Inventory management is a crucial aspect of any business that deals with physical goods. It involves balancing the costs and benefits of holding and ordering inventory, as well as ensuring that customer demand is met. One of the key decisions that inventory managers have to make is how much to order and when to order. This decision affects both the ordering cost and the holding cost of inventory, which are two major components of the total inventory cost.

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**What is Ordering Cost?**

Ordering cost is the cost associated with placing an order for inventory. It includes the expenses of preparing, processing, and transmitting the order, as well as receiving and inspecting the goods. Ordering cost also covers any transportation, handling, and storage costs that are incurred before the inventory is ready for use or sale.

Ordering cost is usually a fixed amount per order, regardless of the order size. For example, if it costs $50 to place an order for inventory, then ordering 100 units or 1,000 units will incur the same ordering cost of $50.

**What is Holding Cost?**

Holding cost is the cost associated with keeping inventory in stock. It includes the expenses of warehousing, insurance, taxes, depreciation, obsolescence, and opportunity cost. Holding cost also reflects the risk of inventory loss due to theft, damage, or spoilage.

Holding cost is usually a variable amount per unit of inventory, depending on the length of time and the level of inventory. For example, if it costs $1 per unit per year to hold inventory, then holding 100 units for one year will incur a holding cost of $100, while holding 1,000 units for one year will incur a holding cost of $1,000.

**How are Ordering Cost and Holding Cost Related to Order Size?**

Ordering cost and holding cost have an inverse relationship with order size. This means that as order size increases, ordering cost decreases, while holding cost increases. Conversely, as order size decreases, ordering cost increases, while holding cost decreases.

This can be explained by the following logic:

- When order size increases, the number of orders placed per year decreases. This reduces the frequency of incurring ordering cost. For example, if annual demand is 10,000 units and order size is 1,000 units, then 10 orders will be placed per year. However, if order size is 2,000 units, then only 5 orders will be placed per year. This reduces the annual ordering cost by half.
- When order size increases, the average level of inventory also increases. This increases the duration and amount of incurring holding cost. For example, if annual demand is 10,000 units and order size is 1,000 units, then the average inventory level is 500 units (half of the order size). However, if order size is 2,000 units, then the average inventory level is 1,000 units. This doubles the annual holding cost.

The following graph illustrates how ordering cost and holding cost vary with order size:

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**How to Minimize Total Inventory Cost?**

The total inventory cost is the sum of ordering cost and holding cost. The goal of inventory managers is to minimize this total cost while meeting customer demand.

One way to achieve this goal is to use the economic order quantity (EOQ) model^{1}. The EOQ model is a mathematical formula that calculates the optimal order size that minimizes the total inventory cost. The EOQ formula is:

���=2×�×��EOQ=H2×D×S

where:

- EOQ = economic order quantity (units)
- D = annual demand (units)
- S = ordering cost (dollars per order)
- H = holding cost (dollars per unit per year)

The EOQ model assumes that:

- Demand is constant and known
- Lead time (the time between placing an order and receiving it) is constant and known
- Ordering and holding costs are constant and known
- Shortages are not allowed
- Price per unit is not affected by order size

Using the EOQ model can help inventory managers determine the optimal trade-off between ordering cost and holding cost. However, the EOQ model may not be applicable in some situations where these assumptions are violated. For example, if demand is uncertain or variable, if lead time is uncertain or variable, if ordering or holding costs are uncertain or variable, if shortages are allowed, or if price per unit is affected by order size. In these cases, inventory managers may need to use other models or methods to optimize their inventory decisions.

**Conclusion**

Annual ordering cost is inversely related to order size. This means that as order size increases, ordering cost decreases, while holding cost increases. Conversely, as order size decreases, ordering cost increases, while holding cost decreases. Inventory managers need to balance these two costs and find the optimal order size that minimizes the total inventory cost. One way to do this is to use the EOQ model, which calculates the optimal order size based on the annual demand, ordering cost, and holding cost. However, the EOQ model may not be suitable for some situations where its assumptions are violated. In these cases, inventory managers may need to use other models or methods to optimize their inventory decisions.