# Questions tagged [simplex-method]

Questions that relates to the "simplex algorithm", from the mathematical optimization field

153 questions
Filter by
Sorted by
Tagged with
11 views

### Optimal Table may change in LPP

If we solve a LPP with let's say 2 constraints with all slack starting variables with non negative right hand side. We get the optimal table. Now suppose we change the constraint coefficient of a ...
• 2,635
34 views

### Initial basic feasible solution for LPP with 'greater than' constraints

While solving a linear programming problem with n variables in m equations (n > m) using the simplex method, an initial feasible solution is found by setting n - m variables to zero. Mostly when ...
• 1
1 vote
13 views

### Linear programming dual simplex method problem [closed]

enter image description here I've this question and I changed the sign for the max Z and then found the dual of primal. But here the problem is that now I have -ve values in ratio. I am thinking of ...
31 views

### Python Native Implementation of Mixed Integer Linear Programming

Is it possible to have pure Python implementation of Mixed Integer Linear Programming, something similar to mip, pulp, cvxpy, etc. - but such simple as https://github.com/ispaneli/lippy - it is ...
25 views

### Finding possible values of entries of a simplex tabeau

While solving a standard form problem, we arrive at the following tableau, with $x_3, x_4, and x_5$ being the basic variables: The entries α, β, γ, δ, η are unknown parameters. We have to determine ...
• 493
1 vote
73 views

### Unbounded slack variables in linear programming problem

I have a linear programming problem: Maximise, $z = x_1 + x_2$ Subject to: $$x_1 + x_2 \ge 10$$ $$2x_1 + x_2 \le 40$$ $$x_1, x_2 \ge 0$$ When I construct the simplex tableau adding 2 slack ...
• 113
19 views

59 views

### Do i have to add an auxiliary variable when adding a new equality constraint at a LP?

For example I have the following problem: \begin{align} &\textrm{min z} = -2x_1 -x_2 +x_3 \\ &\textrm{s.t.} \\ & \qquad x_1 +2x_2 +x_3 \leq 8 \\ & \\ &\quad -x_1 +x_2 -2x_3 \leq 4 ...
85 views

### How does the Simplex method actually work?

I learned about the simplex method, how to pivot by hand before commercial grade solvers were introduced. And I’m still a little foggy on what slack variables and objectives are actually doing. My ...
• 229
299 views

### Why can't we solve a LP problem just by finding all vertices of feasible region and testing the objective function at each vertex?

Why can't we solve a problem just by finding all vertices of the convex polytope of feasible solutions and testing the objective function at each vertex? My guess is basic solution of LP may not be ...
• 159
So i just started with the linear programming topic in my university. And while I was practicing, I found the next question: $$\min Z=3x_1+4x_2-x_3$$ $$\text{Subject to: }x_1+3x_2-x_3\ge1$$ $$2x_1+x_2+... • 21 1 vote 1 answer 209 views ### Initialization of the Network Simplex Method I am studying Chapter 7 (Network Flow Problems) of the book Introduction to Linear Optimization by Bertsimas and Tsitsiklis. On page 286 the authors briefly describe a way to deal with the ... • 689 1 vote 0 answers 40 views ### How is the term for the change of the cost vector in the simplex method derived? Given a minimilization problem of the form: min \ c^t x (c, x \ \in \mathbb{R}^n) where the following constraints have to be met Ax = b (A has dimensions mxn) x \ge 0 (in every entry) rank(... 2 votes 1 answer 290 views ### Is the Simplex Method an exact, approximate or a heuristic method? I'd like to understand whether the simplex method is an exact method (like Branch&Bound, Branch&Cut...), an approximate method or a heuristic method. • 171 1 vote 2 answers 364 views ### How to add a constraint to the final phase of simplex tableau? How does one go about adding a new constraint in the final phase of the simplex tableau? In the case where our optimal solution satisfies the constraint, we can conclude that the optimal solution ... • 25 0 votes 1 answer 147 views ### Linear programming Simplex method f(x) = -2x1 + 3x2 -2x4 -4x5 + x6 -> max constraint: ... 1 vote 2 answers 271 views ### Adjacency of Optimal Basic Feasible Solutions in Linear Programming I am studying linear optimization from the book Introduction to Linear Optimization by Bertsimas and Tsitsiklis and came up with the following question: If a standard form problem$$ \begin{align} \...
Consider a degenerate LP problem: $$\min c^Tx \\\text{subject to: }\qquad\qquad\qquad\qquad\qquad$$ $$Ax=1\quad a_{i,j} \in \{0,1\}$$ $$x\ge0$$ Is it safe to assume given an non-optimal initial basis \$...