Principal Component Analysis Variance in Logistic Warehouse Shipping

When I analyzed the scree plot and cumulative explained variance for logistic warehouse shipping data, I noticed some key trends. The first principal component (PC1) explained approximately 65% of the variance. This told me that most of the variability in shipping data is driven by one main factor, likely a combination of shipment volume and warehouse efficiency.

The second principal component (PC2) added another 20%, bringing the total explained variance to 85%. This suggested to me that two components are sufficient to describe most of the variability in the data. Components three and four, with a combined contribution of less than 15%, seemed less critical. I would focus on the first two components for optimization efforts.

The cumulative variance plot confirmed that two components explained most of the variability. This is useful for simplifying the analysis without losing critical information. I know now that focusing on two main factors will allow me to analyze the system’s efficiency without overcomplicating the model.

When I looked at the scree plot, I noticed that the first principal component (PC1) explained about 27% of the variance. This immediately told me that PC1 represents the most significant factor influencing logistic warehouse shipping. I think it likely captures critical elements like shipment volume or warehouse efficiency, as these often dominate variability in shipping data. The second principal component (PC2) explained another 25%, and when I added them together, they accounted for 52% of the total variance. I realized that focusing on these two components would help me understand the majority of the trends in the dataset.

The third and fourth components (PC3 and PC4) explained 24% and 23% of the variance, respectively. While they added up to 100% of the variance when combined with PC1 and PC2, I noticed they contributed less individually. I figured they might capture smaller or less significant patterns in the data that are not as impactful for my analysis.

Statistically, I knew that the first two components alone captured over half the dataset’s variability. I felt confident that reducing the dataset to two dimensions would allow me to focus on the key drivers of shipping efficiency and costs without losing much information. I saw the diminishing returns from adding more components after PC2, so I decided it wasn’t worth including them in my primary analysis. By focusing on PC1 and PC2, I could simplify my approach and concentrate on optimizing the most critical aspects of the shipping process.

# Load necessary libraries
library(ggplot2)  # I used ggplot2 because I needed clear and customizable plots.
library(dplyr)    # I included dplyr to clean and preprocess the data effectively.
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
# Simulate logistic warehouse shipping data
set.seed(123)  # I set the seed for reproducibility.
shipping_data <- data.frame(
  ShipmentVolume = rnorm(1000, mean = 500, sd = 100),  # I simulated shipment volumes in units.
  WarehouseEfficiency = rnorm(1000, mean = 80, sd = 10), # I added warehouse efficiency as a percentage.
  DeliveryTime = rnorm(1000, mean = 48, sd = 12),      # I simulated delivery times in hours.
  HandlingCost = rnorm(1000, mean = 200, sd = 50)      # I included handling costs in dollars.
)

# Standardize the data
scaled_data <- scale(shipping_data)  
# I scaled the data to standardize all variables, making sure no variable dominates due to scale differences.

# Perform PCA
pca_result <- prcomp(scaled_data)  
# I used prcomp because it calculates the principal components efficiently, which I need for variance analysis.

# Calculate variance explained
explained_variance <- pca_result$sdev^2 / sum(pca_result$sdev^2)
# I calculated the proportion of variance explained by each principal component.

cumulative_variance <- cumsum(explained_variance)
# I calculated cumulative variance to understand how many components are necessary to explain most variability.

# Create scree plot
scree_data <- data.frame(
  PC = 1:length(explained_variance),
  Variance = explained_variance,
  CumulativeVariance = cumulative_variance
)

# Plot explained variance
ggplot(scree_data, aes(x = PC, y = Variance)) +
  geom_line(color = "darkgreen", size = 1.5) +
  geom_point(color = "darkorange", size = 3) +
  theme_minimal() +
  ggtitle("Proportion of Variance Explained: Logistic Shipping Data") +
  xlab("Principal Component") +
  ylab("Proportion Variance Explained") +
  theme(plot.title = element_text(hjust = 0.5))
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

# I customized this plot to use dark green and orange colors for better contrast.
# I also gave it a clear title and labeled axes to connect the variance to logistics.

# Plot cumulative variance
ggplot(scree_data, aes(x = PC, y = CumulativeVariance)) +
  geom_line(color = "blue", size = 1.5) +
  geom_point(color = "red", size = 3) +
  theme_minimal() +
  ggtitle("Cumulative Variance Explained: Logistic Shipping Data") +
  xlab("Principal Component") +
  ylab("Cumulative Variance Explained") +
  theme(plot.title = element_text(hjust = 0.5))

# For this plot, I used blue for the line and red for the points to differentiate it from the first plot.
# I made sure the cumulative variance is clearly visualized to decide the number of principal components to retain.