Inventory management is the process of ordering, storing, using, and selling a company’s inventory. It involves balancing the costs and benefits of holding inventory, as well as meeting customer demand and avoiding stockouts. One of the key decisions in inventory management is how much to order each time a replenishment is needed. This decision affects both the ordering costs and the holding costs of inventory.

Contents

**What Are Ordering Costs and Holding Costs?**

Ordering costs are the costs associated with placing and receiving an order from a supplier. They include the costs of transportation, inspection, paperwork, communication, and any other expenses related to acquiring inventory. Ordering costs are usually fixed per order, regardless of the order size. For example, if a company orders 100 units or 1,000 units from a supplier, the ordering cost may be the same.

Holding costs are the costs associated with keeping inventory in stock. They include the costs of storage, insurance, taxes, depreciation, obsolescence, spoilage, theft, and opportunity cost of capital. Holding costs are usually proportional to the amount of inventory held and the length of time it is held. For example, if a company holds 100 units for one year or 200 units for six months, the holding cost may be the same.

**How Are Ordering Costs and Holding Costs Related to Order Size?**

Ordering costs and holding costs have an inverse relationship with order size. As order size increases, ordering costs decrease and holding costs increase. Conversely, as order size decreases, ordering costs increase and holding costs decrease. This is because ordering more units at a time reduces the frequency of orders and thus the total number of orders per year. However, ordering more units at a time also increases the average inventory level and thus the total amount of inventory held per year.

The following graph illustrates this relationship:

!Graph)

The graph shows that ordering costs are a decreasing function of order size, while holding costs are an increasing function of order size. The total cost curve is the sum of the ordering cost curve and the holding cost curve. The total cost curve has a U-shape, indicating that there is an optimal order size that minimizes the total cost.

**How to Find the Optimal Order Size?**

The optimal order size is also known as the economic order quantity (EOQ). It is the order size that minimizes the total cost of inventory management. The EOQ can be calculated using a formula that takes into account the demand rate, the ordering cost per order, and the holding cost per unit per year. The formula for EOQ is:

���=��������2�������������EOQ=sqrtfrac2timesStimesDH

where:

- �S = Setup costs (per order)
- �D = Demand rate (quantity sold per year)
- �H = Holding costs (per year, per unit)

For example, suppose a company sells 10,000 units per year and has an ordering cost of $50 per order and a holding cost of $5 per unit per year. The EOQ for this company is:

���=��������2�����50�����100005EOQ=sqrtfrac2times50times100005

���=����200000EOQ=sqrt200000

���=447.21EOQ=447.21

This means that the company should order 447 units each time it replenishes its inventory. This will result in the lowest total cost of inventory management.

**What Are the Benefits and Limitations of EOQ?**

The EOQ model is a useful tool for inventory management because it helps to determine the optimal trade-off between ordering costs and holding costs. By using EOQ, a company can reduce its total inventory cost and improve its cash flow and profitability.

However, the EOQ model also has some limitations and assumptions that may not always hold true in reality. Some of these limitations and assumptions are:

- The demand rate is constant and known.
- The ordering cost and holding cost are constant and known.
- The lead time (the time between placing an order and receiving it) is zero or constant and known.
- The order quantity is delivered in one batch at one time.
- There are no quantity discounts or price fluctuations.
- There are no stockouts or shortages.

These limitations and assumptions may not reflect the actual situation of a company’s inventory management. Therefore, the EOQ model should be used with caution and adjusted according to the specific circumstances of each case.

**Conclusion**

Annual ordering cost is inversely related to order size because ordering more units at a time reduces the frequency of orders but increases the average inventory level. To find the optimal order size that minimizes the total cost of inventory management, the EOQ model can be used. The EOQ model is a simple and effective tool for inventory management, but it also has some limitations and assumptions that may not always apply in reality. Therefore, the EOQ model should be used with care and adapted to the specific situation of each company.