Appendix A: Analytical Methods and Calculations

1. Customer Churn Rate

• Definition: The churn rate measures the percentage of customers who stopped engaging with the business over a specific time period.
• Formula:
  • Churn Rate = ((Customers active last period - Customers active this period) / Customers active last period) * 100
• Components:
  • Customers active last period: Number of customers active in the previous time period.
  • Customers active this period: Number of those customers who remained active in the current period.
• Purpose: To identify the rate at which customers stop engaging with the business, providing insight into retention performance.

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Example: Calculating Churn Rate

Suppose we want to calculate the churn rate from January to February for a business.

1. January (Previous Period):

   • Number of customers active at the start of January: 200

2. February (Current Period):

   • Number of those same customers who remain active at the end of February: 160

Formula

Churn Rate = ((Customers active last period - Customers active this period) / Customers active last period) * 100

Calculation

Churn Rate = ((200 - 160) / 200) * 100 = 20%

Interpretation

This means that 20% of the customers who were active in January stopped engaging with the business by February. This churn rate provides insight into customer attrition and can help the business identify areas to improve customer retention efforts.

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2. Customer Retention Rate

• Definition: Retention rate is the percentage of customers who remain active with the business from one period to the next.
• Formula:
  • Retention Rate = (Customers active this period / Customers active last period) * 100
• Components:
  • Customers active last period: Number of customers at the start of the period.
  • Customers active this period: Number of customers who remain active at the end of the period.
• Purpose: To measure the effectiveness of customer retention strategies over time.

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Example: Calculating Retention Rate

Suppose we want to calculate the retention rate from January to February for a business.

1. January (Previous Period):

   • Number of customers active at the start of January: 200

2. February (Current Period):

   • Number of those same customers who remain active at the end of February: 160

Formula

Retention Rate = (Customers active this period / Customers active last period) * 100

Calculation

Retention Rate = (160 / 200) * 100 = 80%

Interpretation

This means that 80% of the customers who were active in January remained active in February. This retention rate helps the business assess the effectiveness of its retention strategies over time.

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3. Customer Lifetime Value (CLV)

• Definition: CLV estimates the total revenue a business expects from a customer over their entire relationship.
• Formula:
  • CLV = Average Purchase Value * Purchase Frequency * Average Customer Lifespan
• Components:
  • Average Purchase Value: The average amount spent per transaction by the customer.
  • Purchase Frequency: Average number of purchases made by a customer over a specific time period.
  • Average Customer Lifespan: Expected duration of the customer relationship.
• Purpose: To estimate the long-term value of a customer, guiding decisions on customer acquisition and retention investments.

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4. Customer Acquisition Cost (CAC)

• Definition: CAC is the average cost spent by the business to acquire a new customer.
• Formula:
  • CAC = Total Campaign Cost / Number of New Customers Acquired
• Components:
  • Total Campaign Cost: The total cost invested in marketing campaigns (including advertising, promotions, etc.) aimed at acquiring new customers.
  • Number of New Customers Acquired: The total number of new customers acquired through specific marketing efforts during the campaign period.
• Purpose: CAC measures the cost efficiency of acquisition campaigns. It helps businesses assess the effectiveness of their marketing spend and understand whether the cost per new customer is sustainable over time.

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5. Average Purchase Frequency

• Definition: Indicates how often customers make purchases within a specific period.
• Formula:
  • Average Purchase Frequency = Total Purchases / Total Customers
• Components:
  • Total Purchases: Sum of all purchases made by the customers.
  • Total Customers: Total number of customers who made purchases in that period.
• Purpose: To assess the frequency of customer purchases, which is a key component in calculating CLV.

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6. Average Customer Lifespan

• Definition: Average duration over which a customer is active with the business.
• Formula:
  • Average Customer Lifespan = Sum of all customer lifespans / Total number of customers
• Components:
  • Customer Lifespan: Duration (in months or years) that a customer remains active with the business.
  • Total number of customers: Total customers tracked for their active duration.
• Purpose: Provides an average lifespan for customers, used in CLV calculation to project long-term value.

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7. Age-Based Segmentation Calculation

• Definition: Segmenting customers based on age to observe differences in retention and CLV by demographic.
• Formula:
  • There is no specific formula; rather, age ranges (e.g., 18-24, 25-34) are used to group customers.
• Purpose: To assess how retention and CLV vary by age demographic, identifying which age groups have higher engagement and value.

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8. Engagement Level Segmentation

• Definition: Categorizes customers based on engagement level (e.g., high vs. low) to understand the impact of engagement on retention and CLV.
• Formula:
  • Total Engagement = open count + login count + checkout count
  • Segmentation Logic: Customers are segmented into “high engagement” if their total engagement is above the median, and “low engagement” otherwise.
• Purpose: To determine how different engagement levels contribute to overall business metrics like retention and CLV.

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9. Promotional Campaign Retention Analysis

• Definition: Measures retention rate by tracking customers across different campaign types to observe which campaigns are most effective.
• Formula:
  • Retention rate is calculated separately for each campaign type using the retention rate formula, comparing post-campaign periods.
• Purpose: To evaluate campaign effectiveness in retaining customers and driving long-term value.

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10. Monthly Retention and CLV Tracking

• Definition: Tracks retention and CLV metrics on a monthly basis to observe fluctuations and identify seasonal patterns.
• Formula:
  • Retention and CLV are calculated using their respective formulas for each month and visualized over time.
• Purpose: Provides insight into monthly trends, helping identify high and low retention months and CLV peaks associated with campaigns.

Each of these formulas and calculations supports the project’s goal to assess and improve customer retention and lifetime value through data-driven insights.

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11. Inventory Management Using Prophet

Demand Forecasting

• Definition: Predict daily demand using historical sales data to optimize inventory levels.
• Tool Used: Facebook Prophet.
• Key Components:
  • yhat: Predicted daily demand.
  • yhat_upper and yhat_lower: Forecast uncertainty bounds.
• Purpose: Ensure sufficient inventory while minimizing overstocking.
• Formula:
  • Safety Stock = (yhat_upper - yhat) * Lead Time.
  • Optimal Inventory Level = yhat + Safety Stock.
• Example Calculation:
  • For a predicted demand (yhat) of 100 units with an upper bound of 120 units and a lead time of 5 days:
    • Safety Stock = (120 - 100) * 5 = 100 units.
    • Optimal Inventory Level = 100 + 100 = 200 units.
• Interpretation:
  • Safety stock ensures coverage for variability in demand.
  • Optimal inventory level balances holding costs and service level requirements.

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12. Price Elasticity of Demand (PED) and Dynamic Pricing

Price Elasticity of Demand (PED)

• Definition: Measures how demand responds to changes in price.
• Formula:
  • PED = (% Change in Quantity Demanded) / (% Change in Price).
• Example Calculation:
  • If a price increase from $20 to $22 causes a decrease in demand from 100 units to 90 units:
    • % Change in Price = ((22 - 20) / 20) * 100 = 10%.
    • % Change in Demand = ((90 - 100) / 100) * 100 = -10%.
    • PED = -10% / 10% = -1.0.
• Interpretation:
  • PED < -1: Demand is price elastic.
  • PED > -1: Demand is price inelastic.
  • A PED of -1.0 indicates unitary elasticity.

Dynamic Pricing Optimization

• Definition: Adjust prices dynamically to maximize revenue based on PED and forecasted demand.
• Formula:
  • Optimal Price = Current Price * (1 + PED / 100).
• Example Calculation:
  • For a product with a current price of $20 and a PED of -1.5:
    • Optimal Price = $20 * (1 + (-1.5 / 100)) = $19.70.
• Interpretation:
  • The adjusted price balances revenue and demand elasticity, aiming for maximum profitability.
• Integration with Prophet:
  • Use forecasted demand (yhat) and PED predictions to dynamically adjust prices for each day.
• Performance Metrics:
  • Compare actual revenue from current pricing to optimal revenue calculated using dynamic pricing.

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Summary

Each of these analytical methods is designed to optimize specific business functions:

1. Inventory Management: Balances holding costs and stockouts with accurate demand forecasting and safety stock calculations.
2. Dynamic Pricing: Maximizes revenue by adjusting prices based on demand elasticity (PED) and forecasted sales. These methods collectively enable data-driven decision-making for better inventory control, pricing strategies, and service-level management.

Appendix B: Technical Glossary

Term	Definition
Abandoned Cart Reminder	A notification or email sent to a customer who added items to their shopping cart but did not complete the purchase, encouraging them to return and complete the transaction.
Anniversary Offer	A personalized promotion provided to customers on key dates, like the anniversary of their first purchase or registration, to foster a stronger relationship.
At-Risk Customers	Customers identified as having a high likelihood of churning based on predictive analytics or behavioral indicators.
Binary Engagement Levels	Basic classification of customer engagement into two groups (e.g., high and low) without accounting for moderate levels or varying engagement behavior.
Churn Rate	The percentage of customers who have stopped engaging with the business during a given time period. Calculated as (Lost Customers / Active Customers in the Previous Month) x 100.
Cohort Analysis	A type of analysis that groups customers based on shared characteristics, such as the month of their first purchase, to observe behavior over time.
Customer Churn	The rate at which customers stop doing business with a company over a specified period. Churn rate is often used to measure the effectiveness of retention efforts.
Customer Lifetime Value (CLV)	The total value a customer is expected to bring to a business over the entire duration of their relationship, factoring in repeat purchases and engagement.
Customer Retention	The ability of a business to keep its customers over a specified period. High customer retention is often a sign of customer satisfaction and loyalty.
Customer Segmentation Model	A framework that classifies customers into groups based on behaviors or demographics, used to target marketing strategies and personalize engagement efforts.
Data-Driven Personalization	A method of customizing customer interactions based on data insights such as purchase history and preferences, aiming to make engagement more relevant and timely.
Double Points Day	A loyalty program feature offering customers double the usual reward points for purchases on specific days, incentivizing repeat engagement.
Dynamic Segmentation	An approach to customer segmentation that updates in real time or periodically based on recent data, allowing for a more flexible, responsive marketing strategy.
Engagement Level	A measure of how actively a customer interacts with a business, which can be categorized into levels such as low or high based on frequency and recency of interactions.
Flash Sale	A type of promotional campaign that offers significant discounts for a short period, aimed at boosting immediate sales and customer engagement.
High CLV During Campaign Peaks	The elevated Customer Lifetime Value (CLV) observed during promotional or seasonal sales events, highlighting periods where customer spending increases sharply.
High Engagement	Customers who interact frequently with the business, indicated by regular purchases and interaction with promotional content.
Loyalty Incentives	Rewards or benefits offered to customers to encourage ongoing engagement, such as discounts, free products, or bonus points.
Machine Learning Model	A computational model that learns from historical data patterns to make predictions or automate decisions, such as predicting customer churn.
Members-Only Specials	Exclusive benefits, products, or sales events available only to loyalty program members or subscribers, encouraging engagement through a sense of exclusivity.
Monthly Retention Rates	The percentage of customers who continue to engage with the business month by month, used to assess the effectiveness of retention strategies over time.
Multivariate Analysis	An analytical approach that examines the influence of multiple variables at once to understand complex interactions and identify patterns across segments.
Personalized Touchpoints	Specific, customized interactions with customers, such as follow-up emails, exclusive offers, or product recommendations, aimed at improving engagement and satisfaction.
Predictive Analytics	Using historical data and statistical techniques to predict future behavior, such as identifying customers likely to churn.
Promotional Campaign	A marketing strategy involving time-limited offers or discounts designed to increase customer engagement and purchases during specific periods.
Real-Time Monitoring	Continuously tracking metrics (e.g., CLV, retention rates) as new data comes in, allowing for timely adjustments to strategies based on recent customer activity.
Recommendation Algorithm	A tool used to suggest products to customers based on their previous purchases, browsing behavior, and similar customer profiles, increasing the relevance of engagement.
Retention Strategy	A set of methods and actions used by a business to keep customers actively engaged and reduce churn over time.
Seasonal Analysis	Reviewing customer behavior in relation to specific seasons or holidays, to identify engagement trends and optimize campaign timing for maximum impact.
Short-Term Retention Success	The initial retention of customers following a recent purchase or campaign event, often indicating immediate engagement effectiveness without a long-term guarantee.
Subscription or Membership Program	A loyalty-based offering where customers pay a recurring fee in exchange for exclusive benefits, encouraging ongoing commitment.
Targeted Retention Strategies	Retention tactics customized to specific customer segments, such as age or engagement level, to address unique needs and enhance engagement.
Tiered Loyalty Program	A structured customer loyalty program that offers increasing benefits as customers reach higher levels or “tiers” based on their spending or engagement.
VIP Support	Enhanced customer service provided to top-tier or high-value customers, often including faster response times, priority handling, and exclusive support options.
Safety Stock	Inventory buffer calculated to cover unexpected demand surges or delays in restocking, ensuring consistent product availability.
Prophet Model	A forecasting tool used to predict future trends in time series data with components for seasonality, trend, and holiday effects.
Root Mean Squared Error (RMSE)	A measure of the differences between predicted and actual values, expressed in the same units as the data being measured.
Forecast Interval	The range (yhat_lower to yhat_upper) provided by Prophet indicating the confidence bounds for the predicted values.
Optimal Inventory Level	The ideal amount of inventory calculated as the sum of forecasted demand and safety stock.
Demand Forecasting	The process of predicting future customer demand for products based on historical sales data and seasonal trends.
Dynamic Pricing	A strategy where product prices are adjusted in real-time based on factors such as demand, elasticity, and forecasted sales.
Price Elasticity of Demand (PED)	A measure of how sensitive customer demand is to changes in price, used to optimize pricing strategies.
Prophet Safety Stock	Safety stock calculated using Prophet’s forecast uncertainty bounds (yhat_upper - yhat) multiplied by lead time.
Cumulative Revenue	The total revenue accumulated over a specific period, calculated as the sum of daily sales multiplied by the selling price.
Current Discount Percentage	The average discount applied to products, based on historical pricing and promotional strategies.
Optimal Discount Rate	The discount rate determined to maximize revenue, calculated using PED predictions and dynamic pricing models.
Forecasted Revenue	The expected revenue calculated by applying the predicted optimal price to the forecasted demand.
Actual Revenue	The realized revenue calculated from historical daily sales and average checkout prices.
Dynamic Inventory Strategy	Inventory management approach that adjusts reorder points and stock levels based on real-time demand forecasts.
Prophet Forecast Components	The elements used in Prophet forecasting, including trend, seasonality, and holiday effects, to predict future demand.
Regressor in Prophet	Additional variables (e.g., holidays, promotions) used to improve forecast accuracy by modeling their effect on demand.
Lead Time	The time between placing a restock order and receiving inventory, critical for calculating safety stock.
Adjusted Price	A price determined using PED to balance demand and revenue, aiming to maximize profitability.
Feature Engineering	The process of creating new input variables for machine learning models, such as day_of_week and month, to enhance model accuracy.
Bayesian Model	A probabilistic approach to modeling and forecasting, often used as an alternative to machine learning for dynamic pricing.
Random Forest Regressor	A machine learning algorithm used to predict PED and optimize dynamic pricing strategies.
Inventory Holding Cost	The cost of storing unsold inventory, typically calculated as a percentage of the product’s value over time.
Forecast Uncertainty Bounds	Confidence intervals around predicted values in Prophet, indicating potential variability in future demand.
Prophet's Yhat	The predicted value of demand for a given date, as calculated by the Prophet model.
Campaign Effects on Demand	Changes in product demand due to promotional campaigns or discounts, modeled using regressors in Prophet forecasts.
PED-Based Pricing Strategy	A pricing model that adjusts prices dynamically based on predicted PED to optimize sales and revenue.
Reorder Lock	A mechanism to prevent placing multiple restock orders before previously ordered stock has arrived.
Forecast Accuracy	The closeness of predicted demand values to actual values, typically measured using RMSE or coverage metrics.
Simulation for PED Training	Using historical data to train machine learning models to predict PED for future dynamic pricing decisions.
Dynamic Reorder Point	The stock level at which a reorder is triggered, adjusted dynamically based on forecasted demand and safety stock.