Inventory Models

Inventory Models are mathematical tools used to determine how much stock to keep, when to reorder, and how to minimize total inventory cost.

Every business that deals with physical goods must manage inventory carefully.

Too much inventory increases cost, while too little inventory leads to shortages and customer dissatisfaction.

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Why Inventory Management Is Important

Inventory represents money tied up in stock.

Poor inventory management leads to:

• High storage costs
• Wastage and spoilage
• Stock-outs and lost sales
• Cash flow problems

Inventory models help balance cost and availability.

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What Is Inventory?

Inventory refers to goods and materials that a business holds for:

• Production
• Sale
• Future use

Inventory is a critical asset in business operations.

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Types of Inventory

Businesses usually deal with three main types of inventory:

• Raw materials
• Work-in-progress (WIP)
• Finished goods

Each type requires different management strategies.

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Inventory-Related Costs

Inventory models focus on minimizing total cost.

The main inventory-related costs are:

• Ordering cost
• Holding (carrying) cost
• Shortage cost

Understanding these costs is essential.

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Ordering Cost

Ordering cost is the cost incurred each time an order is placed.

Examples:

• Administrative work
• Transportation
• Inspection

Ordering cost does not depend on order size.

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Holding (Carrying) Cost

Holding cost is the cost of storing inventory over time.

Examples:

• Warehouse rent
• Insurance
• Deterioration

Higher inventory means higher holding cost.

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Shortage Cost

Shortage cost arises when inventory is insufficient.

Examples:

• Lost sales
• Customer dissatisfaction
• Production stoppage

Many basic models assume no shortages.

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Objective of Inventory Models

The main objective is to:

• Minimize total inventory cost
• Ensure smooth supply of goods

This involves finding optimal order quantity and reorder timing.

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Economic Order Quantity (EOQ)

Economic Order Quantity (EOQ) is the most important inventory model.

It determines the optimal quantity to order that minimizes total inventory cost.

EOQ is frequently tested in exams.

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Assumptions of EOQ Model

EOQ model is based on the following assumptions:

• Demand is known and constant
• Lead time is constant
• No shortages are allowed
• Ordering and holding costs are constant

Understanding assumptions avoids misuse.

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EOQ Formula

EOQ = √(2DS / H)

Where:

• D = Annual demand
• S = Ordering cost per order
• H = Holding cost per unit per year

This formula balances ordering and holding costs.

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Interpretation of EOQ

At EOQ:

• Ordering cost = Holding cost
• Total inventory cost is minimum

This balance is the core idea of EOQ.

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Reorder Level (ROL)

Reorder level is the inventory level at which a new order should be placed.

Reorder Level = Demand × Lead Time

ROL ensures stock arrives before inventory runs out.

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Example: EOQ and Reorder Level

Suppose:

• Annual demand = 10,000 units
• Ordering cost = ₹200
• Holding cost = ₹5 per unit per year

EOQ = √(2 × 10,000 × 200 / 5) = 894 units (approx.)

If daily demand = 40 units and lead time = 5 days:

Reorder level = 40 × 5 = 200 units

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Inventory Cycle (Conceptual)

Inventory level:

• Decreases steadily due to demand
• Reaches reorder level
• Jumps up when new stock arrives

This saw-tooth pattern is typical in EOQ models.

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Inventory Models with Shortages (Overview)

Some models allow controlled shortages.

In such cases:

• Backorders are allowed
• Shortage cost is included

These models are more complex and used in advanced OR.

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Inventory Models with Quantity Discounts

Suppliers may offer discounts for bulk purchases.

Inventory models help decide:

• Whether discount is beneficial
• Optimal order quantity

Lower price must justify higher holding cost.

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Inventory Management in Business

Businesses use inventory models to:

• Avoid stock-outs
• Reduce excess inventory
• Improve cash flow

Good inventory management improves profitability.

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Inventory Models in Retail

Retailers apply inventory models to:

• Plan seasonal stock
• Manage fast-moving goods
• Reduce unsold inventory

Accurate demand estimation is crucial.

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Inventory Models in Manufacturing

Manufacturers use inventory models to:

• Ensure continuous production
• Manage raw material supply
• Reduce production downtime

Inventory directly affects productivity.

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Inventory Models in Analytics

Analytics teams use inventory models to:

• Forecast demand
• Optimize stock levels
• Reduce operational cost

Data improves inventory decisions.

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Inventory Models in Data Science

In data science:

• Demand forecasting feeds inventory models
• Optimization techniques refine EOQ

ML and OR work together in inventory systems.

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Inventory Models in Competitive Exams

Exams often test:

• EOQ formula
• Reorder level calculation
• Cost interpretation

Practice ensures speed and accuracy.

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Limitations of Inventory Models

Inventory models rely on assumptions.

Real-world challenges include:

• Uncertain demand
• Variable lead times
• Changing costs

Models must be adjusted over time.

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Common Mistakes to Avoid

• Ignoring holding costs
• Using EOQ blindly without checking assumptions
• Failing to update demand estimates

Inventory decisions should be reviewed regularly.

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Practice Questions

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Quick Quiz

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Quick Recap

• Inventory models balance cost and availability
• EOQ finds optimal order quantity
• Reorder level ensures continuous supply
• Used in business, analytics, and exams

With inventory models understood, you are now ready to study Business Statistics Math, where statistics directly supports business analysis and decisions.