mmo-modeling-optimizer.py

# initialize model
opt_model = grb.Model(name="Media Budget Optimization")

x_vars = opt_model.addVars(media_roi['media'], vtype=grb.GRB.CONTINUOUS,
              lb=0, name="media")

# keep total spend less than new available budget
opt_model.addConstr(sum(x_vars[i] for i in media_roi['media']) <=
             new_budget, name="New Budget")

# keep new media spend within +-25%
for i in media_roi['media']:
    # minimum
    opt_model.addConstr(
        x_vars[i] >= 0.75 * media_roi.query("media == @i")['spend'].iloc[0], 
        name=f"{i}_min_spend"
    )
    
    # maximum
    opt_model.addConstr(
        x_vars[i] <= 1.25 * media_roi.query("media == @i")['spend'].iloc[0], 
        name=f"{i}_max_spend"
    )
    
# objective function to maximize return on spend
opt_model.setObjective(sum(x_vars[i] * media_roi.query("media == @i")['ROI'].iloc[0]
            for i in media_roi['media']))

# run
opt_model.ModelSense = grb.GRB.MAXIMIZE
opt_model.optimize()