# Questions tagged [big-m]

For questions related to the use of a "big M" (large constant) in a mathematical modeling context, either in the objective function (to initialize the simplex method) or in constraints (to formulate logical constraints, to linearize constraints, and so on).

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### Benders subproblem with product of continuous and discrete variables

I am trying to solve the following problem. The decisions in the problem are $x, y, v,$ and $W$, where $x, y$ are binary and $v, W$ are continuous variables. \begin{equation}\label{eq:3} \begin{...
77 views

### how to apply Big M to model the logic constraint （if-then-else）

I was hoping to get some help in modelling the following logic as an MIP Constraint c_{m,l}^{RC} is binary decision variable. Simplify it：
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### Formulating the conditional constraint

I want to develop a model extension of capacitated location problem. The variables are a binary $x_i$ and a continuous $Q_i$. The following condition must be satisfied: if $x_i = 0$, $Q_i$ must be ...
101 views

### Scenario based approach to value-at-risk optimization using mixed-integer programming

For a discrete set of scenarios, minimising value at risk can be formulated as a mixed integer linear programming problem. If each scenario has equal probability then this can be written as \begin{...
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### Linearize max function in a constraint [duplicate]

I have a constraint as follows: $\sum_i {r_i} \geq \max \{g_j, B_j\}$ where, $r_i$, $g_j$ are variables and $B_j$ is a parameter. How do I linearize the constraint (I suppose using big-M method)?...
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### Using big M values for a constraint

I want to enforce $x_{i,j}=x_{k,j}\implies z_i \neq z_k$ where $k = i-1$ so I used \begin{align}z_k + 1 - (x_{i,j} - x_{k,j})) \leq z_i \leq z_k - 1 - (x_{i,j} - x_{k,j})\quad\text{for each $j$}\end{...
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