## **Learning Outcomes**

After reading this article, you will be able to explain the purpose and process of inventory control, calculate the economic order quantity (EOQ) to minimise inventory costs, determine optimal reorder levels, and understand the rationale and calculation for holding buffer inventory. You will also recognise how these controls help avoid stock-outs, manage costs, and support smooth production or service delivery.

## **ACCA Management Accounting (MA) Syllabus**

For ACCA Management Accounting (MA), you are required to understand the methods used to control materials and inventory within an organisation. Focus on these syllabus points as they regularly feature in assessments:

- Identify, explain and calculate the costs of ordering and holding inventory, including buffer inventory.
- Calculate and interpret optimal reorder quantities (EOQ).
- Calculate and interpret reorder levels where demand and lead time may be constant.
- Explain the calculation and role of buffer inventory.
- Describe the effects of inventory decisions on costs, service levels, and production continuity.

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. State two principal costs associated with holding inventory.
2. If annual demand is 10,000 units, ordering cost is \$10 per order, and holding cost is \$0.50 per unit per year, what is the EOQ?
3. What is the purpose of buffer inventory, and when should it be used?
4. How is the reorder level calculated if maximum daily usage is 100 units and maximum lead time is 12 days?

## **Introduction**

Efficient materials and inventory control helps organisations avoid costly shortages, excessive stock, or interruptions in operations. By optimising how much to order, when to reorder, and how much safety stock to hold, businesses balance supply reliability against minimising inventory-related costs.

> **Key Term: inventory control**
> The process of managing and regulating materials and goods held in stock, ensuring availability for use or sale while minimising associated costs.

## **INVENTORY COSTS AND THE NEED FOR CONTROL**

Businesses keep inventory to ensure uninterrupted production, meet customer demand, and take advantage of purchase discounts. However, excessive inventory ties up capital, increases holding costs, and risks waste or obsolescence, while too little inventory may cause stock-outs and lost sales.

> **Key Term: holding costs**
> The costs incurred by holding inventory in storage, including insurance, storage space, capital tied up, deterioration, and obsolescence.
>
> **Key Term: ordering costs**
> The administrative and logistical expenses incurred to place and receive inventory orders, such as order processing, transport, and receiving checks.
>
> **Key Term: stock-out costs**
> Costs or consequences resulting from running out of inventory, such as lost sales, emergency procurement, production stoppages, or damage to business reputation.

## **THE ECONOMIC ORDER QUANTITY (EOQ)**

### What is EOQ?

The Economic Order Quantity (EOQ) is the order size that minimises total annual inventory costs—specifically, the sum of ordering costs and holding costs. By balancing these two types of costs, the EOQ approach ensures that inventory is replenished efficiently.

> **Key Term: economic order quantity (EOQ)**
> The optimum order quantity that minimises the combined total of ordering and holding costs over a given period.

### EOQ Formula

EOQ can be calculated using the following formula:

$$
\text{EOQ} = \sqrt{\frac{2 C_o D}{C_h}}
$$

Where:

- $ D $ = annual demand (units)
- $ C_o $ = cost per order
- $ C_h $ = annual holding cost per unit

**EOQ Assumptions:**

- Demand and lead time are constant.
- Orders are received in full when placed (no partial deliveries).
- No quantity discounts are considered.
- No buffer inventory is included (unless specified).

### **Worked Example 1.1**

**A company uses 2,400 units of a component per year. The cost per order is \$30, and annual holding cost per unit is \$2. What is the EOQ?**

> **Answer:**  
> $$
> \text{EOQ} = \sqrt{\frac{2 \times 30 \times 2,400}{2}} = \sqrt{72,000} = 268 \text{ units (rounded)}
> $$

This means ordering 268 units at a time minimises total inventory costs.

### EOQ and Total Annual Costs

Total annual inventory cost includes:

- **Ordering costs:** (Number of orders per year) × (Cost per order), or $ \frac{D}{Q} \times C_o $
- **Holding costs:** (Average inventory) × (Holding cost per unit), or $ \frac{Q}{2} \times C_h $
- **Purchase costs:** Usually exclude from EOQ calculation if unit price is constant.

### **Worked Example 1.2**

**Using the EOQ from Worked Example 1.1, what are the annual ordering and holding costs?**

> **Answer:**  
> Number of orders per year $ = 2,400 / 268 = 8.96 $ (about 9 orders)  
> Ordering cost $ = 9 \times \$30 = \$270 $  
> Average inventory $ = 268/2 = 134 $ units  
> Holding cost $ = 134 \times \$2 = \$268 $  
> Total relevant cost = \$270 (ordering) + \$268 (holding) = \$538

### **Revision Tip**

Remember: If unit price changes with quantity ("quantity discounts"), recalculate EOQ for each price level and compare total costs before deciding.

## **REORDER LEVEL AND INVENTORY CONTROL**

Effective inventory control ensures stock does not run out or accumulate excessively. Reorder level helps trigger timely replenishment.

### Reorder Level Calculation

Reorder level (ROL) is the inventory balance at which a new order should be placed, considering usage and lead time. Basic formula (when demand and lead time are constant):

$$
\text{Reorder level} = \text{Usage per period} \times \text{Lead time (in periods)}
$$

If usage or lead time are variable, prudent control may use maximum rates:

$$
\text{Reorder level} = \text{Maximum usage per period} \times \text{Maximum lead time}
$$

This ensures sufficient stock to protect against delivery delays or demand surges.

> **Key Term: reorder level**
> The inventory quantity at which a new order is triggered to replenish stock before it runs out, based on forecast demand and lead time.

### **Worked Example 1.3**

**A hospital uses 200 bandages per day. Lead time from supplier is 4 days. At what stock level should it reorder?**

> **Answer:**  
> Reorder level = 200 × 4 = 800 bandages  
> The hospital should reorder when inventory falls to 800 units.

## **BUFFER INVENTORY (SAFETY STOCK)**

Demand or delivery times are rarely wholly predictable. Buffer (or safety) inventory provides a margin to absorb unexpected usage or supplier delays.

> **Key Term: buffer inventory**
> Extra inventory kept in addition to expected requirements to protect against uncertainties in demand or supply, reducing the risk of stock-outs.

### Calculating Buffer Inventory

Buffer inventory is often set as:

$$
\text{Buffer inventory} = (\text{Maximum usage} \times \text{Maximum lead time}) - (\text{Average usage} \times \text{Average lead time})
$$

Holding more buffer increases service reliability but also raises holding costs.

### **Worked Example 1.4**

**A retail store's average daily demand is 50 units, but could rise to 70. Lead times average 6 days, but can be up to 9. What buffer inventory should be held?**

> **Answer:**  
> Maximum requirement during lead time = 70 × 9 = 630  
> Average requirement during average lead time = 50 × 6 = 300  
> Buffer inventory = 630 – 300 = 330 units

### **Exam Warning**

Do not confuse _reorder level_ (when to order) with _buffer inventory_ (additional stock for uncertainty)—the two are linked but not identical.

## **MAXIMUM AND MINIMUM INVENTORY LEVELS**

Many businesses also define maximum and minimum inventory levels, to avoid excessive holding costs or frequent orders.

- **Minimum inventory** is normally the buffer inventory.
- **Maximum inventory** can be found by:

$$
\text{Maximum inventory} = \text{Reorder level} + \text{Order quantity} - (\text{Minimum usage} \times \text{Minimum lead time})
$$

This guards against overstocking and highlights when to delay or bring forward new orders.

## **ADVANTAGES AND LIMITATIONS OF INVENTORY CONTROL METHODS**

### Benefits

- Reduces risk of stock-outs and lost production/sales.
- Optimises order size and frequency, minimising total costs.
- Frees up working capital otherwise tied in excess stock.
- Sets clear trigger points for ordering and review.

### Limitations

- Assumes constant demand and lead times (can be unrealistic).
- EOQ does not account for quantity discounts, multiple items, or limited storage.
- Buffer inventory increases holding costs.
- Real-world factors (e.g., supplier issues, data errors) may disrupt planning.

## **Summary**

Controlling inventory means deciding how much to order, when to reorder, and how much buffer to keep. EOQ calculations help balance ordering and holding costs. Reorder levels and buffer inventory calculations minimise the risk of running out of stock while avoiding unnecessary excess. Regular review and adjustment ensure inventory policies serve both cost control and operational reliability.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain why materials and inventory control is needed for effective operations.
- Identify and calculate ordering, holding, and stock-out costs.
- Apply and interpret the EOQ formula to find cost-minimising order quantities.
- Calculate reorder levels under constant and variable demand conditions.
- Explain the role and calculation of buffer inventory (safety stock).
- Recognise practical benefits and limitations of these inventory management tools.

## **Key Terms and Concepts**

- inventory control
- holding costs
- ordering costs
- stock-out costs
- economic order quantity (EOQ)
- reorder level
- buffer inventory

Materials and inventory control - EOQ, reorder levels, and buffer inventory