interpretation of simple inventory control charts

4.2 Inventory Management – Managing Inventory

Learning Objective

Interpret simple inventory‑control charts and use them to make short‑term stock decisions, recognising the costs, benefits and strategic context of holding inventory.

1. Why Do Firms Hold Inventory?

Inventory is kept for three distinct purposes. Understanding each purpose helps you decide how much stock is appropriate.

• Raw‑material inventory – protects against supplier delays, price changes or quality problems.
• Work‑in‑progress (WIP) inventory – smooths production when operations are not perfectly synchronised.
• Finished‑goods inventory – enables a firm to meet customer demand promptly and maintain the required service level.

Key cost components of holding inventory

Cost type	What it represents
Ordering cost (S)	Administrative, transport, set‑up and any other expense incurred each time an order is placed.
Holding (carrying) cost (H)	All costs of keeping stock, e.g. warehousing, insurance, security, obsolescence, shrinkage and the opportunity cost of capital tied up in inventory.
Stock‑out (shortage) cost	Lost sales, loss of goodwill, emergency procurement or penalty charges.

2. Core Concepts and Formulas

• Economic Order Quantity (EOQ) – the order size that minimises the sum of ordering and holding costs.
  EOQ = \sqrt{\dfrac{2DS}{H}}
• Lead time (L) – time (in the same period unit as demand) between placing an order and receiving it.
• Demand during lead time (DL) – DL = D × L. This is the amount of stock required while an order is in transit.
• Re‑order level (ROL) – the stock level that exactly covers demand during lead time.
  ROL = D × L
• Safety (buffer) stock (SS) – extra units kept to protect against variability in demand or supply.
  SS = Z × σ_{DL} where σ_{DL} is the standard deviation of demand during lead time and Z is the service‑level factor taken from the standard normal table (e.g. Z = 1.65 for 95 % service level).
• Re‑order point (ROP) – the level that triggers an order when safety stock is added:
  ROP = ROL + SS = (D × L) + SS

3. Strategic Approaches to Inventory

Approach	Philosophy	Typical stock level
Just‑in‑Case (JIC)	Maintain ample stock to guard against any disruption.	High safety stock, higher holding cost.
Just‑in‑Time (JIT)	Receive goods exactly when needed, minimising inventory.	Very low safety stock, relies on reliable suppliers and short lead times.

Choosing between JIC and JIT requires a cost‑benefit analysis that weighs holding costs against the risk and cost of stock‑outs.

4. Simple Inventory‑Control Chart – Structure

A simple chart plots inventory quantity (units) against time. The essential elements are:

1. X‑axis: Time periods (weeks, months, etc.).
2. Y‑axis: Quantity of inventory (units).
3. Consumption line: Downward‑sloping line showing usage of stock.
4. Re‑order level line: Horizontal line at the ROL.
5. Re‑order point line: Horizontal line at the ROP (ROL + SS).
6. Safety‑stock line (optional): Shows the minimum buffer level.
7. Order‑placement marker: Vertical line where the consumption line meets the ROP.
8. Order‑receipt marker: Vertical line after the lead‑time interval where stock jumps up by the order quantity.

5. Interpreting the Chart – Step‑by‑Step

1. Locate the current stock level on the consumption line.
2. Compare it with the re‑order point (ROP). If the current level ≤ ROP, place an order immediately.
3. Identify the lead‑time interval – the horizontal distance between the order‑placement and order‑receipt markers.
4. Check the safety‑stock line. The lowest point of the consumption line during the lead time must stay above this line.
5. Determine the order quantity (often the EOQ). The order should raise inventory back to the desired maximum level (EOQ + SS).

6. Worked Example

A retailer sells a product with the data below.

Parameter	Value	Units
Average monthly demand (D)	500	units
Ordering cost (S)	£30	per order
Holding cost per unit per month (H)	£0.50	per unit
Lead time (L)	1	month
Desired safety stock (SS)	100	units

6.1 Calculate EOQ

\[ \text{EOQ}= \sqrt{\frac{2DS}{H}} = \sqrt{\frac{2 \times 500 \times 30}{0.50}} = \sqrt{60\,000} \approx 245\text{ units} \]

6.2 Calculate Re‑order Level (ROL) and Re‑order Point (ROP)

\[ \text{ROL}= D \times L = 500 \times 1 = 500\text{ units} \] \[ \text{ROP}= \text{ROL} + \text{SS}= 500 + 100 = 600\text{ units} \]

6.3 Plotting on the Chart

• Maximum inventory after receipt: EOQ + SS = 245 + 100 = 345 units.
• The consumption line falls from 345 units toward zero at a rate of 500 units per month.
• When the line reaches the ROP (600 units), an order of 245 units is placed.
• One month later (the lead time) the order arrives and the stock jumps back to 345 units.

This produces the characteristic “saw‑tooth” pattern on the inventory‑control chart.

7. Linking Inventory Management to the Wider Supply Chain

• Inventory decisions affect upstream suppliers (order frequency, batch size) and downstream customers (service level).
• JIT requires close collaboration, reliable transport and real‑time information sharing across the chain.
• JIC can provide a competitive edge when the supply chain is volatile, but at a higher holding‑cost price.
• Effective inventory control balances cost against responsiveness, improving overall supply‑chain efficiency.

8. Common Pitfalls & How to Avoid Them

• Ignoring variable lead times – use the longest realistic lead time or add extra safety stock.
• Setting ROP without safety stock – raises the risk of costly stock‑outs.
• Applying EOQ blindly – verify that the EOQ is not smaller than demand during lead time; otherwise multiple orders will be needed.
• Over‑reliance on a single supplier – diversify sources, especially under a JIC strategy.

9. Quick Checklist for Interpreting an Inventory‑Control Chart

1. Is the current stock level above the ROP?
2. Has the lead‑time interval been correctly accounted for?
3. Is the safety‑stock line high enough to cover demand variability during lead time?
4. Does the order quantity correspond to the EOQ or to a strategically chosen batch size?
5. Are the chart’s data (demand, costs, lead time, variability) up‑to‑date?

10. Summary

Interpreting simple inventory‑control charts enables managers to:

• Maintain optimal stock levels that balance ordering, holding and stock‑out costs.
• Make timely decisions about when to order and how much to order.
• Choose an appropriate inventory strategy (JIT vs. JIC) based on a clear cost‑benefit analysis and the reliability of the supply chain.
• Communicate inventory needs effectively with suppliers and other parts of the supply chain.