Reorder Point Calculator

Reorder Point (ROP)

The reorder point is the inventory level at which an order should be placed to replenish stock before it runs out. It helps you determine the optimal reorder point as well as the safety stock required based on your demand patterns and lead time characteristics.

Basic ROP = Demand During Lead Time + Safety Stock

Where:

Demand During Lead Time = Average Demand × Lead Time
Safety Stock = Buffer for demand and lead time variability

Select Demand and Lead Time Scenario

Choose the model that matches your demand and lead time characteristics:

Constant Demand & Lead Time

Variable Demand

Variable Lead Time

Both Variable

Constant Demand and Lead Time

Use when both demand and lead time are stable with little variation.

Variable Demand (Constant Lead Time)

Use when demand varies but lead time is relatively stable.

Variable Lead Time (Constant Demand)

Use when lead time varies but demand is relatively stable.

Variable Demand and Lead Time

Use when both demand and lead time vary significantly.

Average Demand (units/day):

Demand Standard Deviation:

Average Lead Time (days):

Lead Time Standard Deviation (days):

Service Level (%):

Reorder Point Calculation Results

Reorder Point

0

units

Safety Stock

0

units

Lead Time Demand

0

units

Service Level

95%

probability

Calculation Details

How to Use This Reorder Point Calculator

The reorder point calculator simplifies the inventory planning process. Follow these steps to calculate your optimal reorder point:

Select the appropriate model: Choose the scenario that matches your demand and lead time characteristics (constant or variable).
Enter demand information: Input your average daily demand and, if applicable, demand variability (standard deviation).
Enter lead time information: Provide your average lead time and, if applicable, lead time variability.
Set service level target: Specify your desired service level (the probability of not having a stockout). Usual value used is 95%.
Calculate: Click the "Calculate ROP" button to see your results.

The calculator will provide your reorder point, safety stock requirement, and detailed information about the calculation components.

What is Reorder Point? Understanding Inventory Management

Reorder Point (ROP) is a critical inventory management concept that determines when to place a new order to replenish stock. It represents the minimum quantity of an item that should be in inventory to prevent stockouts during the lead time (the time between placing an order and receiving it).

Reorder point calculation helps businesses maintain optimal inventory levels by considering:

Demand Rate - How quickly inventory is being consumed
Lead Time - How long it takes to receive new inventory
Safety Stock - Buffer inventory to account for variability in demand and lead time

Reorder Point Formulas

1. Constant Demand and Constant Lead Time

When both demand and lead time are stable and predictable:

ROP = d × L

Where:
d = Average demand per period
L = Lead time (in periods)

2. Variable Demand with Constant Lead Time

When demand varies but lead time remains constant:

ROP = (d × L) + Z × σ_d × √L

Where:
d = Average demand per period
L = Lead time (in periods)
Z = Z-score (service level factor)
σ_d = Standard deviation of demand

3. Constant Demand with Variable Lead Time

When demand is stable but lead time varies:

ROP = (d × L) + Z × d × σ_L

Where:
d = Average demand per period
L = Average lead time
Z = Z-score (service level factor)
σ_L = Standard deviation of lead time

4. Variable Demand and Variable Lead Time

When both demand and lead time are variable:

ROP = (d × L) + Z × √(L × σ_d² + d² × σ_L²)

Where:
d = Average demand per period
L = Average lead time
Z = Z-score (service level factor)
σ_d = Standard deviation of demand
σ_L = Standard deviation of lead time

Proper safety stock calculation is essential for balancing the costs of stockouts against the costs of holding excess inventory. These formulas help you determine the optimal safety stock inventory level based on your specific demand and supply variability.

Practical Examples

Example 1: Constant Demand and Lead Time

A retailer sells an average of 20 units of a product per day. The lead time from their supplier is consistently 5 days. They want to maintain a small safety stock of 10 units.

ROP = (Average Demand × Lead Time) + Safety Stock = (20 × 5) + 10 = 110 units

When inventory drops to 110 units, they should place a new order.

Example 2: Variable Demand

A product has an average daily demand of 15 units with a standard deviation of 4 units. Lead time is constant at 7 days. The company wants a 95% service level (Z=1.65).

Safety Stock = Z × σ_d × √L = 1.65 × 4 × √7 ≈ 1.65 × 4 × 2.65 ≈ 17.5 units

ROP = (Average Demand × Lead Time) + Safety Stock = (15 × 7) + 17.5 = 122.5 units

They should reorder when inventory reaches approximately 123 units.

Example 3: Variable Lead Time

A product has constant daily demand of 25 units. Lead time averages 10 days with a standard deviation of 2 days. The company wants a 90% service level (Z=1.28).

Safety Stock = Z × d × σ_L = 1.28 × 25 × 2 = 64 units

ROP = (Average Demand × Average Lead Time) + Safety Stock = (25 × 10) + 64 = 314 units

They should reorder when inventory reaches 314 units.

Frequently Asked Questions (FAQs)

What is the difference between reorder point and safety stock? +

Reorder point is the inventory level at which a new order should be placed. It includes both the expected demand during lead time and the safety stock.

Safety stock is the buffer inventory maintained to protect against variability in demand and lead time. It's a component of the reorder point calculation.

Formula: Reorder Point = (Average Demand × Lead Time) + Safety Stock

How do I calculate safety stock with variable demand? +

When demand is variable but lead time is constant, use this safety stock calculation formula:

Safety Stock = Z × σ_d × √L

Where:

Z = Service factor (based on desired service level)
σ_d = Standard deviation of demand
L = Lead time (in consistent time units with demand)

For example, with a 95% service level (Z=1.65), demand standard deviation of 10 units, and 7-day lead time:

Safety Stock = 1.65 × 10 × √7 ≈ 1.65 × 10 × 2.65 ≈ 43.7 units

You may also visit our Safety Stock Calculator for a more comprehensive explanation.

Safety Stock Calculator

What Z-value should I use for my desired service level? +

The Z-value (service factor) corresponds to your desired service level probability. Common values include:

Service Level	Z-value
85%	1.04
90%	1.28
95%	1.65
97%	1.88
99%	2.33
99.9%	3.09

Higher service levels require more safety stock, which increases inventory holding costs. Most businesses target 95-99% service levels.

If your desired service level is not in the table above (eg. 96%), you will need to manually lookup the value on a normal distribution table. Mathematically, you can also use a process called interpolation to estimate the z value.

How often should I recalculate my reorder point? +

It's recommended to review and recalculate your reorder points:

Quarterly - For stable products with predictable demand
Monthly - For products with seasonal patterns or moderate variability
More frequently - For new products, promotional items, or during periods of significant supply chain disruption

Additionally, recalculate whenever there are significant changes in:

Supplier lead times
Demand patterns
Service level targets
Cost structure (holding costs, stockout costs)

What are the limitations of reorder point models? +

While reorder point models are widely used, they have some limitations:

Assumes normal distribution - Most formulas assume demand follows a normal distribution, which may not always be accurate.
Static parameters - Traditional ROP models use fixed parameters that may not adapt quickly to changing conditions.
Independent items - Standard models treat inventory items independently, ignoring potential correlations between products.
Cost considerations - Basic ROP formulas don't explicitly consider ordering costs and holding costs.
Lead time assumptions - Models may not adequately handle highly variable or unpredictable lead times.

For more complex inventory situations, consider supplementing ROP with other methods like demand forecasting, inventory optimization software, or time-series approaches.

Key Terms and Definitions

Reorder Point (ROP)

The inventory level at which a new order should be placed to replenish stock before it runs out. It's calculated based on demand during lead time plus safety stock.

Safety Stock

Extra inventory maintained as a buffer against uncertainties in demand and supply. It protects against stockouts caused by unexpected demand spikes or supplier delays.

Lead Time

The time between placing an order and receiving the goods. It includes order processing, manufacturing, shipping, and receiving times.

Demand Variability

The degree to which demand fluctuates over time. It's typically measured using standard deviation or coefficient of variation.

Service Level

The probability of not having a stockout during the replenishment cycle. Common service levels range from 90% to 99.9%.

Stockout

A situation where inventory is unavailable when needed, potentially resulting in lost sales, production delays, or customer dissatisfaction.

Bibliography and Further Reading

Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10(2), 135-136, 152.

Wilson, R. H. (1934). A scientific routine for stock control. Harvard Business Review, 13(1), 116-128.

Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory Management and Production Planning and Scheduling. John Wiley & Sons.

Heizer, J., Render, B., & Munson, C. (2020). Operations Management: Sustainability and Supply Chain Management. Pearson.

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Reorder Point Calculator

Reorder Point (ROP)