New answers tagged big-m
2
votes
Accepted
MIP formulation for a lower semi-continuous function
You want to maximize $\max(f(x),0)$. Assume $L \le f(x) \le U$ for constants $L$ and $U$. Maximize $g(x)$ subject to
$$
0 \le g(x) \le U y \\
0 \le g(x) - f(x) \le (0-L)(1-y) \\
y \in \{0,1\}
$$
- 30.4k
3
votes
Accepted
Linearize piecewise function without big-M constraints
I don't see or remember a way around the big-M constraints. Thankfully they are not that hard to write. Or you may use indicator constraints which are even simpler.
We add new binary variables, and ...
- 1,842
2
votes
Travelling salesman problem
The MTZ constraints are big-M constraints that enforce the logical implication
$$x_{ij}=1\implies u_j\ge u_i+d_j.$$
That is, if you traverse arc $(i,j)$, the cumulative demand at $j$ is at least the ...
- 30.4k
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