# Questions tagged [simplex]

For questions related to the simplex method for linear programming (LP), which solves LPs optimally by moving iteratively from in corner point of the feasible region to a better one.

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### Best way to add dummy to transportation problem? Zero cost will be always chosen first?

I know that an unbalanced transportation problem could be made a balanced transportation problem by adding a dummy node which equals the difference between demand and supply. In literature, dummy ...
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### Transformations that leave the linear program unchanged

A typical linear program is written as $$L_0:\min_{x \geq 0; A^\top x \leq b}c^\top x.$$ Here, $x \in \mathbb{R}^n$, $c \in \mathbb{R}^n$, $A \in \mathbb{R}^{m \times n}$, and $b \in \mathbb{R}^m$. ...
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### warmstarting simplex algorithm- how much can problems differ from each other?

I'm working on an implementation of the simplex algorithm. I want to solve problems in real time every 30 minutes. They could be interpreted as a classic transportation problem. I couldn't really say ...
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### Simplex (GLPK) doesn't find a feasible solution on this simple assignment problem, but there is an obvious one

Problem Assign 11 projects to 11 students, based on their preference. For this example, each students chooses only one project, for simplicity shake (as shown below). Student 1 one chooses project 1, ...
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### Provide basic solution to CLP

I'm using Pyomo to formulate an LP with approx 500,000 constraints and 200,000 decision variables. The LP is solved using CLP. Some instances fail to return even a feasible solution after many ...
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### Simplex algorithm and extreme points

For this question my short-hand is LP = linear program, BFS = basic feasible solution, SEF = standard equality form. Since the Simplex algorithm iterates from extreme point to extreme point (...
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### Simplex - Network flow problem : Arc from 1 to P with infinite capacity

The Network - Maximum flow problem below aims to find the maximum flow using simplex method : With the LP as follow : LP : \begin{Bmatrix} Z(Max) = \sum_{i=1}^{m} fi \\ Af =0 \end{Bmatrix} ...
653 views

### Linear optimization problem with user-defined cost function

I have a linear optimization problem for which I am looking for a suitable optimization solution that can fulfill my requirements. Here is an explanation of the optimization problem: There are a ...
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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?
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### Does anyone have the criss cross algorithm programming code to solve linear programming problems?

I have a project that requires programming code for the simplex algorithm and criss-cross algorithm. The purpose of this project is to compare the two methods. I've tried to find it, but the ...
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### Specific usecase of two-phase simplex algorithm

The problem below aims to find to most optimal way to transport the fuel : A company Er must transport a type of fuel from its two refineries Ra and Rb to its two points of sale PV1 and PV2. The ...
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### On solving the Restricted Master Problem in Column Generation technique

I am working on developing a column generation (CG) based optimization framework for a large-scale airline crew pairing problem (a set-covering problem). First, I generate an initial feasible solution ...
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### Manually indicate initial basis for coin-or lp solver CLP

I have a set partitioning formulation with each constraint being an equality constraint to meet the given demand (right-hand side of the constraint). For each constraint, I have a slack and a surplus ...
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### Is the iteration-limited Simplex dual solution of a MIP node useful?

Idea Sometimes I encounter problems where Simplex spends many iterations for final convergence to the optimal objective value. Let's suppose, this happens when solving branch and bound-tree nodes as ...
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### Solving a minimization problem using a Simplex method

There is a method of solving a minimization problem using the simplex method where you just need to multiply the objective function by -ve sign and then solve it using the simplex method. All you need ...
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### Derivations for two formulae for obtaining optimal dual variable values from the optimal primal tableau

We're being taught Industrial Engineering and Operations Research for the first time this semester. Referring to the book by Hamdy A. Taha, I noticed the mention of two formulae for swiftly obtaining ...
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### In Linear programming, how to determine if shadow price does not change linearly?

As the title says, in linear programming, is there a way to determine that the shadow price does not change linearly for a resource? I understand one way is to simulate but is there a way to tell ...
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### All optimal solutions

I have a following problem: If I have some function $aX+bY+cZ+mD+nF$ and I want to maximize it and have some constraints, how can I find ALL solutions for this maximum value of the function? To sum ...
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### Preemptive Goal programming by fixing nonbasic variables with non-zero reduced costs

I have been using the method of fixing nonbasic variables with non-zero reduced costs to do preemptive goal programming. It works for the most part. But I have recently noticed in a certain instance ...
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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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### Demonstrating a given solution is basic for a MCFP?

Given a minimum-cost flow problem, how could I go about demonstrating that a specific solution (as sets of basic and non-basic (!) arcs that build a rooted spanning tree for a given graph) is basic ...
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### Introducing a big M variable in given equations

While I do understand the general workings of the Big-M-method I am struggling with the following sample exercise, in which the Big-M-method has to be used to find a first feasible solution: \begin{...
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### How to access neighboring extreme points to an optimal extreme point of an LP?

Suppose that I have access to an optimal non-degenerate extreme point of an LP. I need to find some $\epsilon$-optimal extreme points. That is, a point $x$ where $c'x \le z^{*} + \epsilon$. One way ...
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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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### Simplex-Implementations in professional Solvers

Which non-textbook variants (primal/dual, revised) and techniques (e.g. steepest-edge) do professional solvers like Xpress, CPLEX, CLP use, to get the best out of the simplex algorithm? This ...
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### Guidelines for Linear Optimization approaches?

When solving a Linear Optimization model (or Linear Program), there are a lot of solution approaches. Just to name a few: Primal Simplex Dual Simplex Ellipsoid Method (as if) ...
Consider the following simple integer program \begin{array}{ll} \text{maximize} & 3 x_1 - x_2\\ \text{subject to} & 3x_1 - x_2 \leqslant 3 \\ & -5x_1 - 4x_2 \leqslant -10 \\ & ...