# 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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### Conditional modelling of a binary variable based on the values of two continous variables

I want to model a binary variable $(b)$ from two continous variables $(x_{in},\:x_{out})$. These variables are $0\leq x_{in} \leq x_{max},\: 0\leq x_{out} \leq x_{max})$. I want the following three ...
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### Excel Solver Linear Optimization : Formula Debugging

I am trying to get a optimization model to work correctly. The background is to use the solver to find a circuit (AC or DC) that would minimize cost. I am trying to use binary variables so the ...
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### How can I convert non-linear constraint to linear one?

Problem: Suppose I have $n$ finished products and each product has its own completion time, such as C$_i$ (C$_i$=completion time of product $i$, where $i=\{1,2,...,n\}$). These products will be ...
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1 vote
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### MIP- If then with either or

I need something like this It may sound silly but I couldn't find a way to express this. x,te,ts decision variables, x bool, te,ts >=0; if $x[m,i]+x[m,j]-1 > 0$ then either $te[i]+d-ts[j]<=0$ ...
1 vote
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### Relationship between number of explored nodes and solution space for a MILP problem

I'm using CPLEX through AMPL to solve a problem using two equivalent formulations. The problem is being solved to global optimality. However, one of the formulations is faster than the other. I have ...
1 vote
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### assymetric graph coloring formulation

I'm reading this articel which is about formulating VCP to eleminate symmetric solution, they say: And then In order to eliminate some of the symmetrical solutions, they say these two constraint is ...
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### Suboptimality of QR decomposition based integer least squares

Given a real n-by-m matrix $A$ and a real vector $y$, the integer least squares problem is to find an integer-valued vector $x$ that minimizes $\left|Ax-y\right|_2^2$. A typical solution when $A$ is ...
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### Formulate constraints to an Integer programming: How to algebraically formulate a geometric constraint that the colored grids must form a rectangle?

I am stuck in a constraint formulation of a discrete optimization problem. Consider a board of Cartesian grids (M rows by N columns). We are going to color some grids among them. There is a geometric ...
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### Linearize optimization problem with absolute value

Is there any method to linearize the following optimization problem? \begin{align} \min_{x,y} &~~ c~[x; y] \\ \text{s.t.} &~~ \sum x\leq \alpha_1 \\ &~~ \sum |y|\leq \alpha_2 \\ &~~ \...
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### How much running time does solving a Mixed Integer Linear Program need?

Given a mixed integer linear program with $m$ constraints and $n$ variables how much time do we need to solve this? I know that MIPs like IPs are in general NP-hard. Nevertheless for IPs one can show ...
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### Alternate approach to formulate this MIP

This is in concern to reformulating a previously formulated set of linear equations in my previous question: This is the link \begin{align} y_i &= 1 &&\text{for $i\in\{0,n+1\}$} \tag1 \\ \...
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### Reformulate IF-statement in mathematical optimization

I have an optimization problem that chooses which location must be opened based on a set of possible locations. And per location we have a certain amount of available spots from which we must buy a ...
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### How to convert non-linear equation to linear equation [closed]

I have a problem with X machines, each one with a specific production. All the production needs to be sent to an specific place via different routes which may or may be not cheaper. I need to minimize ...
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### Mixed Integer Programming - variable that equals the sign of an expression

I want to define the following: y = 1 if x<=th = 0 otherwise Currently I'm doing the following: Let's say we know the lower ...
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### Converting constraint with absolute value equation into linear programming constraint

I have following constraints, w1 = | XR1 - 20 | where w1 is a binary variable and XR1 is a nonnegative variable. How can I convert this into a linear programming ...
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### Modeling contiguity of machine processing in a flow shop environment via a MIP

I'm working on a Mixed-Integer-Programing (MIP) formulation for a flow shop scheduling problem. One of the requirements/wishes is that for each machine $i$, processing should be contiguous, or at ...
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### Benders Decomposition Convergence

I have found James Murphy's "Benders, Nested Benders and Stochastic Programming: An Intuitive Introduction" (http://www.optimization-online.org/DB_FILE/2013/12/4157.pdf) to be quite helpful ...
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### How to write elseif into linear programming

Given: If a < 0 and c < 0: d = 1 else: d = 0 I was wondering how to write it into statement of linear statement?
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### why the code assigns multiple jobs on same position on machines

scheduling n jobs on m machines, each job has a different processing time on each machine. all schedule has n positions indexed by l as l =0,1,...,n as position 0 for dummy job Used this mathematical ...
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1 vote
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### Linear Programming - Job Scheduling Domain Mapping To Binary Decisions

I am trying to maximise machine profit subject to a repair plan (job schedule), but cannot seem to map between the integer domain from the job schedule to the binary domain for the revenue model in ...
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### The difference between subtour-elimination constraints in the symmetric and asymmetric TSP

We know that there are lots of formulations for traveling salesman problem. Some of them are based on the directed graph (asymmetric) and others are based on the undirected graph (symmetric). Also, ...
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### What are Bounds in Branch Bound

I am looking at a video to understand branch and bound more. Specifically, the one found at this link: (21) Ch06-03 Branch and Bound Method (B&B) - YouTube. I have two questions: Around 9:44, I'm ...
I have a MILP looks like following: $$min \sum_i capacity[i] * weight[i]$$ where i=[Mid_North_1, Mid_North_2, North_Mid_1, North_Mid_2] Basically I got 2 sites ...