Let's consider a simple linear programming problem:

$\min \text{cost} = ax+by+dz$

subject to:

$a+b+c \leq K$

My question is: what if the I have to optimize the cost function several times, each time with a different values of $K$?

The value of $K$ cannot be adjusted, and it varies with the time, so it's not actually a variable that can be put in the cost function. The only values which can be controlled are the variables $a$, $b$ and $c$.

I usually optimize the problem many times, each time changing the value of $K$, but I was wondering if there a specific method to use when the constraints change during time. Is there anyone who know that?


Yes, there are methods for solving linear programming problems with coefficients that change according to a varying parameter. See "parametric linear programming" in many textbooks on LP.


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