Verified Commit af496ef7 authored by Theo von Arx's avatar Theo von Arx
Browse files

Add start condition to ILP

parent 362e1c68
......@@ -156,7 +156,7 @@ Produces the following (indep. of priorities)\\
Formally:
\begin{compactenum}
\item Minimize $$L=\tau(v_n) - \tau(v_0)$$ subject to the constraints 2-5
\item Define $l_i$ and $h_i$ for all tasks using ASAP and ALAP respectively.
\item Decision variables binary: $$\forall v_i \in V_S: \quad \forall t: l_i\leq t \leq h_i: \quad x_{i,t}\in\{0,1\}$$
\item Only one variable non-zero: $$\forall v_i \in V_S: \quad \sum_{t=l_i}^{h_i}x_{i,t}=1$$
\item Relation between variables $x$ and starting times $\tau$: $$\forall v_i
......@@ -169,6 +169,10 @@ Formally:
&\sum_{\forall i: (v_i,v_k) \in E_R} \sum_{p'=\max\{0,t-h_i\}}^{\min\{w(v_i)-1,t-l_i\}} x_{i,t-p'} \leq \alpha(v_k)
\end{alignedat}
\end{equation*}
\item Start condition: \begin{equation}
\tau(\nu_0) = 0
\end{equation}
\item Minimize $$L=\tau(v_n) - \tau(v_0)$$.
\end{compactenum}~\newline
Example:
......
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