# Tag Info

### Modeling an either-or-constraint

Based on the clarification about regions, it seems that all you have to do is add the constraints $$x_{ij}=0\quad\forall i\in I,j\notin J.$$ How to handle the "treat it differently" part may ...
• 28.7k
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 ...
• 10k
1 vote

### Impact of soft constraints in MILP

This is to a large extent an expanded version of Joris's comment. Things that have to be a certain way, period, require hard constraints. Examples: "We cannot ship more stuff than we have" -&...
• 28.7k

Accepted

### How to transform a (thermal) range constraint into the objective function

Introduce nonnegative variables $Z^+(t)$ and $Z^-(t)$, impose linear constraints $$T_\min \le T(t)-Z^+(t)+Z^-(t) \le T_\max,$$ and minimize $$\sum_t (Z^+(t)+Z^-(t)).$$ Notice that this approach easily ...
• 21.7k
I think your problem looks like a Multi-resource Generalized Assignment Problem. Here are two papers that describe it: Garvish and Pirkul (1991) and Mazzola and Wilcox (2001). The amount of jobs $a_j$ ...