Python Allocation Optimization

I'm embarking on a new project and would like some help. I am attempting to optimize facings on a shelf from a range of products to generate the highest return of Gross Profit $'s. This project needs to take things into consideration such as Diminishing Returns. I will be able to provide 3 years worth of data for this project.

These are aspects of the project I'm considering.

#1 Data Preprocessing: Start by cleaning and preprocessing your data. Handle missing values, outliers, and normalize or standardize variables as needed.

#2 Exploratory Data Analysis (EDA): Perform EDA on the preprocessed data to gain insights and understand the relationships between variables. Visualize the data and conduct correlation analysis to identify patterns and trends.

#3 Regression Analysis: Use regression analysis to identify the coefficients for each product and understand the relationship between facings and Gross Profit. This step will provide you with a foundation for further optimization.

#4 Consider Diminishing Returns: Analyze the historical data to identify the point of diminishing returns for each product. Determine the inflection point where additional facings provide less value in terms of Gross Profit.

#5 Optimal Facing Determination: Use the coefficients obtained from the regression analysis to calculate the optimal facing for each product. Consider the Gross Profit generated by each product at different facing levels and identify the facing level that maximizes the Gross Profit for each product individually.

#6 Marginal Increase/Decrease: Calculate the marginal increase or decrease in Gross Profit for each additional facing, based on the inflection point determined in the previous step. Understand the incremental impact of facings on Gross Profit.

#7 Allocation of Facings: Utilize the insights gained from the previous steps to allocate the optimal number of facings for each product. Distribute the facings among the products in a way that maximizes the overall Gross Profit while considering the optimal facing determined for each product.

#8 Model Evaluation and Validation: Split your data into training and testing sets. Evaluate the performance of your regression models on unseen data using appropriate metrics like mean squared error (MSE), R-squared, or adjusted R-squared. This step ensures that your models have good predictive power.

#9 Implementation in Python: Once you have a clear understanding of the approach and steps involved, implement the optimization process in Python. Utilize libraries such as scikit-learn, pandas, and scipy to automate the analysis and decision-making processes.

I've worked out some of the code, but I'm running into an issue that I can't seem to figure out. I am by no means a skilled programmer, novice at best, and this project has taken me nearly 9-months to learn and try to figure out.

I'm sure I am doing a lot wrong here, but the main issue I'm having is when I attempt to Run data2.csv with 90 facings, it will generate 0 allocation facings for each product. The same happens for any number higher than 90 and even 89, 88, 87...all the way to 84. At 83 it will optimize.

Likewise, similar issues if I utilize data.csv instead of data2.csv and set it to anything above 20 facings.

I'm looking for this to be remedied and any processes to be corrected.