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authorPeter Wu <peter@lekensteyn.nl>2016-12-12 01:29:52 +0100
committerPeter Wu <peter@lekensteyn.nl>2016-12-12 01:29:52 +0100
commit405549ccd17c5d2709eccef65b1faa228dfad682 (patch)
treee45a5c0460ea108259906f661a5a1451d6a47bb6
parent40c3c72ff09f07e23f4bc6e46c86c6a4be72e94f (diff)
parentd4c22dc2a0dda1f4f210cee038585c62e56e991c (diff)
download2IMF25-AR-405549ccd17c5d2709eccef65b1faa228dfad682.tar.gz
Merge remote-tracking branch 'refs/remotes/origin/master'
-rw-r--r--part1.tex45
1 files changed, 40 insertions, 5 deletions
diff --git a/part1.tex b/part1.tex
index f99b27c..c0d3ce5 100644
--- a/part1.tex
+++ b/part1.tex
@@ -47,10 +47,9 @@ be in the same truck.
% combination: they are not allowed to be put in the same truck.
\subsection*{Solution:}
-\begin{itemize}
- \item[(a)]
- \item[(b)]
-\end{itemize}
+\subsubsection*{(a)}
+
+\subsubsection*{(b)}
\section*{Problem: Chip design}
@@ -151,15 +150,51 @@ We also reformed all previously mentioned requirements into formula's that can b
(=> (<= j10 j7) (<= (+ j10 15) j7))
\end{lstlisting}
+The complete scheduling output, where an integer represents the time at which a job was started is as follows:
+\begin{lstlisting}
+j1 -> 1
+j2 -> 0
+j3 -> 7
+j4 -> 0
+j5 -> 15
+j6 -> 0
+j7 -> 25
+j8 -> 15
+j9 -> 28
+j10 -> 0
+j11 -> 15
+j12 -> 42
+\end{lstlisting}
+
+Note that $42 + 12 + 5$ is indeed equal to $59$.
+
\subsubsection*{(b)}
This solution was retrieved in the same way as answer a. This answer is $m = 65$.
-2 extra lines were added to ensure that job 6 lies withing job 12:
+2 extra lines were added to ensure that job 6 lies within job 12:
\begin{lstlisting}
(>= j6 j12)
(<= (+ j6 11) (+ j12 17))
\end{lstlisting}
+With those 2 extra formula lines, the new schedule becomes:
+
+\begin{lstlisting}
+j1 -> 1
+j2 -> 0
+j3 -> 7
+j4 -> 0
+j5 -> 15
+j6 -> 42
+j7 -> 53
+j8 -> 15
+j9 -> 28
+j10 -> 0
+j11 -> 15
+j12 -> 42
+\end{lstlisting}
+Note that $53 + 7 + 5$ is indeed equal to $65$.
+
\section*{Problem: Integer sum from neighbors}
Eight integer variables $a_1$, $a_2$, $a_3$, $a_4$, $a_5$, $a_6$, $a_7$, $a_8$
are given, for which the initial value of