOQ) model, if the holding cost per unit increases, the EOQ will:

• A. Increase
• B. Decrease
• C. Remain unaffected
• D. Double

Hint:

Remember that variables in the numerator of the EOQ formula (Demand, Ordering Cost) have a direct relationship with EOQ, whereas variables in the denominator (Holding Cost) have an inverse relationship.
Therefore, any increase in holding cost will always decrease the optimal order size.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks about the effect of an increase in the holding cost per unit on the Economic Order Quantity (EOQ).
The Economic Order Quantity represents the optimal quantity of inventory that a company should order to minimize its total inventory-related costs, which primarily consist of ordering costs and holding costs.
An increase in holding cost implies that the expense of storing a unit of inventory over time is higher, which logically suggests that the company should hold smaller amounts of stock.

Step 2: Key Formula or Approach:
The basic formula for the Economic Order Quantity (EOQ) is:
\[ EOQ = \sqrt{\frac{2DS}{H}} \]
where:
\(D\) is the annual demand of the product.
\(S\) is the ordering cost per order.
\(H\) is the holding cost per unit per year.

Step 3: Detailed Explanation:

• The mathematical relation shows that \(EOQ\) is inversely proportional to the square root of the unit holding cost \(H\).

• Mathematically, this relationship is expressed as:
\[ EOQ \propto \frac{1}{\sqrt{H}} \]

• When the holding cost per unit (\(H\)) increases, the denominator of the term inside the square root becomes larger.

• This increase in the denominator results in a lower overall value for the fraction, which in turn leads to a reduction in the square root's result.

• From an economic perspective, higher holding costs make carrying inventory more expensive, prompting businesses to place smaller, more frequent orders.

Step 4: Final Answer:
Hence, an increase in the holding cost per unit leads to a decrease in the Economic Order Quantity.