DM559/DM545 -- Linear and Integer Programming

The exam is digital. To digitalize handwritten text, formulas and graphs digital pen or hand scanner are allowed.

• Important: Exam instructions, Guidelines for Exam Monitor
• You can write your answers as you prefer in Danish or in English

• Being acquainted with some of these tools (or their equivalent in your system) would help you to digitalize your solutions more easily and faster:
• Digital pens, hand scanners.
• Mathematical formulas, if not handwritten, are best encoded in LaTeX
• Latex symbol classifier
• IPython for matrix operations
• IPython for Network flows
• Answer Templates:
  • DM559/DM554 [ Latex | PDF | Word | OpenDocument ]
  • DM545 [ Latex | PDF | Word | OpenDocument ]
• text editor in VERBATIM mode (Unix: EMACS + ORG mode; Win: Gusek, etc)
• For matrix operations Python (see package "numpy" and package "fractions"), R, MATLAB, Maple.
• tools to plot graphs: LP Grapher, grapher in Mac
• gurobipy to solve ILP problems
• tikz for drawing networks in Latex.

• Danish-English Dictionary

• To write ILP models in Latex you can use one of the following templates:

\begin{align}
   \label{ob} \max \; \quad & \sum_{j=1}^nc_jx_j  \\
   \label{c1} \mbox{s.t.} \quad &\sum\limits_{j=1}^n a_{ij}x_j\geq b_i,
   \quad i=1,\ldots,m \\
\label{c2}   &x_j \geq 0, \quad j=1,\ldots,n   
\end{align}


\[
\begin{array}{lrll}
\max & \sum\limits_{j=1}^nc_jx_j\\
&\sum\limits_{j=1}^n a_{ij}x_j&\leq b_i,& i=1,\ldots,m\\
&x_j&\geq 0,& j=1,\ldots,n
\end{array}
\]


\begin{equation}\label{ob}
\max  \sum_{j=1}^nc_jx_j\\
\end{equation}
\begin{equation}\label{c1}
\sum_{j=1}^n a_{ij}x_j\leq b_i, i=1,\ldots,m\\
\end{equation}
\begin{equation}\label{c2}
x_j\geq 0, j=1,\ldots,n
\end{equation}