$L\left(x,y,p\right)={\sum }_{i\in \mathcal{N}}{\sum }_{v<w:\left(v,i,w\right)\in {\Gamma }_{G^{\prime }}}\left[c_i{y}_{vw}^i+p\left(v,i,w\right)\left({\sum }_{t\in T}{x}^t\left(v,i,w\right)-y_{vw}^i\right)+p\left(w,i,v\right)\left({\sum }_{t\in T}{x}^t\left(w,i,v\right)-y_{wv}^i\right)\right]$