Calculating Fill Rate Using Periodic Review

Optimize your inventory levels and service performance with scientific precision.

What is Calculating Fill Rate Using Periodic Review?

Calculating fill rate using periodic review is a critical mathematical process in inventory management that measures the percentage of customer demand satisfied from stock on hand during a specific ordering cycle. Unlike continuous review systems where orders are triggered by a reorder point, periodic review systems involve checking inventory levels at fixed time intervals (e.g., every Monday).

Supply chain managers prioritize calculating fill rate using periodic review because it provides a more accurate reflection of customer experience than simple service levels. While service level measures the probability of a stockout, the fill rate measures the magnitude of lost sales, which is directly tied to revenue performance.

Common misconceptions include treating fill rate and service level as identical. In reality, a 95% service level often results in a significantly higher fill rate (e.g., 99%) because stockouts, when they occur, rarely affect 100% of the cycle’s demand.

Calculating Fill Rate Using Periodic Review Formula and Mathematical Explanation

To perform calculating fill rate using periodic review, we must first understand the “Protection Interval,” which is the sum of the Review Period (P) and the Lead Time (L). The variability during this total time determines our risk.

Variable	Meaning	Unit	Typical Range
d	Average Daily Demand	Units/Day	1 – 10,000
σd	Standard Deviation of Demand	Units	5% – 50% of d
P	Review Period	Days	1 – 30
L	Lead Time	Days	1 – 90
z	Safety Factor (Z-score)	Standard Deviations	1.28 – 3.09

The Step-by-Step Derivation

1. Calculate Standard Deviation of Protection Interval: σ_P+L = σ_d * √(P + L)
2. Calculate Average Demand per Cycle: Q = d * P
3. Determine Expected Shortage per Cycle (ESC): ESC = σ_P+L * G(z)
4. Final Fill Rate Calculation: Fill Rate = 1 – (ESC / Q)

Where G(z) is the unit normal loss function, calculated as: G(z) = φ(z) – z * (1 – Φ(z)).

Practical Examples (Real-World Use Cases)

Example 1: Retail Electronics Store

A store sells an average of 10 headphones a day with a standard deviation of 3. They review stock every 7 days (P=7), and shipping takes 3 days (L=3). They target a 95% CSL (z ≈ 1.645).

• σ_P+L = 3 * √(7+3) = 9.48
• Q = 10 * 7 = 70
• G(1.645) ≈ 0.021
• ESC = 9.48 * 0.021 = 0.20 units
• Fill Rate = 1 – (0.20 / 70) = 99.71%

Example 2: Industrial Spare Parts

A factory uses a critical valve. d=2, σ_d=1.5, P=30 days, L=15 days. Target CSL 90% (z=1.28).

• σ_P+L = 1.5 * √(30+15) = 10.06
• Q = 2 * 30 = 60
• G(1.28) ≈ 0.048
• ESC = 10.06 * 0.048 = 0.48
• Fill Rate = 1 – (0.48 / 60) = 99.2%

How to Use This Calculating Fill Rate Using Periodic Review Calculator

To get the most out of this tool for calculating fill rate using periodic review, follow these steps:

• Input Average Demand: Use historical sales data from the last 6-12 months.
• Define Volatility: Input your σ_d. If unknown, a high-level estimate is 20-30% of your average demand.
• Set Review/Lead Times: Ensure both are in the same time units (days).
• Adjust Service Level: Watch how the Safety Stock and Fill Rate change dynamically.
• Analyze the Chart: Use the SVG chart to see where diminishing returns on safety stock begin.

Key Factors That Affect Calculating Fill Rate Using Periodic Review Results

• Demand Volatility: High σ_d drastically increases ESC, lowering the fill rate unless safety stock is huge.
• Lead Time Duration: Longer lead times increase the protection interval, making calculating fill rate using periodic review more sensitive to errors.
• Review Frequency: Shorter review periods (P) reduce the average cycle demand (Q), which can paradoxically make the fill rate percentage look worse for the same amount of shortage.
• Target Service Level: Increasing the CSL increases the Z-score, which exponentially reduces expected shortages.
• Forecast Accuracy: Better forecasts reduce σ_d, allowing for higher fill rates with lower working capital.
• Supply Chain Risk: Variability in L (Lead Time) itself is not in this basic formula but is a major real-world factor in lead time variability management.

Frequently Asked Questions (FAQ)

Why is fill rate usually higher than the Cycle Service Level?

CSL is the probability of having *any* stockout. Fill rate is the percentage of demand met. Even if you stock out, you usually only miss a small fraction of the total cycle demand.

Can calculating fill rate using periodic review result in a 100% rate?

Mathematically, it approaches 100% as safety stock increases, but it only reaches 100% with infinite stock, as demand is theoretically unbounded in a normal distribution.

How does a longer lead time affect the fill rate?

Longer lead times increase the uncertainty window, requiring more safety stock to maintain the same fill rate performance.

What is the Unit Normal Loss Function G(z)?

It is a statistical function that represents the expected value of the amount by which a random variable exceeds a certain threshold (z).

Is this calculator suitable for lumpy demand?

No, this model assumes a normal distribution. For intermittent or lumpy demand, Poisson or Negative Binomial distributions are better for calculating fill rate using periodic review.

Does order cost affect the fill rate?

Indirectly. Order costs determine the Review Period (P). Larger P increases cycle stock but helps “dilute” the impact of a single stockout event in fill rate terms.

What is a good fill rate target?

Most retailers target 97-99% for A-items, 95% for B-items, and 90-92% for C-items.

How do I reduce my safety stock without hurting my fill rate?

Improve your inventory management system accuracy or shorten the lead time from suppliers.

Related Tools and Internal Resources

• Inventory Management System Guide: Learn how to automate periodic reviews.
• Safety Stock Formula: Deep dive into different ways to calculate buffer stock.
• Reorder Point Calculator: For companies using continuous review instead of periodic.
• Economic Order Quantity: Optimize your order size to minimize total cost.
• Lead Time Variability: How to handle suppliers that aren’t consistent.
• Service Level Optimization: Balancing the cost of inventory against the cost of lost sales.