# Questions tagged [integer-programming]

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### Integer Linear programming formulation if then condition

I want to create constraints such that I can implement the following condition: Let A be an integer variable >= 0 with an upper bound of 12 I want to introduce the following variable B also an ...
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### Minimum spanning tree formulation

Can any expert explain the reasoning behind the constraint in the following formulation of the minimum spanning tree? To formulate the minimum-cost spanning tree (MST) problem as an LP, we ...
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### Integrality gap and LP-rounding

I have a doubt about integrality gap. If I know that there is no integrality gap for a given problem, i.e.: $$\frac{\mathrm{OPT}(\mathrm{ILP})}{\mathrm{OPT}(\mathrm{LP})} = 1 \text{ (right?)},$$ ...
19 views

### Enumerate all solutions to integer programming problem

How can I list all feasible solutions to an integer program? Is there an algorithm whose running time is reasonably related to the total number of such solutions?
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### Finding all feasible solutions to a multiple-knapsack program

How can I find all feasible solutions to a 0-1 integer program that I have based on a knapsack-style problem? I have $n$ items and $m$ knapsacks. Each knapsack has a space limitation and each item ...
52 views

### Integer programming to MAX-SAT translation

Reading A Comparison of Methods for Solving MAX-SAT Problems, I can see that a MAX-SAT problem can be translated to an integer programming (IP) problem. Definition of MAX-SAT [Wikipedia]: The ...
173 views

### Linear programming maximizes the minimum distance problem

I have a problem with creating an equation for linear programming solver. Company wants to open stores in k cities. For the purpose of even coverage of the entire ...
18 views

### Formulate the mathematical model to find the optimal solution

A, B, C and D are standing on the east bank of a river and wish to cross to the west side using a boat. The boat can hold at most two people at a time. A, being the most athletic, can row across the ...
25 views

### Knapsack Problem Via Column Generation

If I were to solve the linear relaxation of a knapsack problem via column generation how could I model the master problem and pricing subproblem? Given a set $N$ of items with value $v_{i}$ and weight ...
43 views

### Convex quadratic approximation to binary linear programming

Munapo (2016, American Journal of Operations Research, http://dx.doi.org/10.4236/ajor.2016.61001) purports to have a proof that binary linear programming  is solvable in polynomial time, and hence ...
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### Check a variable within a range with a binary variable [closed]

I have a value, a, it can be any value from 0 to 1. In an integer linear program, how can I formulate a constraint that uses a binary variable, y, to determine whether a is within a range of 0 and 1 ...
137 views

### Boolean variable that captures whether an inequality holds

I have an integer linear program with variables $x_1,\dots,x_n$. I have an inequality $a_1 x_1 + \dots + a_n x_n \ge b$ that I care about; it may or may or not hold. I want to introduce a boolean ...
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### Big M method for continuous variables

Is there any way to model the big M method for continuous variables? Something similar to this but $B, C \in \mathbb{R}_{\geq 0}$ and $A\in\{0,1\}$. Due to the precision problem, when the $B$ and $C$ ...
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### (M)ILP overlap of two intervals

I got an ILP Model where $c_i$ represents the starting time for a visit$_i$. $c_i$ is already constraint by a number of constraints, one is $c_i > 0$. I have now outside of my model 0 or multiple ...
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### How does prefix summing the count histogram in counting sort result in an array of output indices?

My implementation of counting sort is based on the description I found here. I've also included my code in this REPL, but here it is: ...
128 views

### What is the right term/theory for prediction of Binary Variables based upon their continuous value?

I am working with a linear programming problem in which we have around 3500 binary variables. Usually IBM's Cplex takes around 72 hours to get an objective with a gap of around 15-20% with best ...
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### Computational complexity of maximizing sum of rational functions

I have a optimization problem: $$\max_z\ \sum_{i=1}^n \frac{W_i}{D_i - z_i} \quad \text{s.t.}\ \sum_{i=1}^n z_i \leq k, z_i \in [0,k],$$ where each $W_i$, $D_i$ are constants and $z_i$ are integer ...