Multiplication Decision Variables

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Carlos Davalos

2024年02月21日 14:03

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Hey 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!

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  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:29

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  Ronald van der Velden

  • Gurobi Staff

  2024年02月21日 14:48 編集済み

  Hi Carlos,

  What if you would introduce a variable to represent the magnitude of the reset \(r_t\) ; then you constraint becomes \(p_t=p_{t-1} + w_t * C - r_t\).

  You could then add indicator constraints enforcing

  • \(r_t=0\) when \(x_t=0\)
  • \(p_t=0\) when \(x_t=1\)

  Kind regards,
  Ronald

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  Ronald van der Velden

  • Gurobi Staff

  2024年02月21日 15:29

  In fact, you can simplify further and not introduce \(r_t\) at all. Just use two indicator constraints to ensure

  • \(p_t=p_{t-1}+w_t \cdot C\) when \(x_t=0\)
  • \(p_t=0\) when \(x_t=1\)

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  Carlos Davalos

  2024年02月22日 13:41

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  Thanks Ronald! Worked for me :)

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