I am working on a marketing optimization problem, where the goal is maximize profit by optimally allocating spend to different products. Constraint is getting at least 1 Million revenue.
As a first step, I built a model to predict the revenue using XGboost (which I can use to calculate profit given spend). Now, how can I use this xgboost model as the objective function to optimize overall profit ( allocating spend across different products) given the constraint on revenue. What are some methods for this optimization ?
The Xgboost model uses about 6-7 variables like spend, target population, product, month etc.I came across linear programming for optimization but noticed LP uses linear objective function. I am newbie to optimization. I am not sure if I can/how to use xgboost model as objective function in Nonlinear optimization.
My XGBoost predicts revenue from log(spend), log(population), target encoded product variable, and average of revenue obtained 2 - 4 weeks ago revenue for the product (2 to 4 weeks because of business implementation constraints while predicting with the model). Now, what I am aim is to optimize the spend for a given product (hae about 60 products) that gives maximum profit.