The problem in brief is as follows.
If (T_1 < T_2) Y = 1 ---------------(1)
else Y = 0 ---------------(2)
Then,
Prob(\sigma Y < C) > \alpha -------(3)
In the above problem, T_1, T_2 and C are random variables (lets assume with some normal distributions).
The 1st and 2nd conditions can be linearized using mixed logic constraints. Also, the equation 3 can be solved using chance constrained programming.
The only problem is how to transform/generate the probability distribution of Y (Y is a binary variable) from distributions of T_1 and T_2.
Any help would be highly appreciated.
Hi
I think the answer provided by Dr. Domsta will help you. But I would like to ask you, do you really need to know the distribution of Y to solve the model? If no, I think you can go with pre-processing step. Or Just estimate the value of Y based on the generated random values of T1 and T2 at each scenario. So for each scenario, you generate the values T1 and T2, and based on those two values you can get the corresponding value of Y.
Hope this could help.
I share Zakaria's guess. This would simultaneously explain my doubts. Indeed such a programm is made FOR estimating the probability of Y=1, rather than to implement the probability a'priori.
Thank you very much Joachim Domsta and Zakaria Yahia for your answers.
- Badges
- Science topic
- Similar topics
- Engineering
- Modeling