# 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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### Rake building through mixed integer programming

I have a problem. I need some helps. I have several coils with weight. I have to load coils on wagons. There are two types of wagons. The capacity of two types of wagons are 64 and 67 respectively. I ...
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### Are there any theorems about the existence of feasible solutions to the Mixed-Integer Nonlinear Programming (MINLP) problem?

I am just wondering if there are any theorems about the existence of feasible solutions to the Mixed-Integer Nonlinear Programming (MINLP) problem. For example: Theorems about sufficient conditions ...
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### Tractable formulation of a mixed integer program

Given constant matrices $A_1\in\mathbb{R}^{1\times l}$ and $A_2\in\mathbb{R}^{1\times l}$, and constants $b_i$, $i=1,\dots,n$. Consider the following mixed integer program (MIP) with decision ...
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### Formulating a linear programming/optimization problem with a "soft" constraint

I have an optimization problem which I hope I can formulate as a linear program. The problem involves a vector $x$ of binary decision variables (so each entry of the $x$-vector is either $0$ or $1$). ...
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I have a general assignment problem that assigns a set of payload tasks $T$ to a set of workers $A$, where $|T|$ >> $|A|$. Each task $T_i \in T$ consists of a tuple $(s_i, g_i)$, which represent ...
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### Mixed linear programming: why is big-M needed to set a variable to the max of other variables?

Let's say I want to set a variable $z$ to the maximum of other variables. We'll assume that the objective function is not of help, that is, the objective function doesn't try to minimize the maximum. ...
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### Non-linear optimization programming, with step function in constraint

I want to optimize a non-linear function $f(x)$, $f: \mathcal{R}^{n} \to \mathcal{R}$ (being a log-likelihood over $m$ observations, i.e. $i$ being the observation index) under constraints numerically,...
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### Python Native Implementation of Mixed Integer Linear Programming

Is it possible to have pure Python implementation of Mixed Integer Linear Programming, something similar to mip, pulp, cvxpy, etc. - but such simple as https://github.com/ispaneli/lippy - it is ...
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### Proof of solvable constrained optimization with a subset of a larger set of constraints

Way out of my comfort zone here so apologies if I'm not providing enough or correct information. I work with an application of constrained optimization to assemble test forms (automated test assembly)....
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### How can linear programming condition check if variable is a multiple of number?

Let's say we have linear programming problem with x1 and x2 variables. Maximize x1 + x2 where (for example) 0.3x1 + 0.7x2 <= 2 0.2x1 + 0.3x2 <= 3 How can be added one more condition, so linear ...
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### How to linearize a max function in a constraint? [closed]

I have linear program that has constraint as follows: $\max(x,y) \geq 0$ where $x$ and $y$ are variables. How to linearize this inequality? How to write this constraints in google or tools?
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### Vector simultaneous containment problem

Given a matrix $A\in\mathbb{R}^{n \times k}$, with rows $a_1,\dots,a_n \in \mathbb{R}^k$, I want to find vectors $\ell,u\in\mathbb{R}^k$ such that: The (elementwise) inequality $\ell \le a_i \le u$ ...
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### How many hexagons to fill a square tile

I am filling a square tile of width wTile with equal hexagons stacked flat side on top of each other at an angle I call colourAngle as shown in the diagram. I call the rows of hexagons "Perp Line&...
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### Mutual exclusivity variables in mixed integer programming problems

I am working on a employee scheduling problems (assigning shifts to temporary workers) by modeling it as a MIP. There is a one shift per day constraint for the employees that restricts more than one ...
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### Do linear optimization problems with some infinite coefficients have convex solution spaces?

I am working with an integer linear optimization problem of the form Find $\vec{x}$ such that $\mathbf{A}\vec{x} < 0$ and such that the sum of the entries of $\vec{x}$ is as small as possible. ...
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### Does this linear integer optimization problem have a unique antichain of solutions?

I am working with an integer linear optimization problem which, abstractly, is: Find $\vec{x}$ such that $\mathbf{A}\cdot \vec{x} \leq -1$, and such that the sum of the entries of $\vec{x}$ is as ...
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### Constraint formulation for variable cleaning times - MILP optimization

I have a Mixed Integer Linear Problem where I want to schedule the production of different orders ($O$) in which in each order, there is only one product ($P$) produced. Each order can be produced ...
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### How to apply integer cut to a simple MILP?

I'm self-studying on cutting plane methods, and I'm reviewing the following problem from Bertsimas' book (see below). I know what cutting plane methods do, and how they eliminate infeasible solutions ...
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### MILP to LP; is it possible?

There is a machine that can produce $x_t \in [0, \overline x]$ quantities of a good in hour $t \in T = \{1, 2, \ldots, 8760\}$. The production of a unit has linear costs of $k_t \in \mathbb R_+$. The ...
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### MILP constraint for connected node selection

I am formulating constraints for a network as shown in Figure . Blue circles represent a set of nodes, $N = \{1, 2, \ldots, 5\}$. Three different types of devices are connected to different nodes in ...
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### Maximizing the summation of reward of some users (waiting in different positions and lines) using reinforcement learning or other learning methods

There is a mathematical problem that I think can be solved using reinforcement learning and it would be great if you could help me with it. Some users are standing in some lines. There are N lines. In ...
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### How to write if statement for 3 dimensional problem linear programming

I have a problem regarding formulating the following with math notation. My goal is that if shop i’s arrival time is lower than all the other shop’s arrival times, then shop i must be allocated to the ...
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### Can I linearize this piecewise function so it can be used in an objective function for my LP optimization model?

Thanks for taking the time to read this. I am looking for methods to linearize this piecewise function so that it can be added to an optimization function of a linear programming problem. I figured ...
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### Max condition in Integer programming and MILP

Assume you have 2 binary variables $b$ and $c$. Suppose you want another binary variable, $a$ to be $\max(b,c)$ always. How would you represent this in the constraints of an integer program or of a ...
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### Modeling of a special form of the precedence constraint

Crossposted at Operations Research SE There exists a scheduling problem in which some tasks should be processed on some resources. Additionally, each task needs to be assigned to a specific position ...
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### Linearization of constraint in linear programming

I have the following decision variables: $x$, which is binary, and $a, b, c > 0$, which are continuous. I would like to express in linear form for a linear programming model the following ...
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### Formulating a particular constraint

I have a problem setting similar to bin packing but not exactly. I have to put the few boxes of certain dimensions in a square area besides each other. Like a grid. The boxes should be placed around ...
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### The optimal solution of a relaxation is optimal for the original problem

The question concerns the topic of relaxations in optimization problems. Moreover, proving the following, straightforward proposition. Let $z^P$ be the optimal solution for the problem $P$, $z^R$ be ...
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### What set of crops provide a complete diet? [closed]

I'm trying to find what combination and quantity of crops I should grow to provide a complete diet. Basically, I have a set of n possible crops that I can grow, and I have m nutritional requirements. ...
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