Multiplication Decision Variables
AnsweredHey all,
I have the following decision boolean variables x[t] and w[t], and an auxiliary variable p[t].
p[t] = p[t  1] + w[t] * constant
p[t] <= Max Value
But I have also a condition where if x[t] == 1 then p[t] will reset to 0.
I had the following condition p[t] =(1  x[t]) * (p[t  1] + w[t] * constant) but I was getting a non linear formulation.
Is there a work around this problem?
Thanks!

Hi Carlos,
What if you would introduce a variable to represent the magnitude of the reset \(r_t\) ; then you constraint becomes \(p_t=p_{t1} + w_t * C  r_t\).
You could then add indicator constraints enforcing
 \(r_t=0\) when \(x_t=0\)
 \(p_t=0\) when \(x_t=1\)
Kind regards,
Ronald0 
In fact, you can simplify further and not introduce \(r_t\) at all. Just use two indicator constraints to ensure
 \(p_t=p_{t1}+w_t \cdot C\) when \(x_t=0\)
 \(p_t=0\) when \(x_t=1\)
1 
Thanks Ronald! Worked for me :)
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