Lean Six Sigma with Python — Logistic Regression | by Samir Saci | Towards Data Science

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.
SUMMARYI. Problem StatementWhat should be the minimum amount of daily incentive to get 75% of workers that reach their productivity target?II. Data Analysis1. Exploratory Data AnalysisAnalysis with Python sample data from experiment 2. Fitted Line Plot of your Logistic RegressionWhat is the probability of reaching the target for each value of daily incentive?3. Validation with the p-valueValidate that your results are significant and not due to random fluctuationIII. Conclusion
You are Reginal 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.
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.
QuestionWhat should be the minimum daily bonus needed to reach 75% of the picking productivity target?
Experiment
Randomly select operators in your 22 warehousesImplement a daily incentive amount varying between 1 to 20 eurosCheck if the operators reached their target
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.
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.
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
Code
MinitabMenu Stat > Binary Fitted Line Plot
In order to check that these results, based on sample data, are significant we need to compute the p-value.
p-value: 2.1327739857133364e-141p-value < 5%
The p-value is below 5% so we can conclude that the difference of means is statically significant.
ConclusionIf you fix a value of 15 euros per day of incentives, you will reach 75% of your target.
Code
MinitabMenu Stat > Binary Fitted Line Plot
If you are interested in other applications of Lean Six Sigma Methodology using Python you can have a look at the articles below:
www.samirsaci.com
www.samirsaci.com
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.
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)
Please feel free to contact me, I am willing to share and exchange on topics related to Data Science and Supply Chain.My Portfolio: https://samirsaci.com
[1] P values for sklearn logistic regression, Rob Speare
[2] Improve Warehouse Productivity using Order Batching with Python, Samir Saci, Link
[3] Lean Six Sigma with Python — Kruskal Wallis Test, Samir Saci, Link