# Lean Six Sigma with Python — Logistic Regression

Replace Minitab with Python to perform a Logistic Regression to estimate the minimum bonus needed to reach 75% of a productivity target

Replace Minitab with Python to perform a Logistic Regression to estimate the minimum bonus needed to reach 75% of a productivity target

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

Lean Six Sigma is a method that can be defined as a stepwise approach to process improvements.

In a previous article, we used the **Kruskal-Wallis Test** to verify the hypothesis that a specific training positively impacts operators' **Inbound VAS productivity**. (Link)

In this article, we will implement **Logistic Regression** with Python to estimate the impact of a **daily productivity bonus **on your **warehouse operators picking productivity**.

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**SUMMARYI. Problem Statement**

*What should be the minimum amount of daily incentive to get 75% of workers that reach their productivity target?***Analysis with Python sample data from the experiment**

**II. Data Analysis1. Exploratory Data Analysis****What is the probability of reaching the target for each value of the daily incentive?**

**2. Fitted Line Plot of your Logistic Regression****Validate that your results are significant and not due to random fluctuation**

**3. Validation with the p-value**

**III. Conclusion**

I. Problem Statement

1. Scenario

You are the Regional Director of a **Logistic Company (3PL)** and you have **22 warehouses** in your scope.

In each warehouse, the site manager has fixed a picking productivity target for the operators; your objective is to find the right incentive policy to reach 75% of this target.

*P.S: **Picking Productivity** is defined by the number of cartons picked per hour paid.*

### 2. Find the right incentive policy

Currently, productive operators *(operators that reach their daily productivity target)* receive **5 euros per day** in addition to their daily salary of **64 euros** *(after-tax)*.

However, this incentive policy applied in 2 warehouses **is not that effective**; **only 20% of the operators** are reaching this target.

**Question**

What should be the minimum daily bonus needed to reach 75% of the picking productivity target?

**Experiment**

**Randomly**select operators in your 22 warehouses- Implement a
**daily incentive**amount varying between**1 to 20 euros** - Check
**if the operators reached their target**

Edit: You can find a Youtube version of this article with animations in the link below.

## II. Data Analysis

1. Exploratory Data Analysis

You can find the full code in this Github (Follow Me :D) repository:Link.

My portfolio with other projects:Samir Saci

Box plot of the sample distribution

The median value of incentive for reached target’s day is more than 2 times higher than the one for the days below this target.

### 2. Fitted Line Plot of your Logistic Regression

Logistic Regression will provide us with a probability plot. We can estimate the probability of reaching the target for each value of the daily incentive.

Confirmation of the current trend: 5 euros -> 20% of the productivity target reached

We need at leat 15 euros incentive per day to ensure 75% of probability to reach the target

**CodeMinitab**

### 3. Validation with the p-value

In order to check that these results, based on sample data, are significant we need to compute the p-value.p-value: 2.1327739857133364e-141

p-value < 5%

The **p-value is below 5%** so we can conclude that the difference of means is statically significant.

**Conclusion**

If you fix a value of **15 euros per day** of incentives, you will reach 75% of your target.

**CodeMinitab**

## III. Conclusion

What is the ROI?

Based on this experiment we have fixed a minimum amount of **15 euros/day** for the bonus incentives to **reach 75% of your productivity target**.

Before implementing this new incentive policy you need to check that you have a positive return on investment:

- What is the total
**cost to company (CTC)**(Basic Salary + Social Contributions) per hour paid for picking operators?**(Euros/Hour)** - What is the total amount of hours earned after the productivity increase?
**(Hours)** - What would be the
**CTC of hiring temporary workers**for this number of hours?**(Euros)** - What is the total
**CTC of incentives**?

After answering these questions you’ll be able to estimate the return on investment of this new incentive policy. Depending on the hourly cost of the operators you may lose or save money.

### Next Steps

However, the operator's productivity may not be only driven by their motivation but can be also impacted by the warehouse layout, the picking process or the order profile.

Therefore, this analysis should be completed with a process optimization study to ensure that operators can exploit their full potential motivated by the right amount of incentives. *(for more information you can check my previous series about warehouse picking productivity: **link**)*

### 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.