# Questions tagged [mixed-integer-programming]

A mixed-integer programming (MIP) problem is a linear program where some of the decision variables are constrained to take integer values.

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### How to model iff and union statements in MILP?

I am trying to model $\{Ax\leq b\}\iff\{Bx\leq c\}$. How different is this from $\{Ax\leq b\}\wedge\{Bx\leq c\}$? How to model with binary variables when $b$ and $c$ are $0$ vectors. I am also trying ...
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### IF a == b, then c = 1, else 0. How to turn this to a linear expression? [closed]

I want to turn the following condition into a linear expression: If a == b, then c = 1, else 0. How should I transform this into a linear expression? Thanks!
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### Strict inequality logical implication in optimization problems

I have $x \in \{0,1\}$ and $y \geq 0$ and I want to model that $x=1$ iff $y>0$, is this possible while keeping the constraint linear? Thanks. One part of the implication is easy $y \leq Mx$. The ...
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### What type of optimization problem is this? Ride sharing?

I am given source containers $s_1,s_2, \dots, s_n$, products $p_1, p_2, \dots, p_m$ and an assignment of which container needs to be used to make a certain product, which I represent as follows \...
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### Question to the solution of “Indicator Variable if x is in specific range”

This question is to query the solution provided by Erwin Kalvelagen to the post Indicator Variable if x is in specific range and conditional constraint: if $x \in [a,b]=> z=1$ (Sorry for ...
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### Bus fleet requirement for transporting passengers/baggage between airport terminals

I am trying to determine the optimum number of buses required for loading and unloading of passengers/baggage. The buses perform following tasks: Transport terminating passengers and their carry on ...
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### Do redundant constraints help in big-M reformulation?

I am trying to reformulate an optimisation problem with unknown $x$ of dimension $K\times 1$ into a mixed-integer program using big-M transformation. In this respect, among my constraints, I have ...
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### (Generalized) Benders Decomposition of MINLP Leads to Linear Master and Sub Problem

I have a mixed-integer nonlinear program (MINLP) which I want to apply (Generalized) Benders Decomposition (GBD) to. The nonlinearities exclusively originate from products of first-stage decision ...
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