Conditional milp formulation
I might have found a solution to my problem by using four auxiliary binary variables $\alpha_1$, $\alpha_2$, $\alpha_3$ and  $\alpha_4$     $\epsilon\ \{0,1\} $. The constraints 1.-4. are rewritten using the big-M method.



Constraint 1


$T_{ts}\geqslant -7-M\cdot (1-\alpha_1)$
$T_{ts}\leqslant -7+M\cdot \alpha_1$


Constraint 2


$T_{it}\leqslant 15+M\cdot (1-\alpha_2)$
$T_{it}\geqslant 15-M\cdot \alpha_2$


Constraint 3


$T_{ts}-T_{it}+M\cdot (1-\alpha_3)\geqslant 5$
$T_{ts}-T_{it}-M\cdot \alpha_3\leqslant 5$


Constraint 4


$\alpha_{ts,it}=1-\alpha_{ts,gshp}$


Constraint 5


$\alpha_{ts,it}\geqslant \alpha_1+\alpha_2+\alpha_3+\alpha_4-3$
$\alpha_{ts,it}\leqslant \alpha_1$
$\alpha_{ts,it}\leqslant \alpha_2$
$\alpha_{ts,it}\leqslant \alpha_3$
$\alpha_{ts,it}\leqslant \alpha_4$




This might be a solution. Unfortunately computational time is exploding. Does someone know a less time-consuming workaround?

Best SR89