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We have the following equation:

$\sum_{i=1}^ny_i=A$

By considering this equation I want to find the minimum possible $B$ in the following equation to find the tightest bound and also when that $B$ is achieved.

$\min\Big(\sum_{i=1}^m(y_i-\sum_{j=1(j\neq i)}^my_{ij})\Big)\leq B,$

where, $m

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    Please define the decision variables first, state the objective, and state the constraints. I strongly believe this will help you in future work. – 2017-01-01
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    If we know that $\sum_{j=1(j\neq i)}^my_{ij}=y_i$ isn't B always equal to 0? – 2017-01-01
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    I fixed the problem. – 2017-01-01
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    Cross-posted: http://cstheory.stackexchange.com/q/37236/5038, http://math.stackexchange.com/q/2079033/14578. Please [do not post the same question on multiple sites](http://meta.stackexchange.com/q/64068). Each community should have an honest shot at answering without anybody's time being wasted. – 2017-01-04

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