H1:

Step 0: Compute $q{*}_{v_d}=\arg {\max }_{\Omega \in S^{\prime }}{(-IN{*}_{v_d}^{\Omega n})}^{+}\forall v_d\in V,n\in N$, $K=0$

Step 1: For a node $v\in p_{v_d}$, identify a scenario $\Omega *$ such that ${\delta }_v^{\Omega *}=\arg {\max }_{\Omega \in S^{\prime }}\left({\delta }_v^{\Omega }\right)$

Step 2: Compute $K_{v_d}^v={(-IN{*}_{v_d}^{\Omega *n})}^{+}\forall v_d\in V$.

Step 3: Allocate $q_{v^{\prime }}=\min ((K_{v_d}^v-{\sum }_{i>v}{q}_i),(S{}_v^{\prime }-S_v))\forall v^{\prime }>v;v^{\prime },v,i\in p_{v_d}$; if $C_{v^{\prime }}+h{}_{v^{\prime }}^{\prime }\left(\min ((K_{v_d}^v-{\sum }_{i>v}{q}_i),(S{}_{v^{\prime }}^{\prime }-S_{v^{\prime }}))\right)=\arg {\min }_{v*\in p_{v_d},v*>v}(C_{v*}+h{}_{v*}^{\prime }(\min (k_{v_d}^v-{\sum }_{i>v}{q}_i),(S_{v*}-S{}_{v*}^{\prime })))\forall i\in p_{v_d}$

Step 4: $K_{v_d}^v=S{}_{v^{\prime }}^{\prime }-S_{v^{\prime }}=K_{v_d}^v-\min \left((K_{v_d}^v-{\sum }_{i>v}{q}_i),(S{}_{v^{\prime }}^{\prime }-S_{v^{\prime }})\right),{\beta }_v=1,co=co+K_{v_d}^v\forall v\in p_{v_d}$.

Step 5: If $K_{v_d}^v=0$ then go to step 6 else repeat step 3 and step 4.

Step 6: Repeat step 1 to step 5 for all nodes$v\in p_{v_d}$.

Step 7: Repeat the step 0 to step 6 for all $v_d\in V$

Step 8: Compute $St={\sum }_{v\in V}({\beta }_v{C}_v+h{}_v^{\prime }{q}_v)$

Step 9: Stop