L(\boldsymbol{x},\boldsymbol{y},\boldsymbol{p})=\sum_{i\in\mathcal{N}}\sum_{v<%
w:(v,i,w)\in\Gamma_{G^{\prime}}}\bigg{[}c_{i}y^{i}_{vw}+p(v,i,w)\Big{(}\sum_{t%
\in T}x^{t}(v,i,w)-y^{i}_{vw}\Big{)}+p(w,i,v)\Big{(}\sum_{t\in T}x^{t}(w,i,v)-%
y^{i}_{wv}\Big{)}\bigg{]}