# Questions tagged [integer-programming]

For questions about mathematical optimization problems involving binary or general integer variables.

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### Capacitated Maximum Coverage Location Problem, Python and Gurobi

I am building a variant of the maximum coverage location model and want to limit the amount of points that each "facility" can cover. I am using Gurobi optimization . I have tried using the ...
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### Need help with an appointment scheduling problem

I am currently stuck on writing a linear programming model to describe the process of appointment scheduling for an Oncological Center. I wanted to share it with you guys and see if anyone here could ...
68 views

### An efficient Integer programming model for the minimum spanning tree problem?

Let $T=(V, E')$ be a spanning tree of a graph $G=(V, E)$. Rather than verifying for any subset of vertices $S\subseteq V$ that $|E'(S)|=|S|-1$, is there an efficient way to satisfy the spanning tree ...
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### IP model for k-rooted spanning forest

I am looking for an IP model for finding a $k$-rooted minimum spanning forest on an undirected graph $G$. Given a set of roots $R$ and a set of nodes $N$ $(R\cap N=\emptyset)$, I would find a forest ...
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### How to linearize a max min objective function?

Let us suppose that I have a $\max \min$ objective function that only depends on one set of variables: $\underset{x}\max \underset{y}\min dy$ Associated with the linear set of constraints and right ...
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### Generating numbers that should add up to a fixed value while they follow a known distribution

Suppose a perishable item that is associated with a shelf life $m\in \mathcal{M} = \{1,\dots,M\}$. We have a periodic review system with stock level $S$, i.e., based on the inventory level of the item,...
125 views

### Modeling that there is no feasible solution to a linear system in mixed integer programming

My question is about how to construct a mixed integer programming to model that there is no feasible solution to a given linear system. Specifically, given $x\in \mathbb{R}^{n}$ and $z\in \{0,1\}^{d}$,...
102 views

### 0 1 solution of linear programming problem with only equality constraints

I have a linear programming problem $LP$ where all the variables $x_{i}$ take value in $\left[0, 1\right]$ (that is $0\leq x_{i} \leq 1$). All the constraints are as follow: $a_{1}+a_{2}+a_{3}=1$ that ...
107 views

### Assignment problem with variable tasks to be done

I'm dealing with a kind of assignment problem, in which I have a set of tasks $t$ to be executed by machines $w$, but these tasks depend on the variatns $v$ of components $m$ being selected, which is ...
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### How can I linearise this nonlinear proportional relation constraint?

My optimisation problem has a constraint in the form \begin{array}{*{35}{l}} \text{}\hspace{16.5mm}\text{ C4:} \hspace{2mm}\sum_{u=1}^U d_{u,1}L_{u}:\sum_{u=1}^U d_{u,2}L_{u}:\cdots:\...
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### Can I solve the separation problem efficiently, when I have access to an optimization oracle?

Assume I have given a convex feasible set $X$ and I have an oracle that can optimize some linear objective function $c$ over $X$. Assume that I have given a point $r$. I want to solve the separation ...
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### What underlies intlinprog in MATLAB?

When a paper says they used the intlinprog in MATLAB to solve an integer program, what system actually does the solving? I have seen documentation about Gurobi and MATLAB: does Gurobi always provide ...
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### Flexible Job Shop with Preemption

I'm trying to solve a flexible job shop problem variant that has precedence constraints on jobs along with a few other issues. We have a MIP formulation and also a simulated annealing algorithm to ...
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### Constraint programming and scheduling issues

I have a constraint problem that I need to resolve, but I did not how know to model the problem: I have 11 employees, I will name them from $a$ to $k$: $\{a,b,c,d,e,f,g,h,i,j,k\}$. I have a small ...