# Questions tagged [linear-programming]

Questions on linear programming, the optimization of a linear function subject to linear constraints.

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### Eliminating a free variable in a linear programming problem

Consider the following linear model. \begin{align} \min&\quad z = c^{t}x\\ \mathrm{s.t.}&\quad Ax = b\\ &\quad e^{t} x = 1 \\ &\quad x_{i}\geqslant0 \quad \forall i \in \{1,...,n-1\} \...
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### Why do we need specific linear programming methods now?

I've recently studied different methods of solving linear programming (LP) problems, like simplex method, Dantzig–Wolfe decomposition, Kornai–Liptak decomposition. I suppose all these methods were a ...
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### Formulating problem in CVX

Crossposted on Stack Overflow I am new to CVX and I have to solve the following optimization problem. I have written the code for it and also changed the equalities to make it convex but I think ...
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### How do I set up the initial simplex tableau?

Maximize: Z = x1 + 3x3 Subject to: x1 + 2x2 + 7x3 = 4 x1 + 3x2 + x3 = 5 x1, x2, x3 $\ge$ 0 I am confused on how to put it into a simplex tableau because the constraints are already equations. I know ...
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### Linear Programming - Job Scheduling Domain Mapping To Binary Decisions

I am trying to maximise machine profit subject to a repair plan (job schedule), but cannot seem to map between the integer domain from the job schedule to the binary domain for the revenue model in ...
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### Help in expressing in McCormick Envelope

The statement which I want to express in McCormick envelope is $\sum_ix_iM_{ij}\leq F_j$ for all $j$ The initial McCormick envelope I wrote where $w_{ij}=x_iM_{ij}$, is: $\sum_iw_{ij}\leq F_j$ for all ...
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### Name of Particular Constrained Optimization Problem

I am writing to ask if any of you know what is the name in the research literature of a particular constrained optimization problem I am facing. I would like to find a general name so that I can ...
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### Linear Optimization with Ratio of Constraint Variables

I found a similar question at https://math.stackexchange.com/q/413317 but I could not comprehend the explanation. I am required to optimize the sale for the following question: There are two kinds of ...
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### Transforming inequality constraints into equality constraints

Intro: Suppose we want to find whether the feasibility region of this linear programming is non-empty: $$(1) \quad Ax \leq b\\ \quad \quad C x = 0$$ Suppose that verifying the feasibility of (1) is ...
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### Mixed Integer Linear Programming problem maximizing projects but they can share resources

I need help with this optimization problem. I'm sharing a simplified version for easier discussion. For example, I have projects $x_i$ where $i=1,2,...5$. Each project has factors $a_i, b_i, c_i$ with ...
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### Hungarian algorithm / assignment problem with cost function depending on resultant matching

The standard Hungarian algorithm solves the problem of assigning n workers to n jobs with a given cost function. In my variant, the cost function depends on the final matching produced by the ...