# 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 solve mixed integer programming problems with multiple varibles in one inequality?

Below I need to find the optimal results of $y_i$ and $x_{ij}$, where $a_i$,$b_{ij}$ and $c_i$ are constant numbers. $x_{ij}$ and $y_i$ are binary variables, while $v_i$ and $z_i$ are allowed to be ...
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### Solve Constrained zero-one Integer Linear Program Using Simulated Annealing

Recently, I was reading about several techniques that solves Unconstrained Mixed Integer Linear Programs (UM-ILP) using a meta-heuristic algorithm called simulated annealing. I was thinking about the ...
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### Integer programming : linearize product of constants given conditions

I have some constant values $c_i$ in $(0.5, 2)$. I also have binary variables $x_i$. For my integer program, for a particular constraint, I need to multiply only those $c_i$ when $x_i$ takes the value ...
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### Boundary point in MIP using inclusive inequality?

I want to write if-else condition in linear programming and the only method I can think of is using MIP. I have to write a binary variable called b so that ...
23 views

### Does this fall into a typical optimization problem? (Knapsack??)

MOVED TO OR STACK I am struggling to find a representative problem formulation for this optimization challenge. I have implemented a MILP in Matlab, but the run time is taking more then a day. My ...
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### Need help formulating an event scheduling problem involving multiple clients and class types

I run training classes. A "B" class, a "C" class and an "Adv" advanced class. B classes run every saturday, take 3 hours, and have a maximum 4 clients. C classes follow B classes and take 2 hours. ...
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### Explanation of branch-and-cut method in solving MIP.

I'm reading about the branch and cut algorithm to solve a mixed-integer programming problem. The interface and the steps of the algorithm are as follow: The extreme ray $e^*$, if exists, is from the ...
33 views

### Division in linear program

In my linear program, I have an inequality constraint as follows. $$x + \frac{y}{g(z)} \leq c$$ where $x \in \mathbf{R}^+, y \in \{0, 1\}$, and $g(z)$ is a function of $z \in \mathbf{Z}_{\geq 0}$ ...
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### Linear program decomposition and Column Generation

I needed to decompose a large LP of equality constraints. $\\Dx=B^1,$ $\\Ax=B^2,$ $\\D \in R^{m^{(1)} \times n}$ $\\A\in R^{m^{(2)} \times n}, m<<n$ $A$ has a block diagonal structure and $D$ ...
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### Choosing Variable to generate a Node in a MILP

I'm trying to find or understand rigorous a criterion about choosing the variable to generate a new Node in the Branch and Bound method. Usually the methods I've seen just choose the variable nearly ...
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### The existence of an optimal solution in a MILP guarantees existence of the optimal solution in the relaxation problem?

I'm following a description of the Branch and Bound Method. But I don't understand at all, that if you assume a MILP problem has an optimal solution it implies that the relaxation problem has also ...
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### Integer program for minimizing maximum Lateness with precedence constraints

In studying for an upcoming exam the following problem came up: Write an integer program to: minimize the maximum Lateness for the one machine scheduling problem with precedence constraints and ...
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### Reformulation of min constraints with binary decision variable inside the min()?

I am trying to reformulate a mix integer problem with a binary decision variable lies within the min constraint. That is ${x_1} = \min \left( {c,\frac{d}{\alpha }} \right)$ where $c$ and $d$ are two ...
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### How to model grouping constraint in Knapsack problem?

I would like to add a new constraint to a standard Knapsack problem by introducing groups. My variables are $x_c \in \mathbb{Z}^+, c\in \mathbb{C}$. Where $\mathbb{C}$ is the set of all items. Each ...
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### How to linearize $\min\{\max\{0,x\},y\}$ as constraint in MILP?

I am formulating a MILP and one of the constraints is $\min\{\max\{0,y-x+a\},b\} \leq c$. with decision variables $x, y \geq 0$ and $a,b,c$ as constants. How would I ideally introduce auxiliary ...
28 views