Representing lower bound between indirectly connected nodes

GAMS
1

Hello all,

I am trying to place a lower bound on flow (flow.lo(i,j)=10) between two nodes (i and j) that are not directly connected, but are connected indirectly through a series of other nodes (K,L,M,N etc).

I am trying to represent a minimum gas contract lrvrl between two countries that must be obeyed, but the route of gas transit may take numerous different flow paths.

Is there a way to do this without explicitly telling the model which arcs to send flow=10 along, i.e. flow.lo(i,k)=10, flow.lo(k,l)=10, flow.lo(l,j)=10.

The model is linear, minimising cost.

If someone could point me in the right direction or offer some advice i’d be really grateful.

Thanks,

Stevie

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2

On Thursday, December 10, 2015 at 2:07:31 PM UTC, Stevie Lochran wrote:

Hello all,

I am trying to place a lower bound on flow (flow.lo(i,j)=10) between two nodes (i and j) that are not directly connected, but are connected indirectly through a series of other nodes (K,L,M,N etc).

I am trying to represent a minimum gas contract lrvrl between two countries that must be obeyed, but the route of gas transit may take numerous different flow paths.

Is there a way to do this without explicitly telling the model which arcs to send flow=10 along, i.e. flow.lo(i,k)=10, flow.lo(k,l)=10, flow.lo(l,j)=10.

The model is linear, minimising cost.

If someone could point me in the right direction or offer some advice i’d be really grateful.

Thanks,

Stevie



Bump…anyone?!

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3

Stevie



The topology of your network is not clear and the influence of flow between other countries is also not clear. If there is just one single path from one country to the other and there are no interfering other flows then adding a lower bound on any of the arcs in the path should be enough because the node balance will force the other flows up.



If there are multiple paths you cannot work with lower bounds on individual variables. You will have to define a cut in the network that separates the two countries. The sum of the flow over the arcs in the cut must be more than your lower bound.



The definition of the cut depends on how your network is defined. Note that there probably are multiple valid cuts and you just need one of them.



Good luck



Arne

Arne Stolbjerg Drud

ARKI Consulting & Development A/S

Bagsvaerdvej 246A, DK-2880 Bagsvaerd, Denmark

Phone: (+45) 44 49 03 23, email: adrud@arki.dk



From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of Stevie Lochran
Sent: Monday, December 14, 2015 4:59 PM
To: gamsworld
Subject: Re: Representing lower bound between indirectly connected nodes





On Thursday, December 10, 2015 at 2:07:31 PM UTC, Stevie Lochran wrote:

Hello all,



I am trying to place a lower bound on flow (flow.lo(i,j)=10) between two nodes (i and j) that are not directly connected, but are connected indirectly through a series of other nodes (K,L,M,N etc).



I am trying to represent a minimum gas contract lrvrl between two countries that must be obeyed, but the route of gas transit may take numerous different flow paths.



Is there a way to do this without explicitly telling the model which arcs to send flow=10 along, i.e. flow.lo(i,k)=10, flow.lo(k,l)=10, flow.lo(l,j)=10.



The model is linear, minimising cost.



If someone could point me in the right direction or offer some advice i’d be really grateful.



Thanks,



Stevie





Bump…anyone?!

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