Operations Research topics: SAS/OR,
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Equivalent objective functions?

Posts: 35

Equivalent objective functions?

Is Minimize ∑[x(i)+y(i)] the exact equivalent of ∑x(i)+y(i) for a LPP?

Some time back, I read somewhere that the formulation ∑x(i)+y(i) is more effective than ∑[x(i)+y(i)] because we are minimizing each section of the objective function separately. Same for maximizaton.

Is this correct? Can it be mathematically proved if this is correct or incorrect?

SAS Employee
Posts: 447

Re: Equivalent objective functions?

Yes, they are equivalent, and neither one is more efficient than the other.  In both cases, the LP solver sees a single vector of objective coefficients and optimizes the x and y parts simultaneously.  The variable names do not influence the solver, which internally considers all problems as having one set of variables indexed from 0 to n - 1.

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