Hi all,

I am having a frustrating time trying to keep my model an LP problem. I am writing a simple cost function which takes the form:

deftransportcost(a,i,j)… transportcost =e= sum(aij(a,i,j), ctrans(a,i,j)* f(a,i,j));

where deftransportcost is the objective function , ctrans is a parameter, and f(a,i,j) is the free-moving decision variable (x)

The problem is, this formulation means that if any of the arc flows are negative (which is allowed as the arcs represent reversible-flow pipelines), I get negative values for some of the arc flow costs. Using the abs(f(a,i,j) function works, but as abs is a nonlinear function, I then have to change the solver to DNLP and create extra computational time etc. I want to keep the problem linear.

Can anybody advise the simple way to rearrange this equation, or a trick that will alleviate this problem? My maths isn’t great, but I hope it’s something fairly simple.

Thanks in advance,

Stevie

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