# 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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### Is Converting to Standard Form Necessary to Check if a Proposed Solution is a Basis in Linear Programming?

If I have a Lp problem should I make it to standard form and then calculate number of 0s in the proposed solution and compare it to : number of equation - number of variables; And that's for checking ...
1 vote
188 views

### Solver for Flexible Job Shop Scheduling Problem

I have a FJSSP that I would like to solve. However, the jobs in this problem have deadlines and in addition there are setup times between two jobs. Because of this, my objective function is not just ...
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1 vote
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### Computing simplex tableu for a given basis

I found the following problem in my book. I know that I can compute the simplex tableau , let's call it S for a basis X_b=(x_1, x2, x_5)^T as ...
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644 views

### Modelling if elif else conditions as MIP

I have 4 variables. Xl6, Xs6, Pl6, Ps6. I have a constant C as well. Xl6 and Xs6 are binary whereas Pl6 and Ps6 are integers. Also, all variables can take only positive values. I have to implement ...
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150 views

### Vehicle passenger assignment with capacity constraint

Problem Summary To match passengers (the number of passengers) to capacitated vehicles such that the profit is increased. All the vehicles have the same capacity $c$. It is not important to track ...
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### Set null the next set of N values

I'm dealing with a problem I already modelled by using linear programming. The already existing constraints set at 1 groups of contiguous variables (for ex: ...
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91 views

### How to apply smooth approximation to non-linear complementarity constraints?

$P =$ $x, if U \geq U^{max}$ $y, if U^{up} < U < U^{max}$ $z, if U^{down} < U < U^{up}$ $\alpha, if U^{min} < U < U^{down}$ $\beta, if U \leq U^{min}$ Where $P$, and $U$ ...
367 views

### How to deal this L0 norm of a vector of L2 or L1 norms in objective?

I have an optimization variable denoted as ${\bf A\in\mathbb{C}^{100\times 5}}=[{\bf a}_1\hspace{1mm} {\bf a}_2 \hspace{1mm} {\bf a}_3 \hspace{1mm} {\bf a}_4 \hspace{1mm} {\bf a}_5];$ Here, ${\bf a}_1$...
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### Is this constraint with an indicator function nonlinear?

We have two variables $x\geq0$ and $y\in\mathbb{Z}^{0+}$. We have this constraint in our model $$x = \sum_{i = 0}c_i \mathbb{1}_{\{y=i\}}$$ where $c_i$ is a parameter and $\mathbb{1}_{A} = 1$ if $A$ ...
559 views

### Alternative way to restrict an employee to work on multiple jobs

Suppose I have a set of employee $E$ and set of jobs $J$ in a given time horizon $T$. I would like to make sure that no employee works on multiple jobs where each job $e\in E$ takes a certain amount ...
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### Piecewise constraint using big-M notation

I have a piecewise constraint that I am having a hard time converting using big-M modelling. The context is a gym owner that is updating membership costs subject to churn restrictions. The owner can ...
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1 vote