Inventory Control Principles and Models

Introduction

Inventory is the stock of materials, components, spare parts, finished goods and supplies held to support operations and customer service. In stores and warehouse management, inventory control means deciding what to stock, how much to stock, when to reorder, and how to monitor stock. The central managerial challenge is to balance two competing risks: excessive inventory ties up capital and increases carrying costs, whereas insufficient inventory causes stockouts, production interruptions and poor customer service.

Inventory control is therefore not simply a matter of keeping stock low. It is a system of decisions based on demand, lead time, cost, risk and service requirements. Quantitative models such as economic order quantity (EOQ) provide useful starting points, but their assumptions must be examined before implementation.

Learning Objectives

After studying this chapter, the learner should be able to:

1. Explain stock-level concepts and the inventory control cycle.
2. Calculate EOQ, reorder point, safety stock and related measures.
3. Analyse lead time, demand variability and service levels.
4. Apply ABC, VED, FSN, HML and SDE classification techniques.
5. Evaluate the assumptions, benefits and limitations of inventory models.
6. Recommend practical control policies for different categories of materials.

1. The Inventory Control System

A basic inventory system contains five connected elements:

• Demand: usage or customer requirements during a period.
• Inventory position: stock on hand plus outstanding orders minus confirmed backorders.
• Replenishment policy: rules determining order quantity and timing.
• Lead time: time between placing an order and receiving usable stock.
• Control information: records, forecasts, physical counts and performance indicators.

The inventory control cycle can be represented as follows:

Figure: The recurring inventory control cycle.

Important stock terms

Stock on hand is physically available inventory. Reserved stock is allocated to a known requirement and should not be treated as freely available. On-order stock has been ordered but not yet received. Available stock is stock on hand less reservations. Inventory position normally includes on-hand stock, on-order stock and outstanding commitments.

A stock record should identify item code, description, unit of measure, location, receipts, issues, adjustments, balance, reorder point and supplier information. Accurate records are essential because even a theoretically excellent model fails when the physical and recorded balances differ.

2. Stock Levels and Control Policies

Minimum, maximum and average stock

The minimum stock level is the planned lower boundary, often related to safety stock. The maximum stock level is the target upper boundary after replenishment. Average inventory is the typical quantity held over time.

For a simple replenishment cycle with instantaneous replenishment and no safety stock, average cycle stock is approximately half the order quantity:

Here, Q is the order quantity in units. This relationship assumes steady demand, immediate replenishment and a gradual depletion of stock. If safety stock is held, approximate average inventory becomes:

where SS is safety stock in units. In reality, pipeline stock, anticipation stock and seasonal stock may also be relevant.

Reorder point

The reorder point (ROP) is the inventory position at which a replenishment order should be placed. Under constant demand and lead time:

where d is average demand per time unit, L is lead time in the same time unit, and SS is safety stock. Unit consistency is essential: daily demand must be multiplied by lead time in days, not weeks.

If demand and lead time are certain and no buffer is required, SS = 0. When demand or lead time varies, safety stock protects against uncertainty.

Continuous and periodic review

In a continuous-review system, stock position is monitored continuously or after every transaction. An order is placed when the reorder point is reached. A common policy is the (Q, R) system: order a fixed quantity Q when inventory position reaches R.

In a periodic-review system, stock is reviewed at fixed intervals. The order quantity varies so that inventory is raised to a target level. A typical order-up-to policy is represented by (P, S), where P is the review period and S is the order-up-to level. Periodic review requires additional protection because demand can occur during the review period as well as during lead time.

3. Economic Order Quantity

The economic order quantity identifies the order size that minimises relevant annual ordering and holding costs under simplified conditions.

Where:

If annual holding cost is expressed as a percentage of unit value, then:

where i is the annual carrying-rate fraction and C is unit purchase cost. For example, a 20% carrying rate is i = 0.20, not 20.

Derivation of EOQ

Assume demand is constant, replenishment is instantaneous, shortages are not allowed, unit price is constant and ordering and holding costs are the only relevant variable costs. Annual ordering cost is:

Average cycle stock is Q ÷ 2, so annual holding cost is:

Total relevant annual cost is therefore:

The minimum occurs where the two variable cost components are equal:

Solving gives the EOQ formula. Purchase cost D × C is excluded from the optimisation when unit price is constant because it does not change with order quantity.

Worked example: EOQ

A maintenance store uses 12,000 bearings per year. The ordering cost is ₹600 per order and annual holding cost is ₹24 per bearing.

The practical order quantity is approximately 775 bearings. Orders per year are:

The average time between orders, assuming 300 operating days per year, is approximately:

EOQ is a cost benchmark, not an instruction that must be followed regardless of supplier minimums, storage capacity, price breaks or transport economics.

4. Safety Stock, Lead Time and Service Level

Lead-time analysis

Lead time may include requisition approval, supplier processing, transportation, receiving, inspection and put-away. It should be measured from the actual point of order release to the point when stock becomes usable. A supplier's quoted shipping time is not necessarily the warehouse's total replenishment lead time.

Lead-time data should be analysed using average, minimum, maximum and variation. Repeated delays may indicate a supplier reliability problem rather than random uncertainty.

Safety stock under demand variability

If demand during lead time is approximately normally distributed and lead time is constant, safety stock can be estimated as:

where σ_d is the standard deviation of demand per period, L is lead time in periods, and z is the standard-normal service factor. The formula assumes independent demand periods and a stable distribution.

If lead time varies but demand per period is constant:

where σ_L is the standard deviation of lead time in periods.

If both demand and lead time vary independently, a commonly used approximation is:

This omits the interaction term involving simultaneous demand and lead-time variation. It is suitable as an approximation, not as a universal law. Where demand and lead time are correlated, or distributions are highly skewed, historical simulation or a more suitable probabilistic model is preferable.

Worked example: reorder point and safety stock

Daily demand has a mean of 80 units and standard deviation of 15 units. Lead time is constant at 6 days. Management selects a 95% cycle-service target, for which z ≈ 1.645.

Thus, safety stock is approximately 60 units. The reorder point is:

The operational policy may therefore use a reorder point of 541 units, subject to the organisation's rounding and unit-pack rules.

Service levels and trade-offs

A cycle service level is the probability of not experiencing a stockout during a replenishment cycle. It is not identical to fill rate, which measures the proportion of demand supplied immediately from stock. A high service target requires more safety stock and therefore more capital. The correct target depends on criticality, shortage consequences, customer expectations and supply alternatives.

Managers should avoid applying one service level to every item. A life-support spare, a low-value office supply and a regularly available commodity do not have the same consequences of shortage.

5. Inventory Classification Techniques

Classification focuses managerial attention where it produces the greatest benefit. Methods may be used separately or combined in a multi-criteria matrix.

ABC analysis

ABC analysis ranks items by annual usage value:

Typical, though not universal, groupings are:

The percentages are conventions, not natural laws. An item with low annual value may still be operationally critical.

VED analysis

VED classifies items by criticality:

• Vital: absence can stop operations or create serious safety consequences.
• Essential: shortage reduces performance but may be manageable temporarily.
• Desirable: shortage has limited immediate effect.

VED is especially useful for maintenance and spare parts. It should be based on operational consequence, not merely price.

FSN analysis

FSN classifies materials by movement:

• Fast-moving: frequent issues or high consumption.
• Slow-moving: occasional movement.
• Non-moving: no issue for a defined period.

The time boundary must be stated and should reflect the item's expected usage cycle. Non-moving stock should be investigated for obsolescence, project completion, specification change or inaccurate records before disposal.

HML analysis

HML classifies items by unit price:

• High-cost: strong authorization, security and purchase scrutiny.
• Medium-cost: normal controls.
• Low-cost: simplified procurement and issue procedures may be economical.

HML differs from ABC: HML uses unit price, whereas ABC uses annual consumption value.

SDE analysis

SDE classifies items by procurement difficulty:

• Scarce: difficult to obtain or dependent on limited sources.
• Difficult: procurement involves long lead times, technical approval or few suppliers.
• Easy: readily available from several sources.

SDE supports sourcing strategy and safety-stock decisions. A scarce item may require an approved substitute, supplier development or strategic reserve.

Combining classifications

A practical store may label an item A-V-F-H-S: high annual usage value, vital, fast-moving, high unit cost and scarce. Such an item deserves accurate records, cycle counting, supplier monitoring, technical substitution review and an explicitly approved service policy. In contrast, a C-D-S-L-E item may justify simplified controls, provided safety and regulatory requirements are not compromised.

6. Physical Control and Performance Measures

Quantitative models depend on disciplined execution. Essential practices include:

• standard item descriptions and units of measure;
• segregation of incompatible or hazardous materials;
• barcode or RFID identification where economically justified;
• batch, serial-number and expiry-date control where required;
• bin locations and labelled storage;
• authorised receipts and issues;
• cycle counting based on risk and value;
• investigation of variances rather than routine adjustment;
• review of excess, obsolete and slow-moving inventory.

Useful performance measures include:

Inventory turnover

The numerator and denominator must use comparable valuation bases. Days of supply can be estimated as:

Other measures include stockout frequency, order-fill rate, record accuracy, supplier on-time delivery, obsolete inventory percentage and carrying cost. A high turnover is not automatically good if it produces unacceptable stockouts.

7. Illustrative Case: Critical Spare Parts in a Processing Plant

Background

This fictional case concerns Meridian Processors, a plant whose compressors require a specialised seal kit. The store recorded annual demand of 240 kits. Each kit costs ₹4,000, ordering cost is ₹1,500, and annual holding cost is estimated at 25% of unit cost. Average demand is 20 kits per month. Supplier lead time averages two months but varies considerably. A compressor shutdown costs approximately ₹150,000 per day.

Problem

The buyer used a low unit price and monthly consumption as the main decision criteria. The plant experienced two shutdowns because replenishment orders were placed only after the physical balance reached zero. At the same time, several unrelated spare parts had become obsolete.

Analysis

Annual holding cost per kit is:

EOQ is:

The cost model therefore suggests an order quantity of approximately 27 kits. However, this result does not determine the reorder point. Because lead time is long and the item is vital, the plant must estimate demand during lead time, safety stock and the financial consequence of a stockout. The item is likely classified as B or A by annual usage value, V by criticality, S by procurement difficulty, and possibly H by unit price.

Approach and solution

The plant introduced the following controls:

1. A critical-item register linking each spare to equipment and approved substitutes.
2. A continuous-review policy with a reorder point based on actual lead-time demand.
3. Supplier lead-time records and monthly supplier performance review.
4. A management-approved service target for vital spares.
5. Cycle counting every month for critical items.
6. Review of repairable, surplus and obsolete stock with engineering participation.
7. Dual sourcing investigation and a controlled emergency reserve.

The EOQ was retained as a starting point but adjusted for supplier pack size and storage constraints. The reorder point was not set equal to EOQ; quantity and timing were treated as separate decisions.

Outcome

In this illustrative case, stockout incidents declined after the reorder point and supplier monitoring were implemented. The value of obsolete stock also fell after engineering reviewed substitutes and equipment changes. The plant accepted somewhat higher safety stock because the expected cost of a compressor shutdown exceeded the annual carrying cost of the additional kits.

Learning points

The case demonstrates that inventory decisions must combine cost, criticality and supply risk. EOQ cannot compensate for inaccurate records, late suppliers or an inappropriate service target. Classification methods are most effective when they lead to differentiated controls.

8. Assumptions, Limitations and Governance

Inventory models simplify reality. EOQ assumes stable demand, fixed ordering cost, constant unit price, known holding cost, instantaneous replenishment and no shortages. These assumptions may be violated by seasonal demand, quantity discounts, supplier constraints, inflation, capacity limits or transport consolidation.

Safety-stock formulas based on standard deviation assume that historical variation is relevant to future conditions. Structural changes, new products, unusual disruptions and intermittent demand may invalidate this assumption. For intermittent or lumpy demand, Croston-type methods, judgmental review or simulation may be more appropriate than a normal approximation.

Governance requires clear authority for parameter changes, documented item master data, audit trails for adjustments and periodic review of obsolete inventory. Safety and environmental regulations may require special storage, traceability, expiry control and disposal procedures. Deliberately overstating demand to obtain excessive stock or hiding obsolete stock through unauthorised adjustments is both poor control and an ethical failure.

Technology can improve visibility through warehouse-management systems, barcode scanning, RFID, electronic procurement and dashboards. AI and predictive analytics may support demand forecasting, anomaly detection and supplier-risk monitoring, but outputs require human review. Poor master data can produce highly confident but incorrect recommendations. Automated replenishment should therefore include approval thresholds, exception reporting, cybersecurity controls and explainable parameter changes.

9. Best-Practice Implementation Sequence

A practical implementation sequence is:

1. Clean item master data and standardise units of measure.
2. Measure actual demand, lead time, variability and stockout history.
3. Segment items using value, criticality, movement, price and supply difficulty.
4. Select review policies appropriate to each segment.
5. Calculate initial EOQ, reorder points and safety stocks with documented assumptions.
6. Check supplier minimums, pack sizes, storage capacity and budget.
7. Pilot the policy on selected items.
8. Monitor service, inventory value, record accuracy and obsolescence.
9. Review parameters after demand, supplier or operating changes.
10. Integrate purchasing, stores, maintenance, finance and users in governance.

Chapter Summary

Inventory control balances availability against the cost and risk of holding stock. Stock on hand, inventory position, lead time, reorder point, safety stock and service level are distinct concepts. EOQ minimises ordering plus holding cost under restrictive assumptions; it does not determine when to order and does not address criticality or supply risk. The reorder point combines expected demand during lead time with a safety-stock allowance. Safety stock should reflect demand variation, lead-time variation and the selected service objective.

ABC, VED, FSN, HML and SDE analyses provide different perspectives: annual usage value, criticality, movement, unit price and procurement difficulty. Combining these perspectives supports differentiated controls. Effective inventory management also requires accurate records, disciplined receiving and issuing, cycle counting, supplier monitoring, ethical governance and informed use of technology. Models should guide professional judgment rather than replace it.

Key Terms

Inventory control: Planning and regulating stock quantity, timing and availability.

Stock on hand: Physical quantity currently held in the store.

Inventory position: On-hand stock plus on-order stock less outstanding commitments.

Lead time: Time from order release until usable stock is available.

Reorder point: Inventory position at which replenishment is initiated.

Safety stock: Additional stock held to protect against uncertainty.

EOQ: Order quantity that minimises relevant ordering and holding costs under stated assumptions.

Ordering cost: Cost incurred each time an order is placed or a setup is made.

Holding cost: Annual cost of carrying one unit of inventory.

Cycle stock: Inventory resulting from replenishment lot size.

Service level: A measure of the desired probability or extent of immediate supply.

Cycle service level: Probability of no stockout during a replenishment cycle.

Fill rate: Proportion of demand supplied immediately from available stock.

ABC analysis: Classification by annual consumption or usage value.

VED analysis: Classification by vital, essential and desirable criticality.

FSN analysis: Classification by fast, slow and non-moving behaviour.

HML analysis: Classification by high, medium and low unit price.

SDE analysis: Classification by scarce, difficult and easy procurement.

Obsolescence: Loss of usefulness or saleability caused by age, change or non-demand.

Inventory turnover: Annual consumption or cost of issues divided by average inventory value.

Review Questions

Short Answer Questions

1. What is the difference between stock on hand and inventory position?
2. Define reorder point and safety stock.
3. State the main assumptions of the basic EOQ model.
4. How does ABC analysis differ from HML analysis?
5. What is meant by cycle service level?

Long Answer Questions

1. Explain the inventory control cycle and discuss the importance of accurate stores records.
2. Derive the EOQ relationship from annual ordering and holding costs, and explain its limitations.
3. Explain continuous-review and periodic-review systems, including situations in which each may be appropriate.
4. Compare ABC, VED, FSN, HML and SDE analyses and show how they can be combined.
5. Discuss how lead-time uncertainty and service-level decisions affect safety-stock requirements.

Analytical / Application Questions

1. Annual demand is 10,000 units, ordering cost is ₹400 per order and annual holding cost is ₹20 per unit. Calculate EOQ and explain two practical reasons why the calculated quantity might be adjusted.
2. Average daily demand is 50 units, lead time is 8 days and safety stock is 120 units. Calculate the reorder point. Explain what could happen if the store incorrectly uses a lead time of 8 weeks.
3. A low-value spare part is vital, slow-moving and difficult to procure. Recommend an inventory policy using at least three classification methods and justify your recommendation.

Multiple Choice Questions with Answers

Question 1

Which expression represents the basic economic order quantity?

A. √(2DS ÷ H)

B. √(2DH ÷ S)

C. (D × S) + H

D. D ÷ (S × H)

Correct Answer: A. √(2DS ÷ H)

Question 2

Daily demand is 80 units, lead time is 6 days and safety stock is 60 units. What is the reorder point?

A. 140 units

B. 480 units

C. 540 units

D. 560 units

Correct Answer: C. 540 units

Question 3

Which classification is based primarily on operational criticality?

A. ABC

B. VED

C. FSN

D. HML

Correct Answer: B. VED

Question 4

In ABC analysis, annual usage value is calculated as:

A. Unit price ÷ annual demand

B. Annual demand × unit price

C. Ordering cost × lead time

D. Average stock ÷ holding cost

Correct Answer: B. Annual demand × unit price

Question 5

What does safety stock primarily protect against?

A. Uncertainty in demand or replenishment

B. Constant unit prices

C. Correct item descriptions

D. The fixed portion of purchase cost

Correct Answer: A. Uncertainty in demand or replenishment

Question 6

Which system places an order when inventory position reaches a specified level?

A. Periodic-review (P,S) system

B. Continuous-review (Q,R) system

C. VED system

D. FSN system

Correct Answer: B. Continuous-review (Q,R) system

Question 7

An item with no issues for a defined period is generally classified in FSN analysis as:

A. Fast-moving

B. Standard-moving

C. Non-moving

D. Vital

Correct Answer: C. Non-moving

Question 8

If annual demand is 12,000 units and order quantity is 600 units, how many orders are placed per year?

A. 12

B. 20

C. 600

D. 7,200,000

Correct Answer: B. 20

Question 9

Which statement about EOQ is correct?

A. It directly determines the required service level.

B. It remains valid without change when demand is highly seasonal.

C. It balances relevant ordering and holding costs under stated assumptions.

D. It is always equal to the reorder point.

Correct Answer: C. It balances relevant ordering and holding costs under stated assumptions.

Question 10

A high cycle service level generally requires:

A. Less safety stock in every situation

B. More protection against stockout and potentially more inventory

C. No lead-time information

D. Elimination of physical counting

Correct Answer: B. More protection against stockout and potentially more inventory