Lean Six Sigma with Python — Chi-Squared Test

Perform a Chi-Squared Test to explain a shortage of drivers impacting your transportation network

Solve a Driver Allocation Problem with Chi-Squared Test — (Image by Author)

As a logistics professional, it’s essential to constantly improve your operations.

That’s where Lean Six Sigma with Python comes in. In this article, we will use the Chi-Squared Test to analyze transportation delays caused by a bad allocation of drivers.

Follow our step-by-step guide to optimize your supply chain management.

Introduction

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 specific training positively impacts operators' Inbound Value-Added Services (VAS) productivity.

In this article, we will implement the Chi-Squared Test with Python to understand if transportation delays are due to a bad allocation of drivers.

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SUMMARY
I. Problem Statement
Transportation delays are due to drivers' allocation issues?
II. Data Analysis
1. Exploratory Data Analysis
Analysis with Python sample data from historical records
2. Perform Cross Tabulation
Summarise the relationship between several categorical variables.
3. Pearson’s Chi-Square Test
Validate that your results are significant and not due to random fluctuation
III. Conclusion

If you prefer to watch, have a look at the video version of this article

I. Problem Statement

Addressing Transportation Delays with Chi-Squared Test

You are the Inbound Transportation Manager of a small factory in the United States.

Your transportation network is simple, you have two routes:

• Route 1: coming from your northern regional hub (with difficult road conditions and busy traffic)
• Route 2: coming from your southern regional hub (with no traffic and a beautiful modern road)

Transportation is managed by an external service provider with a fleet of three trucks (with three different drivers: D1, D2, D3).

Replenishment order process from the request of the factory to driver allocation — (Image by Author)

Replenishment Process: Understanding Driver Allocation in Transportation Network

1. The Factory sends a replenishment order to your ERP
2. The Southern regional hub receives the order first
3. If the stock in the southern hub is too low then the order is transferred to the northern hub
4. ERP sends a pick-up request to the transportation service provider (From Selected Hub to Factory)
5. The first driver accepting the request is delivering the raw materials to the factory

P.S: As a customer, we do not have any visibility on the process of driver allocation.

Problem
When an order is allocated to the northern regional hub the lead time to get the request accepted is 35% higher than the southern hub.

Question
Are there drivers avoiding as much as possible to be allocated to the north route?

Experiment
We have analyzed the shipments of the last 18 months to build a sample of 269 records.

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II. Data Analysis

Exploratory Data Analysis: Stacked Bar Charts to Visualize Driver Allocation

Stacked Bart Charts — (Image by Author)

Cross Tabulation: Analyzing Shipments by Hub and Driver

A cross-tabulation of the data can provide some insights and help us to discover a potential pattern in the repartition of driver’s allocation.

Split of shipments by HUB for each driver

Split of shipments (%) per Driver for each HUB

Example
82.65 % of shipments handled by Driver 1 are from SOUTH HUB

Split of shipments (%) per HUB for each Driver

Example
38.89 % of shipments from SOUTH HUB are handled by Driver 1

Minitab
Menu Stats> Tables > Cross Tabulation and Chi-Square 

Pearson’s Chi-Squared Test: Evaluating the Significance of Driver Allocation

The first table is called also called a Contingency table. It is used in statistics to summarise the relationship between several categorical variables.

We’ll calculate the significance factor to determine whether the relation between the variables is of considerable significance using the Chi-Squared Test.

p-value is 0.410

Conclusion
Because the p-value >0.05, there is no significant proof that the driver’s allocation is linked to the Hub.

Code

If you are interested in other applications of Lean Six Sigma Methodology using Python you can have a look at the articles below:

Lean Six Sigma with Python — Logistic Regression

Lean Six Sigma with Python — Kruskal Wallis Test

III. Conclusion

By applying the Chi-Squared Test in Python, we were able to determine that driver allocation was not the root cause of the transportation delays.

This data-driven approach helped us identify areas for further investigation to find the actual cause of the problem.

Therefore, leveraging Lean Six Sigma methodologies with Python can lead to significant improvements in productivity and efficiency.

Stay tuned for more data-driven solutions to optimize your operations and reduce costs.

About Me

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

If you are interested in Data Analytics and Supply Chain, have a look at my website

Samir Saci | Data Science & Productivity

References

• Pearson’s Chi-Squared Test, geeks for geeks, link
• “Optimize Luxury Warehouse Value-Added Services Scheduling with Python”, Towards Data Science, Samir Saci
• “Lean Six Sigma with Python — Kruskal Wallis Test”, Towards Data Science, Samir Saci
• “4 Impacting Projects to Start Your Data Science for Supply Chain Journey”, Towards Data Science, Samir Saci