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

2021 ◽  
Vol 70 (3) ◽  
pp. 165-181
Author(s):  
Wolfgang Britz
Keyword(s):  
Monte Carlo Analysis ◽  
Order Conditions ◽  
Programming Models ◽  
Mixed Integer ◽  
Optimal Solutions ◽  
Integer Programs ◽  
First Order ◽  
Mixed Integer Programs ◽  
Automated Calibration ◽  
Best Fit

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.

Distances between optimal solutions of mixed-integer programs

2018 ◽  
Vol 179 (1-2) ◽  
pp. 455-468 ◽  
Author(s):  
Joseph Paat ◽  
Robert Weismantel ◽  
Stefan Weltge
Keyword(s):  
Mixed Integer ◽  
Optimal Solutions ◽  
Integer Programs ◽  
Mixed Integer Programs

Support Set Invariancy for Interval Bimatrix Games

2019 ◽  
Vol 27 (02) ◽  
pp. 225-237
Author(s):  
Milan Hladík
Keyword(s):  
Mixed Integer ◽  
Necessary Condition ◽  
Linear Programs ◽  
Bimatrix Games ◽  
Bimatrix Game ◽  
Integer Programs ◽  
Mixed Integer Programs ◽  
Support Set ◽  
First Case ◽  
Pure Strategies

Traditionally, game theory problems were considered for exact data, and the decisions were based on known payoffs. However, this assumption is rarely true in practice. Uncertainty in measurements and imprecise information must be taken into account. The interval-based approach for handling such uncertainties assumes that one has lower and upper bounds on payoffs. In this paper, interval bimatrix games are studied. Especially, we focus on three kinds of support set invariancy. Support of a mixed strategy consists of that pure strategies having positive probabilities. Given an interval-valued bimatrix game and supports for both players, the question states as follows: Does every bimatrix game instance have an equilibrium with the prescribed support? The other two kinds of invariancies are slight modifications: Has every bimatrix game instance an equilibrium being a subset/superset of the prescribed support? It is computationally difficult to answer these questions: the first case costs solving a large number of linear programs or mixed integer programs. For the remaining two cases a sufficient condition and a necessary condition are proposed, respectively.

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