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Calibration with Positive Mathematical Programming (PMP)

Calibration with Positive Mathematical Programming (PMP). Uwe A. Schneider. Strategy.

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Calibration with Positive Mathematical Programming (PMP)

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  1. Calibration with Positive Mathematical Programming (PMP) Uwe A. Schneider

  2. Strategy • Modify the objective function such that the first order conditions look exactly as the first order conditions of the unmodified problem with an additional constraint that forces the solution to be equal to the observations/expectations.

  3. Original linear model

  4. First Order Conditions (FOC) of original linear problem

  5. Force solution to replicate observed values

  6. FOC when Solution is forced to observed values

  7. Objective function adjustment The following two conditions must hold:

  8. Quadratic Term (often used in PMP)

  9. A more general term

  10. Conclusions • There are infinite alternatives to modify the objective function, which all perfectly calibrate the model • Different alternatives do not affect the basic solution but will impact scenario solutions • If PMP is used, make sure you can justify the value of the parameter alpha • If alpha is not determined, try to use a relatively small value which corresponds to a flat slope • Try to avoid calibrating non-observed activities because there is no justification for this

  11. Alternatives • Linear calibration (+ post solution processing) • Duality restrictions

  12. Illustration • Gams Program (pmp.gms)

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