the costs and benefits of holding inventory

4.2 Inventory Management – Managing Inventory

Objective

To understand why firms hold inventory, to identify the costs and benefits of holding inventory, and to evaluate inventory‑related decisions using appropriate calculations and models (EOQ, safety‑stock, reorder‑point, etc.).

1. Why Hold Inventory? – Types of Inventory

Inventory type	Where it sits in the production‑sales process	Primary purpose
Raw‑material inventory	Before production begins	Ensures raw inputs are available when production is scheduled.
Work‑in‑progress (WIP) inventory	During the transformation process	Buffers against process‑time variability, machine breakdowns and set‑up time.
Finished‑goods inventory	After production, before sale	Allows rapid response to customer orders and protects against demand spikes.
Speculative (or “stock‑piling”) inventory	Any stage, usually finished goods	Held to take advantage of expected price falls, seasonal demand or anticipated shortages.

2. Costs of Holding Inventory

Recurring costs can be grouped as follows:

Cost type	Description	Typical calculation
Capital (opportunity) cost	Cost of money tied up in stock; expressed as a % of the inventory value.	\(\text{Capital Cost}= \text{Average Inventory Value}\times \text{Interest Rate}\)
Storage (carrying) cost	Warehousing, handling, insurance, security, utilities.	\(\text{Storage Cost}= \text{Average Units}\times \text{Cost per Unit per Period}\)
Risk cost	Losses from obsolescence, damage, theft, price decline.	Often estimated as a % of inventory value (e.g., 5 %).
Administrative cost	Record‑keeping, order processing, control systems.	\(C_{\text{admin}}=C_{\text{order}}+c\times Q\)

The total holding cost per period is the sum of the four components:

\[ \text{Total Holding Cost}= \text{Capital Cost}+ \text{Storage Cost}+ \text{Risk Cost}+ \text{Administrative Cost} \]

3. Benefits of Holding Inventory

• Improved customer service – faster order fulfilment and higher fill‑rate (driver: service level).
• Economies of scale – bulk‑purchase discounts and lower unit transport costs (driver: cost reduction).
• Production smoothing – continuous output despite variable demand or supply lead‑times (driver: operational efficiency).
• Risk mitigation – protection against supplier unreliability, price fluctuations, or unexpected demand spikes (driver: risk management).
• Market responsiveness – ability to launch promotions or react to trends quickly (driver: competitive advantage).

4. Simple Inventory‑Control Chart (Inventory Balance Sheet)

A basic inventory‑balance chart records the flow of stock over a period (usually a week or month). It enables students to spot trends such as over‑stocking or impending stock‑outs.

Period	Opening Stock	Receipts (in)	Issues (out)	Closing Stock
Week 1	500	300	400	400
Week 2	400	200	350	250
Week 3	250	250	300	200

How to interpret:

• If the closing‑stock line consistently stays above the safety‑stock level, the firm is likely over‑stocking (high holding cost).
• If the closing‑stock line falls below safety stock, a reorder should be triggered to avoid a stock‑out.
• A trend line (e.g., a downward slope) signals decreasing inventory and may indicate rising demand or insufficient replenishment.

5. Buffer (Safety) Stock, Re‑order Level & Lead Time

• Safety stock (SS) – extra units held to achieve a required service level.
• Lead time (L) – time between placing an order and receipt of the goods.
• Re‑order point (ROP) – inventory level that triggers a new order.

Assuming normally distributed demand:

\[ \text{Safety Stock}=Z \times \sigma_{L} \] \[ \text{Re‑order point}= (\text{Average demand per period}\times L) + \text{Safety Stock} \]

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

6. Economic Order Quantity (EOQ) Model

The EOQ model identifies the order size that minimises the sum of ordering (set‑up) costs and holding costs.

\[ Q^{*}= \sqrt{\frac{2DS}{H}} \]

• \(D\) = Annual demand (units)
• \(S\) = Ordering (set‑up) cost per order
• \(H\) = Holding cost per unit per year (includes capital, storage, risk)

Assumptions (A‑Level depth)

1. Demand is constant and known.
2. Lead time is constant; replenishment is instantaneous.
3. Only one product is considered (no interactions).
4. No quantity‑discounts or price breaks.
5. Holding cost per unit is constant.

Remember: EOQ is an assumed‑knowledge tool for Paper 3 and Paper 4 of the A‑Level exam.

Limitations

• Real‑world demand fluctuates and lead times vary.
• Bulk discounts, seasonal demand, or capacity constraints are ignored.
• The model assumes a single, fixed ordering cost – not always realistic with electronic ordering systems.

Alternative Models (brief overview)

• Economic Production Quantity (EPQ) – used when items are produced internally; incorporates a production rate.
• Quantity‑Discount Model – incorporates price breaks for larger orders; the optimal order may be at a discount break rather than the EOQ.
• ABC Analysis – classifies inventory items by value/usage to apply different control policies.

7. Example Calculation (EOQ & Total Cost)

ABC Ltd produces a product with the following data:

• Annual demand, \(D = 12{,}000\) units
• Ordering cost, \(S = £50\) per order
• Holding cost per unit, \(H = £2\) per year (covers capital, storage & risk)

1. EOQ: \[ Q^{*}= \sqrt{\frac{2\times12{,}000\times50}{2}}= \sqrt{600{,}000}\approx 775\text{ units} \]
2. Number of orders per year: \[ \frac{D}{Q^{*}}= \frac{12{,}000}{775}\approx 15.5\text{ orders} \]
3. Total ordering cost: \[ \text{Ordering Cost}= \frac{D}{Q^{*}}\times S\approx 15.5\times £50 = £775 \]
4. Average inventory level: \[ \frac{Q^{*}}{2}= \frac{775}{2}=387.5\text{ units} \]
5. Total holding cost: \[ \text{Holding Cost}= \frac{Q^{*}}{2}\times H\approx 387.5\times £2 = £775 \]
6. Combined annual inventory cost: \[ \text{Total Cost}= £775 + £775 = £1{,}550 \]

8. Key Ratios for Monitoring Inventory

Ratio	Formula	Interpretation
Inventory Turnover	\(\displaystyle \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}}\)	Higher values indicate efficient use of stock.
Days Sales of Inventory (DSI)	\(\displaystyle \frac{365}{\text{Inventory Turnover}}\)	Average days inventory is held; lower is generally better.
Gross Margin Return on Investment (GMROI)	\(\displaystyle \frac{\text{Gross Profit}}{\text{Average Inventory Cost}}\)	Profit generated per £ invested in inventory.

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

Aspect	JIT	JIC
Philosophy	Produce/receive only what is needed, when it is needed.	Maintain a buffer to guard against uncertainty.
Typical inventory level	Very low (often zero safety stock).	Higher – safety stock is a core component.
Key requirements	Highly reliable suppliers, accurate demand forecasting, fast information flow.	Stable demand, less‑reliable supply chain, higher tolerance for holding cost.
Impact on total inventory cost	Reduces holding cost dramatically but may increase ordering cost and risk of stock‑outs.	Higher holding cost, lower ordering cost, lower risk of stock‑outs.
Real‑world example	Toyota’s “lean” production system – synchronised deliveries from suppliers to the assembly line.	Traditional automotive parts distributors that keep large regional depots.

10. Inventory Management within Supply‑Chain Management (SCM)

Inventory decisions are not isolated; they interact with upstream and downstream activities:

• Supplier reliability & lead‑time variability – directly affect safety‑stock levels and reorder points.
• Distribution network design – determines where inventory is held (central warehouse vs. regional depots) and influences total holding cost.
• Information systems – real‑time data enable JIT, reduce safety stock, and improve reorder accuracy.
• Customer‑service strategy – high‑service markets justify higher inventory levels despite the cost.

11. Decision‑Making Checklist

1. Identify the type of inventory (raw, WIP, finished, speculative) and its purpose.
2. List all relevant cost components and, where possible, assign monetary values.
3. Quantify benefits (e.g., discount savings, avoided lost sales) and express them in monetary terms.
4. Calculate safety stock using the required service level and demand variability.
5. Determine the reorder point: ROP = (Average demand × Lead time) + Safety Stock.
6. Apply the EOQ (or an appropriate alternative model) to find the cost‑optimal order quantity.
7. Check the model’s assumptions; adjust for quantity discounts, production rates, or fluctuating demand if needed.
8. Monitor key ratios (Turnover, DSI, GMROI) regularly to spot over‑stocking or stock‑outs.
9. Review supplier performance, lead‑time changes, and market trends; revise safety‑stock and reorder parameters accordingly.
10. Decide whether a JIT or JIC approach better fits the firm’s operational environment and strategic objectives.