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MITx: 15.053x Optimization Methods in Business Analytics

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When the integrality constrains are relaxed, the feasible region gets larger. The optimal objective value won’t get worse. It can stay the same or get better. In this case, the optimal objective value increases or remains the same.

SOLUTION

y≤x1. If x1=0 , then y≤0. y≤x2. If x2=0, then y≤0. y≥x1+x2−1. If x1=x2=1, then y≥1. This enforces y=x1x2, x1,x2∈{0,1}

On choosing the parameter M

Any redundant constraint will be OK.

But, it is often best to choose M minimal:

l choose M so that constraint is redundant

l with any lower value of M, it is not redundant.

Binary Logic

a valid transformation when the objective is to minimize z subject to z=max{2x−4,

x−y

}

Min {z:z≥2x−4,z≥x−y,z≥y−x}.

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