# Questions tagged [linear-programming]

For questions related to problems that optimize (i.e., minimize or maximize) a linear objective subject to linear constraints.

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### GLPK: meaning of the "marginal' column in the solution output

I'm using GLPK to solve an LP. I use it through its standalone solver, that I call with the glpsol command, and I get the solution detail written in a file using ...
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### Modeling Linear Program to decide if an inequality is facet

Suppose you have a set of points $v_1,\ldots,v_n$, which are the vertices of the polytope $P=\operatorname{conv}\{v_1,\ldots,v_n\}$ and a linear inequality $a^\top v \leq b$. What would be a linear ...
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### Workforce Scheduling problem - Modelling to minimize resources

I am working on a scheduling program for a service desk. I want to decide the number of people required to come in at each shift. The data I have is: There are 4 overlapping shifts Arrival pattern at ...
320 views

### if-else condition for the objective variable using big M notation

Let $0\leq \beta\leq 1$ be an objective variable. The size of $\beta$ is $N\!\times\!N$. Now, how can I impose the following? if $\beta_{i,j}>0$ then $\beta_{j,i}=0$ Big M notation can be ...
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### Choosing better objective function for vehicle routing problem

I have a graph $G$ and the following variables. $b_{i,j}$ is $(i,j)$ edge is taken or not. $t_{i,j}$ is time to travel $(i,j)$ $A_{i}$, $D_{i}$ are arrival and departure time at node $i$. My first ...
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### What is the Bound Flipping Ratio test?

The bound flipping ratio test (BFRT) appears to be an important feature of modern Simplex implementations. What is it, and how does it work?
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### Negative reduced cost for basic variable

I am observing something unusual : after solving a linear program, some basic variables have negative reduced costs (instead of $0$) : ...
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### Linearizing objective function with absolute differences

I want to turn this objective function $$\max \sum_{i=1}^{N-1} \sum_{j=i+1}^N |TX_i^T - TX_j^T|$$ where $T$ is just a vector with increasing integers (e.g $[1 \ 2]$) and $X_i$ is a vector ...
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### Proof that the leaving variable cannot be selected as the entering one in the next round

Using the Dantzig's pivoting rule, can it be proven that the leaving variable of one round cannot be selected as the entering variable in the next round?