Inventory Management: Models, Costs, and Control Techniques

1. Static Inventory Problem Under Risk

Definition

A static inventory problem under risk involves a single-period decision where demand is uncertain but follows a known probability distribution. Examples include seasonal products like newspapers, ice cream, or festival items.

General Characteristics

• Single Period Decision: A one-time decision with no repeated ordering.
• Uncertain Demand: Demand is not fixed, though probabilities are known.
• Risk Factors: Potential for overstock or understock.
• No Replenishment: Stock cannot be reordered within the same period.
• Probabilistic Approach: Decisions are based on expected values.
• Cost Consideration: Includes overstock (unsold goods) and understock (lost sales) costs.
• Objective: Maximize expected profit or minimize expected loss.
• Techniques: Uses incremental analysis, opportunity loss, and Expected Monetary Value (EMV).
• Suitability: Ideal for seasonal or perishable goods.

Example: The Newspaper Vendor

A vendor buys newspapers in the morning. Since they cannot reorder later, unsold papers result in a loss, while shortages result in lost profit. This is a classic example of static inventory under risk.

2. Relevant Costs in Inventory Management

Effective decision-making requires analyzing all costs directly affected by inventory levels.

Types of Relevant Costs

• Ordering Cost: Expenses incurred each time an order is placed (e.g., administrative, transport). Formula: Number of Orders × Cost per Order.
• Carrying Cost: Costs of holding stock (e.g., storage, insurance, depreciation, taxes). Formula: Average Inventory × Holding Cost per Unit.
• Shortage Cost: Costs incurred when inventory runs out (e.g., lost sales, customer dissatisfaction).
• Purchase Cost: The cost of buying raw materials or goods.
• Setup Cost: Costs for changing production setups in batch systems.
• Opportunity Cost: Profit lost by having capital tied up in inventory.
• Spoilage/Obsolescence: Losses due to perishable items or technological changes.

3. ABC Analysis

ABC Analysis is a selective inventory control method based on the Pareto Principle (80:20 rule), where a small percentage of items accounts for a large portion of inventory value.

Classification

• A Items (10–20% of items, 70–80% of value): Require strict control and frequent review.
• B Items (20–30% of items, 15–25% of value): Require moderate control and periodic review.
• C Items (50–70% of items, 5–10% of value): Require simple control and minimum effort.

4. Static vs. Dynamic Inventory

• Static Inventory: Single-period, one-shot decisions under risk (e.g., newspapers).
• Dynamic Inventory: Multi-period, continuous decision-making aimed at minimizing total costs over time (e.g., raw materials for production).

5. Safety Stock

Safety stock is extra inventory kept as a buffer against demand and supply uncertainties to prevent stockouts and ensure production continuity.

Key Situations for Safety Stock

• Uncertain demand or supply delays.
• Long lead times.
• Seasonal demand peaks.
• Critical materials essential for production.

6. Decision Criteria Under Uncertainty

When probabilities are unknown, managers use these criteria:

• Maximax: Optimistic approach; selects the option with the highest possible payoff.
• Maximin: Pessimistic approach; selects the option with the best of the worst-case scenarios.
• Minimax Regret: Minimizes the maximum potential loss (regret).
• Hurwicz: A weighted average of the best and worst outcomes.
• Laplace: Assumes all outcomes are equally likely; selects the highest average payoff.

7. Inventory Control Models

• Deterministic Models: Assume demand and lead time are constant (e.g., EOQ).
• Probabilistic Models: Account for uncertainty in demand or lead time (e.g., Safety Stock, Newsvendor Model).

8. Economic Order Quantity (EOQ)

EOQ is the optimal order size that minimizes the sum of ordering and carrying costs.

EOQ Formula

EOQ = √((2 × D × S) / H)

• D = Annual Demand
• S = Ordering Cost per Order
• H = Holding Cost per Unit per Year

9. Selective Inventory Analysis (SIA)

SIA prioritizes inventory management efforts based on item importance. Common methods include:

• ABC: Based on value.
• VED: Based on criticality (Vital, Essential, Desirable).
• FSN: Based on frequency of use (Fast, Slow, Non-moving).
• SDE: Based on scarcity (Scarce, Difficult, Easy).