Inventory Management for Retail — Periodic Review Policy

Implement inventory management rules based on a periodic review policy to reduce the number of stores replenishments.

Design inventory management rules to simplify logistics, minimise stock levels, and meet store demand.

In a previous article, we built a simulation model based on a continuous-review inventory policy, assuming a normal distribution.

A three-panel graph showing inventory dynamics under a continuous review policy. The top panel (red) displays fluctuating customer demand over time. The middle panel (blue) shows replenishmen — In blue the orders triggered by our inventory management rule - (Image by Samir Saci)

However, such a policy can be inefficient for large portfolios of items with varying replenishment cycle lengths.

In this article, we will improve the solution periodic review policy in Python to limit the number of replenishments.

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SUMMARY
I. Scenario
1. Problem Statement
2. Limits of the continuous review policy
What is the impact a continuous review policy on the number of replenishments when you handle several hundred SKUs?
II. Periodic Review Policy: Order-Up-To-Level (R, S)
1. Introduction of the Inventory Policy
2. Definition of the Safety Stock3. How do you define k?
III. Example of Replenishment Policies
IV. Conclusion

Scenario

Inventory Management for Retail

As an Inventory Manager at a mid-sized retail chain, you are responsible for setting replenishment quantities in the ERP.

Because your warehouse operations manager is complaining about order frequency, you begin to challenge the replenishment rules implemented in the ERP, especially for the fast-runners.

Previously, we implemented several inventory rules based on continuous review policies.

At each time t, we check the inventory on hand (IOH):

A mathematical explanation of a continuous review inventory policy, detailing variables such as Q (quantity per replenishment order), s (minimum reorder point), IOH(t) (inventory on hand at t

Example for 1 SKU

We need 27 replenishment orders per year.

How often do you need to order when managing 2,294 SKUs?

Limits of the continuous review policies

We suppose that we only have 365 days of sales

10 stores (STORE_1, … STORE_10)
1 product family (FOOD_GROCERY)
2,294 unique SKU (STORE ID + PRODUCT FAMILY + ITEM CODE)

Simulation 1
Let’s implement the continuous review policy for 1 SKU

SKU: STORE_1-FOOD_GROCERY_009
Safety stock designed with k = 3
(3 times the standard deviation of the demand distribution)
Order Quantity: Q = 3 x Average_Annual_Sales

A three-panel graph depicting the inventory management of a SKU with higher variability in demand. The top panel (red) shows volatile demand spikes over time. The middle panel (blue) shows re — Continuous review policy **1 SKU**— (Image by Author)

18 replenishments in the first 100 days

Simulation 2
What if we now have 10 SKUs to manage?

A bar chart representing the frequency of replenishment orders for a single SKU over a specific time period. The bars indicate periods when replenishment orders were placed, showing variation — Replenishments with **10 SKUs** — (Image by Author)

54 replenishments in the first 100 days

Simulation 3
What if we have 100 SKUs to manage?

A black bar chart displaying the total replenishment orders for a SKU over time. The bars are distributed along the x-axis, indicating replenishment events across different time intervals. — Replenishments with **100 SKUs** — (Image by Author)

935 replenishments in the first 100 days with less than 10 days without orders

Simulation 4
What if we have 2,294 SKUs to manage?

A red bar chart showing the total replenishment activity for a SKU over time. The height of each bar represents the number of orders placed at different points in time, with taller bars indic — Replenishments with **2,994 SKUs** — (Image by Author)

19,267 replenishments in the first 100 days (less than 10 days without orders)

With this method, the number of replenishments is exploding when you have a large portfolio.

Solution
We will develop a replenishment policy based on periodic reviews.

Periodic Review Policy: Order-Up-To-Level

Introduction of the Inventory Policy

To solve this issue of replenishment frequency, let us introduce a periodic review policy (s, Q)

At each period R, the inventory on hand (IOH) level will be reviewed
Stores will order to reach an inventory level of S

To simplify the comprehension, let’s introduce some notations:

Equations explaining the periodic review inventory policy, known as the Order-Up-To-Level policy. It defines variables like R (inventory review period), S (maximum inventory level target), IO

Definition of the Order-Up-To-Level S

How to calculate the level S:

Equations used to calculate the inventory target level (S) in a periodic review system. It includes variables such as average daily demand (μ_day), lead time (LD), safety stock factor (k), an

The level S is calculated to ensure the inventory covers demand during the review period and the replenishment lead time.

How do you define k?

Your performance metrics will be directly impacted by the safety stock level

You fix a target for either of the two metrics (e.g, I want the Cycle Service Level to be 95%)
You calculate k to reach this target based on the distribution of your demand (Normal, Poisson)
You fix your reorder point

Code

Example of replenishment policies

Example with SKU: STORE_1-FOOD_GROCERY_009

Review Period: R = 10 days
k = 1

A chart demonstrating the periodic review policy for SKU STORE_1-FOOD_GROCERY_009 over a 100-day period. The top panel (red) shows fluctuating demand. The middle panel (blue) indicates replen — Periodic review policy for empirical demand SKU = **STORE_1-FOOD_GROCERY_009** — (Image by Author)

10 replenishments vs. 18 replenishments in the first 100 days with 0 stock-outs

How many replenishments if you handle the full portfolio?

A red bar chart showing the number of replenishments over a 100-day period for SKU STORE_1-FOOD_GROCERY_009 under a periodic review policy. The bars illustrate 10 replenishments spaced at reg — Replenishments with **2,994 SKUs** — (Image by Author)

Comments
13,986 replenishments vs. 19,267 replenishments in the first 100 days with only 10 days of replenishments

13,986 replenishments vs. 19,267 replenishments in the first 100 days with only 10 days of replenishments

You can implement this model for your company.

Find the source code with dummy data in my GitHub repository: Link

Conclusion

💡

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After implementing this policy, you will reduce your operating costs by

Limiting the time windows of replenishments
This will optimise your resources for inventory management, order preparation and transportation management.
Reducing the number of replenishments
This will increase the quantity per replenishment and enable shipment consolidation for stores delivered at the same time.

With the overall objective of optimising the performance of your distribution chain.

How to measure logistic performance?

In this short explainer video, I define the indicators used to measure the performance of a distribution chain, illustrated with a fashion retailer example.

About Me

Let’s connect on LinkedIn and Twitter. I am a Supply Chain Engineer who is using data analytics to improve logistics operations and reduce costs.

If you’re looking for tailored consulting solutions to optimize your supply chain and meet sustainability goals, feel free to contact me.