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author | Koen van der Heijden <koen.vd.heijden1@gmail.com> | 2016-12-12 01:09:59 +0100 |
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committer | Koen van der Heijden <koen.vd.heijden1@gmail.com> | 2016-12-12 01:09:59 +0100 |
commit | 9b7c783f1fd590f4e2f2209a4871cee84ee569ec (patch) | |
tree | c81792d5e7ec09d7a8c37c8b60eb73f6a7d59ff8 | |
parent | f87214b976eedee65be49d87b081c8331babcba7 (diff) | |
download | 2IMF25-AR-9b7c783f1fd590f4e2f2209a4871cee84ee569ec.tar.gz |
solution job sched
-rw-r--r-- | part1.tex | 45 |
1 files changed, 40 insertions, 5 deletions
@@ -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} @@ -139,15 +138,51 @@ 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 |