Lesson 22 : Safety First

Once you have watched the instructions, read the following explanations carefully and model the example before you watch the correction-lesson.

1) Vidéo 1
                                                  video(2 min)
2) Example (following the example in lesson 20)
  • open GAMS
  • run the model primal0_risk_base.gms
  • write the model ON YOUR OWN : Add the risk factor using the Safety First method (add the income safety constraint)
    Take your time !

In the face of risk, the Safety-First method consists in wanting to avoid seeing the income fall below a minimum threshold, a sort of safety income. In the Pr{Z̃≤Z0} ≤ α  inequation, α = 0, which means that the income must always be higher than our minimum threshold.

State of nature Probability Gross margin of wheat Gross margin of maize
E1 0.2 460 2000
E2 0.2 440 500
E3 0.2 450 300
E4 0.2 430 1400
E5 0.2 470 800
AVERAGE 450 1000

Assuming that the farmer wishes to earn at least 18000 euros a year in order to meet his expenses, regardless of the year, the model is therefore written as follows :

Max Z = 450×1+1000×2
avec  x1+x2 ≤ 50
25×1+50×2 ≤ 2000
460×1+2000×2 ≥ 18000
440×1+500×2 ≥ 18000
450×1+300×2 ≥ 18000
430×1+1400×2 ≥ 18000
470×1+800×2 ≥ 18000  x1,x2 ≥ 0

It is your turn to write it in GAMS !
3) Correction-lesson
video(4 min)

Modèle Safety First