# Inventory Management for Retail — Stochastic Demand

Simulate the impact of safety stock level on inventory management performance metrics assuming a normal distribution of your demand

Simulate the impact of safety stock level on inventory management performance metrics assuming a normal distribution of your demand

*Article originally published on **Medium**.*

For most retailers, inventory management systems take a fixed, rule-based approach to forecast and replenishment orders management.

Considering the distribution of the demand, the objective is to build a replenishment policy that will minimize your ordering, holding and shortage costs.

In a previous article, we have built a simulation model **assuming a deterministic constant demand** *(Units/Day)*.

In this article, we will improve this model and introduce **a simple methodology using a discrete simulation** **model** built with Python to test **several inventory management rules** assuming a normal distribution of the customer demand.

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**1. Problem StatementAs an Inventory Manager of a mid-size retail chain, you are in charge of setting the replenishment quantity in the ERP.2. Limits of the deterministic modelWhat could be the results with a normally distributed demand?**

**SUMMARYI. Scenario****1. Introduction of the Inventory Policy2. Definition of the Safety Stock3. How do you define k?**

**II. Continuous Review Policy: Order Point, Order Quantity (s, Q)****1. Target of CSL = 95%2. Target of IFR = 99%**

**III. Example of replenishment policies**

**III. Conclusion & Next Steps**## I. Scenario

1. Problem Statement

As an Inventory Manager of a mid-size retail chain, you are in charge of setting the replenishment quantity in the ERP.

Based on the feedback of the store manager, you start to doubt that the replenishment rules of the ERP are the most optimal especially for the fast runners because your stores are facing lost sales due to stock-outs.

For each SKU, you would like to build a simple simulation model to test several inventory rules and estimate the impact on:

**Performance Metrics**

**Cycle Service Level (CSL)**: probability to have a stock-out for each cycle**(%)****Item Fill Rate (IFR)**: percentage of customer demand met without stock-out (%)

In this article, we will build this model for,

**# Number of days of sales per year (days)**

**D = 2000****# Customer demand per day (unit/day)**

**T_total = 365****# Purchase cost of the product (Euros/unit)**

**D_day = D/T_total****# Cost of placing an order (/order)**

**c = 50****# Holding Cost (% unit cost per year)**

**c_t = 500****c_e = h * c# Selling Price (Euros/unit)**

**h = .25****# Lead Time between ordering and receiving**

**p = 75****# Cost of shortage (Euros/unit)**

**LD****Q = 82 (units/order)**

**c_s = 12# Order Quantity**To simplify the comprehension, let’s introduce some notations

### 2. Limits of the deterministic model

In the previous article, we assumed a constant deterministic demand; we’ll now introduce randomness to get closer to real demand.

What could be the results with a normally distributed demand?

**µ_D = 2000 (items/year)σ_D = 50(items/year)**

You need to improve your replenishment policy to compensate for the volatility of your demand.

*You can find the full code in my Github repository:*

*Link*## II. Continuous Review Policy: Order Point, Order Quantity (s, Q)

1. Introduction of the Inventory Policy

To solve this issue of demand volatility, we’ll introduce a continuous review policy (s, Q)

- Continuous Review = your inventory level will be checked every day
- (s, Q) = if your inventory level ≤
**s**your ERP will order**Q**

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

### 2. Definition of the Safety Stock

The reorder point can be defined as the minimum inventory level you need to meet your customers’ demand during the lead time between your ordering and receiving.

The safety stock** **is a buffer to compensate for the volatility of the demand.

### 3. How do you define k?

Your performance metrics will be directly impacted by the safety stock level; the highest k is the best your performance will be:

- You fix your target for any of the two metrics (e.g: I want my CSL to be 95%)
- You calculate k to reach this target
- You fix your reorder point

## III. Example of replenishment policies

1. Target of CSL = 95%

Based on the definition of the CSL, we have:

k = 1.64

Reoder point with CSL: 36 units

*Comments*

In this example, we can see that we do not face any stock and the minimum stock level is very close to zero.

**Code**

### 2. Target of IFR = 99%

In this previous example, our target was to have 95% of the replenishment cycles without stock-out.

In this example, we’ll focus more on our capacity to deliver products in full with a target of IFR.

This formula is using the Unit Normal Loss Function (you can find more information about this function here: **Link**).

# G(k) = Q/sigma_ld * (1 - IFR)

IFR = 0.99

G_k = (Q/sigma_ld) * (1 - IFR) = 0.14# Final value of k

k = 0.71

Reoder point with CSL: **31 units**

*Comments*

To reach 99% of demand units fulfilled without stock-out you need a lower safety stock. (31 units vs. 32 units)

**Code**

## IV. Conclusion and next steps

Conclusion

This improved model is bringing better results as it considers the variability of the demand in the safety stock sizing.

The process is simple, you start by fixing your performance metrics targets (IRF, CSL) and then you calculate your safety stock level using the k value.

### Next Steps

The main issue with the continuous review policy is the high number of replenishment if you have many SKUs in your portfolio.

As a store manager (or Warehouse Manager), you would prefer to fix the replenishment time (e.g: 2 times per week). Therefore, we will introduce the periodic review policy in the next article.

### About Me

Let’s connect on Linkedin and Twitter, I am a Supply Chain Engineer that 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.