# Questions tagged [integer-programming]

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

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### Modeling Multi-Agent Collision in Google CP-SAT Solver

I would like to implement a solution for Multi-Agent Pathfinding Problem using Google's CP-SAT Solver. How do I implement the constraint that prohibits 2 or more agents from occupying the same cell at ...
403 views

### How to model Max-Cut as ILP

I want to model Max-Cut in IBM's CPLEX, but I fail at modeling the objective function. My attempt is to use is to sum the XOR of inclusion for vertices of each edge, as exactly then an edge is ...
1 vote
235 views

### Google CP-SAT Infeasible ILP for Large Problem Area

I am trying to generate a shortest path between source and sink in a square grid of cells. I am using the Google CP-SAT solver ...
67 views

### Good encoding for grid layout problem

How would you encode the problem given by https://oeis.org/A337663 with an off-the-shelf solver? You need to lay out $n$ ones and $2, 3, ..., m$ on an infinite grid, for $m$ as large as possible. For ...
359 views

### Is it possible to merge two objective functions using the LpSolve package in R?

I have been using the LpSolve package to solve a minimization problem in my final course work, but I need to reconcile this problem with a maximization problem. Conducting several researches, I ...
1 vote
146 views

### How to model this problem?

I have recently tasked with a problem in which I have to locate electric vehicle charging points (new) keeping in mind that there continue to exist older charging points. The problem is to model the ...
589 views

### Modeling an either-or-constraint

We would like to model a constraint for an assignment problem that dictates that either assign a specific subset of nodes $I\subset\mathcal{I}$ to a specific subset of nodes $J\subset\mathcal{J}$, or ... 1k views

### How can we write a binary variable as a power to a constant number?

Let $x_{i,j}$ be a two-dimensional binary variable. Is it possible to write $x_{i,j}$ as a power to a number? For example: $$1- 0.3^{x_{i,j}}$$
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257 views

### Binary decision variable to indicate whether a continous decision variable is equal to its upper bound

Given a continuous nonnegative decision variable $x\in [0,T]$ bounded by $T$, how can we enforce a relation between $x$ and another binary decision variable $y$ such that when $x$ is equal to its ...
153 views

### Binary decision variable to indicate whether an inequality is satisfied or not

I have a problem where I have a continuous decision variable (let's call it $m$) that is bounded between $(0, T]$ where $T>0$ is a predefined parameter. I also have another binary decision variable ...
246 views

### How to make Gurobi solve huge LP/IP model with only using A,b,c matrices?

I work on the scaling of MIP. I have scaled the A,b,c matrices of the huge original model. These matrices have more than 25000 rows and columns. I need to make Gurobi solve the scaled model. Normally, ...
56 views

### How does a ratio of fixed cost to variable cost affect the problem difficulty?

I am working on an OR scheduling problem where OR opening cost is considered a fixed cost when a surgery is scheduled. If OR is used beyond a certain time, overtime cost is incurred. I would like to ...
2k views

### How to compute all paths between two given nodes in a network?

In this post, Erwin Kalvelagen describes a method to compute all paths between two nodes in a given network, such that: no arc is used more than once a given path does not contain more than $M$ arcs ...
519 views

### How to formulate and solve a variant of the Cutting Stock Problem

I should mention up front that I'm new to this forum and operations research in general. A problem has come up recently at work that I'm having a tough time solving. Our machine shop acquires many ...