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2

It's hard to answer this without knowing more about your model. Let's say that you have variables for the quantity produced on each machine (say, $x_m$ where $m\in\lbrace 1,\dots, M\rbrace$ indexes the machine). It sounds as if there is a nonzero lower bound $L$ for the output of a machine when it is running. Rather than say $x_m \ge L\,\, \forall m$, what ...

2

As per you mentioned, your problem divided into two parts. The first is, related to the power system optimization and the second is about machinery scheduling system. I don't know, how do you formulate the first one, (linear or non-linear) but, the second one can be represented as the mixed-integer programming as well. Also, other techniques such as CP would ...

3

Start by defining the appropriate binary variable: $x_{ij}=1$ if and only if task $i$ is assigned to resource $j$. A given task can only be assigned to one resource: $$\sum_j x_{ij}=1 \quad \forall i$$ Daily capacity for each resource: $$\sum_i \Delta_i x_{ij}\le 8 \quad \forall j$$ ($\Delta_i$ denotes the duration of task $i$) task $t_3$ must be ...

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