# Tag Info

### Can the (famous) "Problem of Apollonius" be Considered as a "Constraint Optimization" Problem?

You have the inputs and outputs confused. The three black circles are given, and the purple circle is a desired output. But, yes, any system of equations can be thought of as an optimization problem ...
• 21.7k
Accepted

• 21.7k
Accepted

### Modeling an either-or-constraint

You can introduce an additional binary variable $y$ that takes value $1$ if and only if at least one node from $I$ is matched with another one from $J$: \begin{align*} x_{ij} &\le y \quad \forall ...
• 10.1k
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### How to specify an objective function that prohibits trading in both directions linearly

Yes, you can drop the big-M constraints and the binary variables, if there are no other constraints involving $\sf varWaterIn$ and $\sf varWaterOut$. Note that if you take any optimal solution and ...
• 28.8k
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### Lot-sizing problem variant

You could try and get rid of variables $Y_{p,t,j,c}$: remove constraints $(6)-(7)$; constraints $(6)$ simply link $x$ and $Y$ variables, so removing them should not have any impact on the feasibility ...
• 10.1k
I assume for you have a binary matrix $S_{i,t}$ (tasks)$\times$(time steps) which tells you whether some task $i$ is active at time $t$. This approach introduces additional variables unless you have ...