Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose there is an integer programming problem:

$$\min_{x_i \in \{0,1 \}, i=1,\cdots,k} \sum_{i=1}^k c_i x_i$$ subject to $$ \sum_{i=1}^k a_i x_i \leq W. $$

Suppose the cost coefficients are negative, i.e., $c_i < 0, i=1, \cdots, k$. I was wondering if it is possible to convert the problem to another with the same form, so that the cost coefficients are nonnegative and the minimization solutions are still the same?

I have thought about the conversion $c_i \mapsto c_i - \min_{j=1}^k c_j$. But it changes the solution.

Thanks in advance!

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

Try using $1-x_i$ instead of $x_i$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.