# Decision Optimization

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## Model and solve a problem in which the objective function has the form of max( max f1(x) - max f2(x))

• #### 1.  Model and solve a problem in which the objective function has the form of max( max f1(x) - max f2(x))

Posted Sun March 12, 2023 12:17 PM

Dear all,

I aim to use CPLEX to solve an optimization problem where the objective value is the maximum difference of two other objective values.
Is it possible to model and solve such problem? In more detail, I have a linear optimization of the following form:

P:
max obj
subject to some constraints.
and I have two copies P1, P2 of the same problem.

and I want to solve the following problem.

max (max obj1 - max obj2)
subject to :
set of constraints subject to P1
set of constraints subject to P2
some constraints to link between P1, P2

Is is possible to model this problem as another linear programming problem? or Is it possible to model and solve it as a multi-objective LP problem that can be solved with the current version of CPLEX.

Thanks,

M.

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Minh Vu
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• #### 2.  RE: Model and solve a problem in which the objective function has the form of max( max f1(x) - max f2(x))

Posted Fri March 17, 2023 12:49 PM

You can define the two values as expressions and then maximise the difference.

max (obj1 - obj2)

https://www.ibm.com/docs/en/icos/20.1.0?topic=keywords-dexpr

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[Nzube] [Nzube]
[Optimisation Research]
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• #### 3.  RE: Model and solve a problem in which the objective function has the form of max( max f1(x) - max f2(x))

IBM Champion
Posted Fri March 17, 2023 02:56 PM

This would lead CPLEX to choose the minimum rather than maximum value of obj2.

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Paul Rubin
Professor Emeritus
Michigan State University
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