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problem.tex
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problem.tex
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\documentclass[12pt, letterpaper]{article}
\usepackage[utf8]{inputenc}
\usepackage{geometry}
\geometry{left=1in,right=1in,top=1in,bottom=1in}
\title{Facility location problem}
\author{Sudhan Bhattarai}
\date{October 2020}
\begin{document}
\maketitle
\section*{Notations}
m = number of facilities, index: i = 0, 1, 2, ... \\
n = number of customer nodes, index: j = 0, 1, 2, ... \\
k = X and Y coordinates: (0, 1) \\
$d_{jk}$ = k coordinate (X, Y) of customer j \\
\section*{Decision variables}
$f_{ik}$ = coordinate k of facility i \\
$x_{ij}$ = distance between facility i and customer j \\
$y_{ij}$ = 1 if customer j is assigned to cluster of facility i, 0 otherwise \\
\section*{Problem formulation}
\subsection*{objective function}
minimize: $\sum_{i,j} y_{ij} x_{ij}$ \hspace{0.5cm} (non-linear) \hfill (1)
\subsection*{s.t:}
$\sum_j y_{ij} = 1$ \hspace{1cm}\forall i \hfill (2) \\
$x_{ij}$ = euclidean distance (f_i, d_j) \hspace{1cm} \forall i,j \hfill (3) \\
$y_{ij} \in (0, 1)$ \hfill (4) \\
\end{document}