Automated Calibration of Farm-Sale Mixed Linear Programming Models using Bi-Level Programming

We calibrate Linear and Mixed Integer Programs with a bi-level estimator, minimizing under First-order -conditions (FOC) conditions a penalty function considering the calibration fit and deviations from given parameters. To deal with non-convexity, a heuristic generates restart points from current best-fit parameters and their means. Monte-Carlo analysis assesses the approach by drawing parameters for a model optimizing acreages under maximal crop shares, a land balance and annual plus intra-annual labour constraints; a variant comprises integer based investments. Resulting optimal solutions perturbed by white noise provide calibration targets. The approach recovers the true parameters and thus allows for systematic and automated calibration.

Automated summary

The study introduces a method for calibrating Linear and Mixed Integer Programs using a bi-level estimator, which effectively addresses non-convexity issues. Monte-Carlo analysis was conducted to assess the effectiveness of the approach.