Originally posted by: ORA17

Hi Experts,

I have below linear programming to solve:

Max c1x1 +c2 x2 +c3 x3 + c4 x4

S.T.

MaxMin Ratio constraints : Max(ax1,bx2,cx3,dx4) / Min(ax1,bx2,cx3,dx4) >= b1

General constraints :  x1+x2+x3+x4 = b2

all x are binary

How can I model this constraint in CPLEX?

Thank you.

What programming API do you use? Do you use OPL?

Originally posted by: ORA17

Hi Daniel,

I am using .NET concert Technology. I don't use OPL.

You can rewrite the constraint as

Max(ax1,bx2,cx3,dx4) >= b1 * Min(ax1,bx2,cx3,dx4)

and then use IloCplex.Max() and IloCplex.Min() to model the max and min expressions.

Originally posted by: ORA17

Hi Daniel @danielJunglas ,

Is it possible to get maxmin ratio for variables with solution 1 with the approach you have suggested?

Kindly refer below example:

Max 54 x1 + 10 x2 + 51 x3 + 95 x4

S.T.

x1 + x2 + x3 + x4  = 2

Max(54 x1 , 10 x2 , 51 x3 , 95 x4) <= 6 Min(54 x1 , 10 x2 , 51 x3 , 95 x4)

because, if we only consider variables with solution 1 then  constraints becomes Max(95,51) <= 6 * min(95,51)

but if we consider all variables then solution does not exist as constraints becomes Max(95,51,0,0) <= 6 * min(95,51,0,0)

Kindly advice.

And what should happen if all variables in the min expression become 0? Then your expression is undefined again.

Assuming that you can guarantee that at least one variable is non-zero then you could replace min(54 x1, 10, x2, ...) by min (54 x1 +  M*(1-x1), 10 x2 +  M*(1-x2), ...) where M is a number that is bigger than all the coefficients.