Hi all,

I am writing a flow balance constraints for a multicommodity flow problem. devision variable is x-kst, representing flow or order k arrive at the destination of service s at time t by service s.

forall(k in orders, j in orders_nodes[k])
sum (<n,<i,j>,dt,c,tt,dist,cap,f> in services:<i,j> in orders_arcs[k],t in time) x[k][<n,<i,j>,dt,c,tt,dist,cap,f>][t]
- sum (<n,<j,i>,dt,c,tt,dist,cap,f> in services:<j,i> in orders_arcs[k],t in time) x[k][<n,<j,i>,dt,c,tt,dist,cap,f>][t] == k.SupDem[j];

However, some arcs which are not belonging to order k (not in the set of orders_arcs[k]) ,  are also selected. I mean that flow should not pass by those arcs not in its possible arcs. How to deal with it?

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Dario
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#DecisionOptimization

Duplicate of https://community.ibm.com/community/user/datascience/communities/community-home/digestviewer/viewthread?MessageKey=aa703440-d7ed-46a3-a794-5c2ade873a65&CommunityKey=ab7de0fd-6f43-47a9-8261-33578a231bb7&tab=digestviewer#bmaa703440-d7ed-46a3-a794-5c2ade873a65

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Daniel Junglas
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Original Message:
Sent: Mon June 22, 2020 10:11 AM
From: Dario Pisinger
Subject: Flow Balance

Hi all,

I am writing a flow balance constraints for a multicommodity flow problem. devision variable is x-kst, representing flow or order k arrive at the destination of service s at time t by service s.

forall(k in orders, j in orders_nodes[k])
sum (<n,<i,j>,dt,c,tt,dist,cap,f> in services:<i,j> in orders_arcs[k],t in time) x[k][<n,<i,j>,dt,c,tt,dist,cap,f>][t]
- sum (<n,<j,i>,dt,c,tt,dist,cap,f> in services:<j,i> in orders_arcs[k],t in time) x[k][<n,<j,i>,dt,c,tt,dist,cap,f>][t] == k.SupDem[j];

However, some arcs which are not belonging to order k (not in the set of orders_arcs[k]) ,  are also selected. I mean that flow should not pass by those arcs not in its possible arcs. How to deal with it?

------------------------------
Dario
------------------------------

#DecisionOptimization