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Let us suppose we have an optimization problem which we have modeled as an ILP. Suppose we solve this problem using some set of constraints which restricts the search space. Let us suppose we model th …

In a mathematical integer optimization problem, if the objective function is represented as $\sum x_k \cdot M_k$, where $M_k$ is a non-linear function whose value is known and just plugged in to the o …

How to express a chain of OR operations in an ILP in which each expression is a less than or equal constraint and the left hand side variable in all inequalities is always the same? All the variables …

We have a set of constraints in an ILP of the following form : $ \gamma (X_{11} + X_{12} + X_{13}) \leq C_1$ where $X_{ij} \in \{0,1\}$ and the value of $\gamma$ is going to depend on the actual value …

If $X_{ijklm}$ are Boolean Variables, where $i,j,k,l,m$ range from $1$ to $n$, then write an ILP constraint to ensure that for each value of $k$, either all the $jth$ variables are set to $0$ or all t …

Consider several Integer (0/1) ILP variables, i.e., Boolean variables, $x_i$'s. Consider an ILP constraint $x_1 + x_2 + x_3 \geq 1$ and another constraint $x_4 + x_5 + x_6 \geq 1$. I would like to rep …

How can I express a chain of OR operations in an ILP, given that each operand is an inequality between two binary variables? I have asked a similar question here: Chain of Boolean ORs. In that questio …

Consider an implication of the form $A \implies B$ where both $A, B$ comprises a chain of Boolean OR variables. For example, $(a_1 \lor a_2 \lor a_3) \implies (b_1 \lor b_2 \lor b_3)$. How can this b …

We are given three binary indicator variables $X_{ij}, Y_{jk}$ and $Z_{jl}$. Write linear constraints such that, a) if $X_{ij}$ is equal to 1, then for that $j$ when $X_{ij} = 1$, exactly one $Y_{jk} …