Questions tagged [binary-variable]

For questions that involve variables than can only take on one of two values, usually 0 or 1.

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Integrality gap in bilevel binary linear programming problem

I have a bilevel max-min optimization problem over binary variables, with constraints expressed using linear inequalities. The inner (minimization) problem is $$ \begin{alignat}2 \min\limits_x&\...
2
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64 views

Indicator function for integer variable with inequality constraint

I have $n$ integer variables $\vec{x}$ with the following integer programming problem. $$ COST = \sum^{n-1}_{i = 0} a_i x_i + \sum^{n-1}_{j=0} b_j I(x_j > 0) $$ Here, $a_i, b_j \in \mathbb{R}_+$ ...
1
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Interger programming using gray encoding

Could anyone suggest me a tool or library which takes an integer programming problem written in DOCPLEX or CVXPY as input and outputs the equivalent problem using Gray binary encoding? I am happy to ...
-4
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67 views

maximizing paid time off

A friend of mine is trying to optimize his use of paid time off using IP/BP and I thought maybe you would be able to help (see below). John Doe works only on business days and loves to travel in his ...