Explanation:

The Economic Order Quantity (EOQ) model is a tool used in inventory management to determine the optimal quantity of goods to order at any given time. The formula for EOQ is:

EOQ = √((2DS)/H)

where:

D = annual demand
S = setup or ordering cost per order
H = holding cost per unit per year

Effect of doubling unit ordering cost on EOQ:

When the unit ordering cost is doubled, it means that 'S' in the EOQ formula is doubled. Let's see how this affects the EOQ.

EOQ = √((2DS)/H)

If 'S' is doubled, the formula becomes:

EOQ = √((2D(2S))/H)

Simplifying this:

EOQ = √((4DS)/H)

We can see that the EOQ increases by a factor of √2, which is approximately 1.414. This means that the EOQ increases by 41.4% when the unit ordering cost is doubled.

Why EOQ increases when unit ordering cost is doubled?

The EOQ increases when the unit ordering cost is doubled because the cost of placing an order has a direct impact on the total cost of holding inventory. When the unit ordering cost is high, it becomes more expensive to place an order, which means that you need to order more units to make the order cost-effective. This leads to an increase in the EOQ.

Conclusion:

In the EOQ model, if the unit ordering cost is doubled, the EOQ increases by a factor of √2, which is approximately 1.414. This is because the cost of placing an order has a direct impact on the total cost of holding inventory. When the unit ordering cost is high, it becomes more expensive to place an order, which leads to an increase in the EOQ.