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\begin{slide}{Grid Model}
\begin{itemize}
\item Grid $G = \lbrace S_1, S_2, \dots, S_r\rbrace$
\item $S_i$ is $i$th site participating in $G$
\item $S_i = \lbrace H_{i,1}, H_{i,2}, \dots,H_{i,m} \rbrace \cup D_i$
\item $H_i$ and $D_i$ are set of host machines and data repository/storage at $S_i$
\end{itemize}
\end{slide}

\begin{slide}{Grid Figure}
\centering\includegraphics[scale=0.5]{grid.eps}
\end{slide}

\begin{slide}{Application Model}
\begin{itemize}
\item Application $J$
\item $n$ heterogeneous independent task $\lbrace T_1, T_2, \dots, T_n\rbrace$
\item no inter-task communications and dependencies
\item set $I_i$ of input data objects $\lbrace I_{i,1}, I_{i,2}, \dots I_{i,d}\rbrace$
\end{itemize}
\end{slide}

\begin{slide}{Application Figure}
\centering\includegraphics{task-data.eps}
\end{slide}

\begin{slide}{Problem}
Find a transmission and execution schedule to minimize makespan.
\begin{itemize}
\item For $\#hosts > 1$, this problem is NP-hard.
\item No idea if $\#hosts = 1$.
\end{itemize}
\end{slide}

\begin{slide}{Simplified Problem}
\begin{itemize}
\item It has only one site $S_1$
\item $S_1$ has only one data repository $D_1$
\item $S_1$ has only one host $H_{1,1}$
\item no data sharing between tasks
\end{itemize}
In this configuration, the problem degenrates into
``printing machine and binding machine''
\end{slide}

\begin{slide}{Solution from jjchen}
For book printing:
\begin{itemize}
\item process the books with $p_i \leq b_i$ in order of nondecreasing order $p_i$
\item process the remaining books in order of nonincreasing $b_i$
\end{itemize}
For book binding:
\begin{itemize}
\item bind books with the same order of book printing
\end{itemize}
It is based on
S. M. Johnson, Optimal two- and three-stage production schedules
with setup times included, Naval Res. Logist. Quart. 1, (1954), 61-68.
\end{slide}

\begin{slide}{Scheduling}
\begin{itemize}
\item $n$ jobs $J = \lbrace j_1, j_2, \dots, j_n\rbrace$
\item $m$ processors $P = \lbrace p_1, p_2, \dots, p_m\rbrace$
\item each job has $m$ tasks $j_{i,1}, j_{i,2}, \dots j_{i,m}$
\item task $j_{i,j}$ runs on $p_j$
\item each processor can run one job at one time
\end{itemize}
\end{slide}

\begin{slide}{Scheduling}
\begin{itemize}
\item Open shop
\item Job shop
\item Flow shop
\end{itemize}
\href{http://www.mathematik.uni-osnabrueck.de/research/OR/class}{http://www.mathematik.uni-osnabrueck.de/research/OR/class}
\end{slide}

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