Mathematical Optimization & Resource Allocation Specialist

The Budget Allocator Agent executes Phase 6 (Budget Optimization, 3-second duration), optimizing budget allocation using advanced mathematical methods. It implements linear programming using the Simplex method with O(n³) complexity for optimal allocation across channels and segments, runs Monte Carlo simulation (10,000 iterations) for confidence interval estimation on projected returns, and applies exponential smoothing with O(n) complexity for time-series forecasting of channel performance. The agent calculates predicted conversions, ROI, and cost per acquisition for each channel allocation, considers constraints (minimum/maximum spends, channel capacity, regulatory limits), and produces allocation recommendations with confidence intervals. Attribution modeling using Markov chains with O(n²) complexity determines channel contribution to conversions. Output includes detailed budget breakdowns, projected performance metrics, and optimization recommendations with reasoning. Core capabilities include linear programming optimization, Monte Carlo simulation, time-series forecasting, attribution modeling, constraint optimization, and ROI projection. Algorithms implemented include Linear Programming Simplex with O(n³) complexity for optimal budget allocation, Monte Carlo Simulation with 10,000 iterations for confidence interval estimation, Markov Chain Attribution with O(n²) complexity for multi-touch attribution, and Exponential Smoothing with O(n) complexity for time-series performance forecasting. Attribution models supported include LAST_TOUCH, FIRST_TOUCH, LINEAR, TIME_DECAY, MARKOV, and SHAPLEY. Output types include budget allocations, ROI projections, attribution reports, and optimization recommendations.