LaTeX Forum

\documentclass{scrartcl}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[
	ngerman,
	american % hier könnte stattdessen auch USenglish oder english stehen
]{babel}
\usepackage[babel]{microtype}
\usepackage{mathtools}

\useshorthands{"}
\addto\extrasamerican{\languageshorthands{ngerman}}

\begin{document}
For each operation $(i,k)$ and each start"=period $t$ with $(i,k,t) \in A$ (i.e., $t$ is a permissible start time for $(i,k)$), we have a binary variable $\alpha_{i,k,t} \in \{0,1\}$, which is interpreted as 
\begin{align*}
	\alpha_{i,k,t} &=
	\begin{cases}
		1 & \parbox{0.35\columnwidth}{
				\raggedright Processing of operation $(i,k)$ starts in period $t$.
			}\\
		0 & \text{Else.}
	\end{cases}
\intertext{For each machine $j \in M$, each state $s \in S$, and each period $t \in [T] \cup \{-1,~T\}$, we have a binary variable $\beta_{j,s,t} \in \{0,1\} $, which means}
	\beta_{j,s,t} &=
	\begin{cases}
		1 & \parbox{0.3\columnwidth}{
				\raggedright In period $t$ machines $j$\\is in operational state $s$.
			} \\
		0 & \text{Else.}
	\end{cases}
\end{align*} 

\end{document}

\documentclass[a5paper]{article}
\usepackage{mathtools}
\begin{document}
   For each operation $(i,k)$ and each start-period $t$ with $(i,k,t) \in A$ (i.e., $t$ is a permissible start time for $(i,k)$), we have a binary variable 
   $\alpha_{i,k,t} \in \{0,1\}$, which is interpreted as 
   $$\alpha_{i,k,t}= 
      \begin{cases} 
         1 & \text{Processing of operation $(i,k)$} \\[-2pt] 
            & \hphantom{} \text{starts in period $t$.} \\ 
         0 & \text{Else.} 
      \end{cases}$$ 
For each machine $j \in M$, each state $s \in S$, and each period $t \in [T] \cup \{-1,~T\}$, we have a binary variable 
   $\beta_{j,s,t} \in \{0,1\} $, which means     
   $$\beta_{j,s,t}= 
      \begin{cases} 
         1 & \text{In period $t$ machines $j$} \\ 
            & \hphantom{} \text{is in operational state $s$.} \\ 
         0 & \text{Else.} 
      \end{cases}$$ 
\end{document}

	For each operation $(i,k)$ and each start-period $t$ with $(i,k,t) \in A$ (i.e., $t$ is a permissible start time for $(i,k)$), we have a binary variable 
	$\alpha_{i,k,t} \in \{0,1\}$, which is interpreted as 
	$$\alpha_{i,k,t}=
		\begin{cases}
			1 & \text{Processing of operation $(i,k)$} \\[-2pt]
				& \hphantom{} \text{starts in period $t$.} \\
			0 & \text{Else.}
		\end{cases}$$
For each machine $j \in M$, each state $s \in S$, and each period $t \in [T] \cup \{-1,~T\}$, we have a binary variable 
	$\beta_{j,s,t} \in \{0,1\} $, which means 	
	$$\beta_{j,s,t}=
		\begin{cases}
			1 & \text{In period $t$ machines $j$} \\
				& \hphantom{} \text{is in operational state $s$.} \\
			0 & \text{Else.}
		\end{cases}$$