Inventory Optimization: Models, Safety Stock, and Supply Chain Strategy
Posted on Oct 23, 2025 in Business Administration and Innovation Management
Continuous Review Inventory Model Fundamentals
Key Parameters and Calculations
- Optimal Reorder Interval
- Safety Stock Calculation: SS = z × σL = NORM.INV(α, 0, 1) × √L × σ
- Example Parameters:
- Lead time (Factory to Europe): 5 weeks
- Cycle Service Level: 98%
- Product Cost: $400
- Annual Holding Cost: 30% of product cost
- NORM.INV(0.98, 0, 1) = 2.053748911 (Z-score)
Continuous Review Inventory Metrics
- Average Inventory: AI = (Q/2) + Safety Stock
- Order-Up-To Level (Base Stock): S = s + Q
Factors Driving Safety Inventory
- Replenishment Lead Time (L): If lead time is reduced by a factor of k, safety inventory is reduced by √k.
- Demand Uncertainty (σ): If the standard deviation (σ) is reduced by a factor of k, safety inventory is reduced by a factor of k.
- Service Level: Higher service levels require higher safety stock.
Periodic Review Policy (P-Model)
Key Variables and Average Inventory
- r: Reorder interval (Review period)
- S: Order-up-to level (Base-stock level)
- Average Inventory: AI = (rD/2) + Safety Stock
Comparing Continuous Review and Periodic Review Policies
Safety Inventory Drivers in Periodic Review
- Demand uncertainty
- Replenishment lead time
- Reorder interval (r)
- Service level
Implementation Comparison
- Periodic review policy is generally easier and cheaper to implement.
- Periodic review policy requires more safety inventory than continuous review policy for the same lead time and service level.
Newsvendor Model: Cost Definitions and Optimal Decisions
Cost Variables
- p = Sale price
- c = Purchase price
- s = Outlet price or salvage value
- Cu = Underage cost per unit (Cost of shortage)
- Co = Overage cost per unit (Cost of excess inventory)
Optimal Decision Rule
Let a be the probability that demand will be at or below the optimal order quantity (Critical Fractile).
Expected Marginal Cost: aCo = a(c – s)
Strategic Proposals for Supply Chain Improvement
i. Proposals for a European Factory
| Pros | Cons |
| 1 | Reduce lead time and transportation cost | High initial setup cost |
| 2 | Increase responsiveness | Less economies of scale |
| 3 | Improve service level | Increase uncertainty and cost of raw materials |
| 4 | Avoid lost sales | |
ii. Proposals for Better Forecasting
| Pros | Cons |
| 1 | Minimize inventory levels | High system setup cost |
| 2 | Improved production planning | Based on assumptions |
| 3 | Better material management | Based on past data |
| 4 | Effective handling of uncertainty | Requires long-term behavioral insight from market research |
| 5 | Better utilization of capital | |
iii. Proposals for Increasing Inventory Levels
| Pros | Cons |
| 1 | Improve service level | Higher inventory holding cost |
| 2 | Avoid lost sales | Risk of inventory damage or loss |
| 3 | Higher economies of scale | Risk of inventory obsolescence |
| 4 | Provide buffer for supply or demand uncertainty | Less cash flow flexibility |
| 5 | Reduce production lead time | |
| 6 | Lower unit transportation or production setup costs | |
| 7 | Fully utilize production capacity | |
Inventory Aggregation and Safety Stock Reduction
Factors Affecting the Value of Aggregation
- Demand Correlation
- Aggregation reduces demand variance (and thus safety inventory) if demands are not perfectly positively correlated.
- Square Root Law: If demand in different regions is roughly the same size and independent, aggregation reduces safety inventory by the square root of the number of areas aggregated.
- Note: Inventory aggregation does not require physical centralization. Information centralization (virtual aggregation) achieves the same goal of reducing safety inventory.
- Coefficient of Variation (CV) of Demand
- CV = Standard Deviation / Mean
- The higher the CV of demand for a product, the larger the impact on safety stock reduction achieved through aggregation.
- Value of Product
- High-value products yield a greater benefit from aggregation than low-value items.
Levers to Reduce Safety Inventory
- Reduce information uncertainty in demand (improve forecasting).
- Reduce replenishment lead time.
- Reduce supply uncertainty or replenishment lead time uncertainty.
- Increase review frequency in a periodic review policy or switch to a continuous review policy.
- Implement physical centralization and information centralization.
- Specialization and Stocking Strategy:
- Centralize slow-moving products (high CV) to maximize aggregation benefits.
- Decentralize fast-moving, low-value products closer to customers for faster service and lower delivery costs.
- Product Substitution:
- Substitution aggregates demand across components, reducing safety inventory.
- Higher demand uncertainty yields greater benefits from substitution.
- If the cost difference is small, carry more higher-value components to substitute for shortages of lower-value products.
- If demands are strongly positively correlated, there is little benefit of substitution (similar to aggregation).
- Requires joint management of inventories across substitutable products.
- Component Commonality and Postponement:
- Component commonality allows the aggregation of raw material inventory.
- As a common component is shared by more finished products, the cost of the component or the finished products using it may increase due to required flexibility in design.
- By postponing product differentiation or customization until closer to the point of sale, the producer maintains common components in the supply chain throughout most of the push phase.
