documentclass{article}
usepackage[a4paper,margin=1in]{geometry}
usepackage{mathtools,zref-savepos}

% Linear Programm Tex Example
newcommand{objective}[2] { & text{#1} quad mathrlap{#2}}
% includes s.t. in front
newcommand{stconstraint}[4] { & text{s.t.} & #1 & quad #2 quad #3 && quad  #4}
newcommand{constraint}[4] { & & #1 & quad #2 quad #3  && quad #4}

newcommand{lpnamereset}{noindentzsavepos{text-left-margin}}
newcommand{lpnamebegin}{zsavepos{top-lp}}
newcommand{lpnameend}[1]{ zsavepos{bottom-lp}
    raisebox{0.5dimexprzposy{top-lp}sp-zposy{bottom-lp}sp}[0pt][0pt]{%
      makebox[0pt][r]{rlap{(#1)}hspace*{dimexprzposx{bottom-lp}sp-zposx{text-left-margin}sp}}}}
 % End Linear Programm Tex Example


begin{document}

setlength{jot}{10pt}
lpnamereset
begin{alignat}{4}
 lpnamebegin
 objective{min}{sum_{a in A} k_a u_a + sum_{r in R} sum_{a in A} f_a^r y_a^r}  \
 stconstraint{smashoperator{sum_{a in delta_i^+}} y_a^r - smashoperator{sum_{a in delta_i^-}} y_a^r}{=}{left{begin{array}{@{}rl@{}}
       1, & text{falls $i = O^r$} \
      -1, & text{falls $i = D^r$} \
       0, & text{sonst} \
    end{array}right.}{(forall r in R)(forall i in V)} \
    constraint{y_a^r}{leq}{ u_a}{ (forall r in R)(forall a in A)} \
    constraint{u_a}{in}{{0,1}}{(forall a in A)} \
    constraint{y_a^r}{in}{[0,1}{(forall r in R)(forall a in A)}
     lpnameend{LP}
end{alignat}

end{document}

documentclass{article}

usepackage[a4paper,margin=1in]{geometry}
usepackage{mathtools,zref-savepos}

begin{document}

noindentzsavepos{text-left-margin}%
Here is some text.

%setlength{jot}{10pt}
begin{alignat}{4}
  & zsavepos{top-lp}text{min} quad mathrlap{sum_{a in A} k_a u_a + sum_{r in R} sum_{a in A} f_a^r y_a^r} \
  & text{s.t.} quad & smashoperator{sum_{a in delta_i^+}} y_a^r - smashoperator{sum_{a in delta_i^-}} y_a^r
    &= left{begin{array}{@{}rl@{}}
       1, & text{falls $i = O^r$} \
      -1, & text{falls $i = D^r$} \
       0, & text{sonst}
    end{array}right. & quad & (forall r in R)(forall i in V) \
  & & y_a^r &leq u_a && (forall r in R)(forall a in A) \
  & &   u_a &in {0,1} && (forall a in A) \
  & & y_a^r &in [0,1] && (forall r in R)(forall a in A)zsavepos{bottom-lp}
    raisebox{0.5dimexprzposy{top-lp}sp-zposy{bottom-lp}sp}[0pt][0pt]{%
      makebox[0pt][r]{rlap{(LP)}hspace*{dimexprzposx{bottom-lp}sp-zposx{text-left-margin}sp}}}
end{alignat}

end{document}

begin{equation}
    sysdelim..  % No '{' or other decorations
    systeme[x_1x_2s_1s_2s_3z]{  % Order for the variables
        x_1 +   x_2 + s_1     = phantom{0}9,
        x_1 + 3 x_2 + s_2     = 12,
      - x_1 + 2 x_2 + s_3     = phantom{0}2,
      - x_1 - 2 x_2       + z = phantom{0}0
    }