buffer inventory, re-order level and lead time

4.2 Inventory Management – Managing Inventory

Learning Objectives

• Explain why businesses hold inventory (raw materials, work‑in‑process, finished goods).
• Identify the main costs and benefits of holding inventory and link each to the desired service level.
• Define and calculate:
  • Buffer (safety) inventory – deterministic method (Cambridge IGCSE) and statistical method (A‑Level depth).
  • Lead time.
  • Re‑order level (re‑order point).
• Read and interpret a basic inventory‑control chart.
• Explain how inventory decisions interact with supply‑chain management (SCM) and the contrasting approaches of Just‑In‑Time (JIT) and Just‑In‑Case (JIC).

1. Why Do Companies Hold Inventory?

Inventory is held at three key stages of production and sales:

Stage	What is held?	Reason for holding it
Raw materials	Un‑processed inputs	Ensures production can start when demand arises; protects against supplier delays.
Work‑in‑process (WIP)	Part‑finished goods	Buffers between production stages; smooths variations in processing time.
Finished goods	Completed products ready for sale	Allows firms to meet customer demand promptly and avoid lost sales.

2. Costs, Benefits & Service Level

Holding inventory involves a trade‑off between costs and the benefit of a high service level (the probability of meeting demand without a stock‑out).

Cost / Benefit	Description	Effect on safety stock
Carrying (holding) cost	Interest, warehousing, insurance, obsolescence (usually % of inventory value per year)	Higher cost → lower safety stock (to keep total cost down).
Ordering cost	Cost of processing a purchase order, transport, handling	Higher cost → larger order quantities, which can increase the amount of safety stock needed to cover longer periods between orders.
Stock‑out (shortage) cost	Lost sales, loss of goodwill, emergency expediting charges	Higher cost → higher safety stock to avoid the expensive stock‑out.
Benefit: Service level	Probability of satisfying demand from stock on hand	Higher desired service level → higher safety stock.

3. Key Concepts

3.1 Buffer (Safety) Inventory

Extra stock kept to protect against:

• Variations in demand (higher than average sales).
• Variations in supply lead time (delays from the supplier).

Deterministic method (Cambridge IGCSE)

$$\text{Buffer}= (\text{Maximum Daily Usage}\times\text{Maximum Lead Time})-(\text{Average Daily Usage}\times\text{Average Lead Time})$$

Statistical method (A‑Level depth)

Assumes demand during lead time follows a normal distribution.

$$\text{Safety Stock}= Z \times \sigma_{d}\times\sqrt{L}$$

• $Z$ = standard‑normal value for the required service level (e.g., 1.65 for 95 %).
• $\sigma_{d}$ = standard deviation of daily demand.
• $L$ = lead time in days.

3.2 Lead Time

The total time from placing a purchase order with a supplier until the goods are ready for use or sale.

• Order processing time.
• Supplier production time.
• Transportation time.
• Receiving & inspection time.

When lead time is variable, the “maximum lead time” used in the deterministic formula is larger, increasing the required buffer.

3.3 Re‑order Level (Re‑order Point)

The inventory quantity at which a new order should be placed so that the order arrives just as the buffer stock is about to be exhausted.

Deterministic formula

$$\text{Re‑order Level}= (\text{Average Daily Usage}\times\text{Average Lead Time})+\text{Buffer}$$

3.4 Inventory‑Control Chart (Cambridge requirement)

A simple line chart showing:

• Stock on hand (declining line as sales occur).
• Re‑order level (horizontal line).
• Safety‑stock level (horizontal line above the re‑order level).

Interpretation:

1. When the stock‑on‑hand line reaches the re‑order level, a purchase order is triggered.
2. The order should arrive before the stock line falls below the safety‑stock line.
3. If the stock line drops below safety stock, a stock‑out risk exists.

4. Link to Supply‑Chain Management (SCM)

Inventory decisions are not made in isolation. They are influenced by:

• Supplier reliability: Consistent lead times reduce safety‑stock requirements.
• Information flow: Accurate forecasts and real‑time order status enable tighter control.
• Logistics performance: Faster, more predictable transport shortens lead time.

Improving any of these SCM elements directly lowers the amount of buffer inventory a firm must hold.

5. Just‑In‑Time (JIT) vs. Just‑In‑Case (JIC)

Aspect	JIT (Low inventory)	JIC (Higher inventory)
Philosophy	Produce/receive only what is needed, when it is needed.	Maintain enough stock to cover unexpected demand or supply delays.
Typical environment	Highly reliable suppliers, stable demand, strong information systems.	Variable demand, longer or unpredictable lead times, higher risk of stock‑outs.
Impact on safety stock	Very low or zero safety stock.	Significant safety stock (buffer inventory).
Advantages	Reduced carrying costs, less waste.	Higher service level, protection against disruptions.
Disadvantages	Vulnerable to any supply‑chain disruption.	Higher carrying costs, risk of obsolescence.

6. Calculations

6.1 Buffer (Safety) Inventory – Deterministic

$$\text{Buffer}= (\text{Maximum Daily Usage}\times\text{Maximum Lead Time})-(\text{Average Daily Usage}\times\text{Average Lead Time})$$

6.2 Re‑order Level – Deterministic

$$\text{Re‑order Level}= (\text{Average Daily Usage}\times\text{Average Lead Time})+\text{Buffer}$$

6.3 Safety Stock – Statistical (A‑Level depth)

$$\text{Safety Stock}= Z \times \sigma_{d}\times\sqrt{L}$$

6.4 Example – Deterministic Method

Assume:

• Average daily usage = 120 units
• Maximum daily usage = 150 units
• Average lead time = 5 days
• Maximum lead time = 7 days

1. Buffer inventory: $$\text{Buffer}= (150\times7)-(120\times5)=1050-600=450\text{ units}$$
2. Re‑order level: $$\text{Re‑order Level}= (120\times5)+450=600+450=1050\text{ units}$$

When stock on hand falls to **1 050 units**, place a new order.

6.5 Example – Statistical Method (A‑Level)

Data:

• Average daily demand = 80 units
• Standard deviation of daily demand, $\sigma_{d}=12$ units
• Lead time = 4 days (average)
• Desired service level = 95 % → $Z=1.65$

Safety stock:

$$\text{Safety Stock}=1.65\times12\times\sqrt{4}=1.65\times12\times2=39.6\approx40\text{ units}$$

Re‑order level (using average demand):

$$\text{Re‑order Level}= (80\times4)+40=320+40=360\text{ units}$$

7. Summary Table

Term	Definition	Key Formula(s)
Buffer (Safety) Inventory	Extra stock kept to protect against demand or supply variability.	Deterministic: $(\text{Max Daily Usage}\times\text{Max Lead Time})-(\text{Avg Daily Usage}\times\text{Avg Lead Time})$ Statistical (A‑Level): $Z\times\sigma_{d}\times\sqrt{L}$
Lead Time	Total time from placing an order to receipt and readiness for use.	Sum of order processing, production, transport, receiving.
Re‑order Level (Re‑order Point)	Stock quantity that triggers a new purchase order.	$(\text{Avg Daily Usage}\times\text{Avg Lead Time})+\text{Buffer}$

8. Practical Tips for Managers

• Review demand forecasts regularly – any change alters buffer and re‑order calculations.
• Monitor supplier performance – reductions in average lead time or its variability directly lower safety stock.
• Use inventory‑management software to:
  • Calculate safety stock automatically (both deterministic and statistical methods).
  • Generate alerts when stock reaches the re‑order level.
  • Produce inventory‑control charts for quick visual checks.
• Weigh the cost of holding extra stock against the cost of a stock‑out; choose the service level that maximises profit.
• Consider the wider supply chain – reliable logistics and information sharing can shorten lead time and reduce buffer requirements.

9. Exam Practice Question

Question: A retailer sells an average of 80 units of a product per day. The maximum daily sales recorded in the last year were 110 units. The average lead time from the supplier is 4 days, but on occasion it can extend to 6 days. Calculate the buffer inventory and the re‑order level for this product.

Answer outline:

1. Buffer inventory: $$\text{Buffer}= (110\times6)-(80\times4)=660-320=340\text{ units}$$
2. Re‑order level: $$\text{Re‑order Level}= (80\times4)+340=320+340=660\text{ units}$$

When the stock on hand falls to **660 units**, the retailer should place a new order.