Case16.1-Groceryshopping(Group3)(PhucDang)

Case 16.1: Grocery shopping Seattle University FINC 5130: Financial modeling Nathan Narayana Minh Dinh Abhishek Patel Phuc Dang Ajinkya Teli Professor: Anya Chowdhury March 10, 2024

Context In the context of grocery shopping at a local store, understanding customer behavior and spending patterns across various product categories is crucial for managing inventory, pricing strategies, and ultimately maximizing revenue. The store manager is interested in a detailed analysis of customer spending by product categories: fresh baked goods, meat and dairy, produce, and frozen food. Each category has its unique purchasing probability and spending distribution, reflecting the diverse preferences and needs of the store's clientele. Approximately 30% of shoppers are drawn to fresh baked goods, spending between $3 and $19, following a uniform distribution that suggests a wide range of price points and product selections within this category. The meat and dairy section see a higher footfall, with 70% of customers making purchases. The spending here is normally distributed, with an average of $21 and a standard deviation of $5.27, indicating a central tendency for most customers to spend around the mean value, albeit with some variability. The produce section is the most frequented, with 80% of shoppers spending an average of $15, following a normal distribution with a relatively low standard deviation of $2.31, pointing towards consistent spending habits in this category. The frozen food aisles attract 65% of the shoppers, where spending is uniformly distributed between $7.25 and $28.50, highlighting a broad range of products and price sensitivities among customers. Given that the store welcomes around 220 customers daily, the manager aims to utilize a Monte Carlo simulation and risk analysis model. This advanced statistical approach will enable the simulation of thousands of shopping trips to estimate daily revenue and understand its fluctuation over time. By meticulously modeling customer spending behavior across these four key categories, the simulation will provide insights into the daily revenue's potential variability, helping the manager make informed decisions to enhance store operations, tailor product offerings, and optimize pricing strategies for improved profitability and customer satisfaction. Objective The primary objective of this project is to develop and implement a comprehensive Monte Carlo simulation and risk analysis model to deeply understand and predict customer spending behaviors across four major product categories—fresh baked goods, meat and dairy, produce, and frozen food—within a grocery store environment. Given the variability in customer

Spending Distribution Parameters (These parameters determine how much each customer spends in each category): baked_goods_range: The range of spending on baked goods, uniformly distributed between $3 and $19. meat_dairy_params: The average and standard deviation of spending on meat and dairy, normally distributed with a mean of $21 and a standard deviation of $5.27. produce_params: The average and standard deviation of spending on produce, normally distributed with a mean of $15 and a standard deviation of $2.31. frozen_food_range: The range of spending on frozen food, uniformly distributed between $7.25 and $28.50. Simulation Process: The simulation iterates through the number of days specified by num_simulations. For each product category, it calculates the spending of the simulated number of customers who decide to purchase, determined by the respective purchase probability. It adds up the spending from all customers across all categories to get the total revenue for the store for each day. Output: The script prints the total revenue for the first day of the simulation. If the simulation is run for more than one day, it generates and displays a histogram of the total daily revenue distribution, showing how frequently different revenue amounts occurred during the simulation. Analysis Total spending by category import numpy as np import matplotlib.pyplot as plt # Set the seed for reproducibility

np.random.seed( 42 ) # Number of customers per day num_customers = 220 # Probabilities of purchasing from each category prob_baked_goods = 0.3 prob_meat_dairy = 0.7 prob_produce = 0.8 prob_frozen_food = 0.65 # Simulate the number of customers buying from each category customers_baked_goods = np.random.binomial(num_customers, prob_baked_goods) customers_meat_dairy = np.random.binomial(num_customers, prob_meat_dairy) customers_produce = np.random.binomial(num_customers, prob_produce) customers_frozen_food = np.random.binomial(num_customers, prob_frozen_food) # Simulate spending amounts for each category spending_baked_goods = np.random.uniform( 3 , 19 , customers_baked_goods) spending_meat_dairy = np.random.normal( 21 , 5.27 , customers_meat_dairy) spending_produce = np.random.normal( 15 , 2.31 , customers_produce) spending_frozen_food = np.random.uniform( 7.25 , 28.50 , customers_frozen_food) # Calculate total daily revenue total_revenue = np. sum (spending_baked_goods) + np. sum (spending_meat_dairy) + np. sum (spending_produce) + np. sum (spending_frozen_food) # Print the total daily revenue print ( f "Total Daily Revenue: $ {total_revenue :.2f } " ) # Visualize simulation results categories = [ 'Baked Goods' , 'Meat & Dairy' , 'Produce' , 'Frozen Food' ] spendings = [np. sum (spending_baked_goods), np. sum (spending_meat_dairy), np. sum (spending_produce), np. sum (spending_frozen_food)] plt.figure(figsize=( 10 , 6 )) plt.bar(categories, spendings, color=[ 'blue' , 'orange' , 'green' , 'red' ]) plt.title( 'Total Spending by Category' ) plt.xlabel( 'Category' ) plt.ylabel( 'Total Spending ($)' ) plt.show()

modeled with a normal distribution, reflecting a consistent spending pattern with less variance, whereas spending on Baked Goods and Frozen Food followed a uniform distribution, suggesting a wider range of spending behaviors within these categories. The aggregation of these spending patterns across the categories culminated in a substantial daily revenue, demonstrating the critical role of understanding consumer preferences and spending behaviors in maximizing retail profitability. This simulation underscores the complexity of consumer purchasing patterns and their significant implications for revenue generation within the retail sector. Distribution of total spending per customer import numpy as np import matplotlib.pyplot as plt # Set the seed for reproducibility np.random.seed( 42 ) # Define the number of simulations, which is the number of customers per day num_simulations = 220 # Define the probabilities and distributions for each category prob_baked_goods = 0.3 prob_meat_dairy = 0.7 prob_produce = 0.8 prob_frozen_food = 0.65 # Define the spending distributions for each category spending_baked_goods = { 'low' : 3 , 'high' : 19 } spending_meat_dairy = { 'mean' : 21 , 'std' : 5.27 } spending_produce = { 'mean' : 15 , 'std' : 2.31 } spending_frozen_food = { 'low' : 7.25 , 'high' : 28.50 } # Initialize an array to store the total spending for each simulation total_spending = np.zeros(num_simulations) # Perform the Monte Carlo simulation for i in range (num_simulations):

    if np.random.rand() < prob_baked_goods:         total_spending[i] += np.random.uniform(spending_baked_goods[ 'low' ], spending_baked_goods[ 'high' ])     if np.random.rand() < prob_meat_dairy:         total_spending[i] += np.random.normal(spending_meat_dairy[ 'mean' ], spending_meat_dairy[ 'std' ])     if np.random.rand() < prob_produce:         total_spending[i] += np.random.normal(spending_produce[ 'mean' ], spending_produce[ 'std' ])     if np.random.rand() < prob_frozen_food:         total_spending[i] += np.random.uniform(spending_frozen_food[ 'low' ], spending_frozen_food[ 'high' ]) # Calculate the average daily revenue and its standard deviation average_daily_revenue = np.mean(total_spending) std_dev_daily_revenue = np.std(total_spending) # Print the results print ( f "Average Daily Revenue: $ {average_daily_revenue :.2f } " ) print ( f "Standard Deviation of Daily Revenue: $ {std_dev_daily_revenue :.2f } " ) # Plot the distribution of total spending plt.hist(total_spending, bins= 20 , color= 'blue' , edgecolor= 'black' ) plt.title( 'Distribution of Total Spending per Customer' ) plt.xlabel( 'Total Spending ($)' ) plt.ylabel( 'Number of Customers' ) plt.show()

extending towards both higher and lower ends. This suggests that while a majority of customers spend within a relatively predictable range, there exists a subset of customers whose spending patterns significantly deviate from the norm, either due to higher-value purchases or more conservative spending. Such insights are invaluable for retail management and marketing strategies, allowing for more tailored approaches to inventory management, pricing strategies, and promotional activities. Specifically, the data suggests a potential for segmenting customers based on their spending patterns, enabling targeted marketing efforts designed to elevate spending in lower- performing categories or to further capitalize on the categories with higher spending. Understanding the nuances of customer spending behavior through such simulations can significantly enhance revenue optimization strategies, ensuring that retail operations are more closely aligned with consumer demand. Total daily revenue distribution import random import numpy as np import matplotlib.pyplot as plt random.seed( 123 ) # Set the number of customers and the number of simulations (days) num_customers = 220 num_simulations = 2   # For one day # Probabilities of purchasing from each category prob_baked_goods = 0.3 prob_meat_dairy = 0.7 prob_produce = 0.8 prob_frozen_food = 0.65 # Spending distribution parameters for each category baked_goods_range = ( 3 , 19 ) meat_dairy_params = ( 21 , 5.27 )   # Mean and standard deviation produce_params = ( 15 , 2.31 )     # Mean and standard deviation frozen_food_range = ( 7.25 , 28.50 ) # Initialize an array to store the total revenue for each simulation total_revenue = np.zeros(num_simulations) # Run the Monte Carlo simulation

for i in range (num_simulations):     # Simulate customer decisions and spending for each category     baked_goods_spending = np.random.uniform(*baked_goods_range, size= int (num_customers * prob_baked_goods))     meat_dairy_spending = np.random.normal(*meat_dairy_params, size= int (num_customers * prob_meat_dairy))     produce_spending = np.random.normal(*produce_params, size= int (num_customers * prob_produce))     frozen_food_spending = np.random.uniform(*frozen_food_range, size= int (num_customers * prob_frozen_food))     # Calculate total revenue for the day     total_revenue[i] = np. sum (baked_goods_spending) + np. sum (meat_dairy_spending) + np. sum (produce_spending) + np. sum (frozen_food_spending) # Output the results print ( f "Total Revenue for the day: $ {total_revenue[ 0 ] :.2f } " ) # Plot the revenue distribution if more than one day was simulated if num_simulations > 0 :     plt.hist(total_revenue, bins= 30 , edgecolor= 'black' )     plt.title( 'Total Daily Revenue Distribution' )     plt.xlabel( 'Total Revenue ($)' )     plt.ylabel( 'Frequency' )     plt.show

produce, and frozen food. The histogram visualizes the distribution of total daily revenue across the two simulated days, showing a very narrow range due to the low number of simulations. With only two data points, we can't derive a broad distribution, but it's clear that the total revenue hovers around $9,200 to $9,300 for this specific setup. For more robust insights into revenue variability, increasing the number of simulations would be beneficial, providing a wider spread of potential revenue outcomes and allowing for a more detailed analysis of the revenue distribution. Actionable Insights and Recommendations Actionable Insights Optimizing Inventory for Demand: With produce having the highest purchase probability (80%) and frozen food being the second-highest in terms of spending range, stocking up more efficiently on these items can cater to customer demand and drive sales. It is advisable to analyze the sales patterns to avoid overstocking and reduce waste, especially for perishable goods. Targeted Marketing for High-Value Categories: Given that meat and dairy have a high purchase probability (70%) and the highest mean spending, marketing efforts can be focused on these categories to increase customer spending. Special promotions, loyalty programs, or showcasing a variety of meat and dairy products could enhance visibility and sales. Strategic Pricing for Baked Goods: Despite the lower purchase probability (30%), there's potential in the baked goods category to optimize pricing strategies. Implementing a tiered pricing structure that encourages buying in bulk or bundling with high-demand categories like produce could stimulate higher revenue from this category. Customer Experience Improvement: Investing in the shopping experience, particularly around high-traffic areas of produce and frozen food aisles, could lead to increased customer satisfaction and spending. This could include better layout, signage, and information on product origin or nutritional values. Revenue Forecasting for Resource Allocation: Utilizing the simulation to forecast revenue can help in scheduling adequate staffing on expected high-revenue days, ensuring efficient operations and customer service.

Recommendations Prioritize stocking and promotional efforts for produce and frozen foods, leveraging their high purchase probabilities of 80% and 65% respectively. Introduce a range of organic produce and premium frozen items to tap into the spending power evident in the upper range of $28.50 per customer. For the meat and dairy section, with a strong purchase probability of 70% and an average spend of $21, consider implementing 'buy one, get one at half price' offers on select days to boost the average customer spend. Address the 30% purchase probability for baked goods with strategic placement and morning deals, such as a '15% off before 10 AM' promotion, to drive sales during off-peak hours. Enhance the store's layout, focusing on creating an intuitive flow that naturally guides customers through high-demand sections, potentially increasing the per-visit spend. Align staff shifts to coincide with peak shopping times, identified through sales trends, ensuring customer service is optimized when most needed. Emphasize data-driven decision-making by continuously integrating new sales data into the revenue simulation model. A regularly updated model can refine revenue forecasts, leading to better-informed decisions regarding inventory levels, staffing, and marketing campaigns. This data-centric approach should maintain a degree of agility within the business strategy, allowing for rapid adaptation to emerging trends or shifts in consumer behavior. Conclusion In conclusion, the Monte Carlo simulation has provided a valuable quantitative foundation for understanding customer spending behaviors and the resulting revenue implications for each product category within the store. By strategically focusing on the highest probability areas— produce and frozen foods with 80% and 65% purchasing likelihoods—and enhancing marketing for meat and dairy with an average spend of $21, the store can expect to see an increase in customer spend and overall revenue. Implementing targeted promotions for baked goods, which currently have a lower purchase probability of 30%, could also yield a positive uptick in sales. Adjustments to store layout and staffing based on these insights can further optimize operational efficiency and customer experience.