# 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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### How to linearize this multiplicative constraint?

I have a constraint in the form $\sqrt{|\sum_{c\in C}{h_cw_c}|^2}\ge\sqrt{x}\zeta$ Here, $h_c$ is s row vector (know), $w_c$ is a column vector (variable). $x$ and $\zeta$ are also optimization ...
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### How can I see the engine log when solving a LP using pulp (python)?

I wonder which command should I use to see how the steps the pulp solver is doing when solving a linear program.
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### Determine set of “arbitrage-free” regional prices

I am seeking for a way how to determine set of "arbitrage-free" regional prices for a single commodity market. There are $N>1$ production units with costs $C^{prod}_i, i=1,\dots,N$ and ...
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### Reading MPS file for linear programming and reconstructing the Optimization model

Are you aware of any tutorial that can help me learn on how to reconstruct the objective function and constraints from a MPS file once it's loaded in MATLAB. I can load the mps file given to me and ...
41 views

### High-mix manufacturing capacity

I'm not an expert in OR but I would like to determine what is the maximum manufacturing capacity of a plant (or how much a plant can produce of mix products). Each person in the plant has a known set ...
288 views

### Canonical form of a linear program

I have a linear programming problem that I want to write in the canonical form: \begin{align}\min&\quad c^\top X\\\text{s.t.}&\quad A\cdot X\le b\end{align} The problem is given by \begin{...
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242 views

### What is wrong with my linear programming model?

I tried solving this problem Here is my cplex code I have mentioned stored[month] as float+ but in the final result I get negative values. What is wrong with my model?
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### How can I formulate this specific if-then constraint?

IF $\sum\limits_d X_{i,d}\ge6$ THEN $Y_i = 1$ (strictly) AND IF $\sum\limits_d X_{i,d}<6$ THEN $Y_i = 0$ (strictly) $X$ and $Y$ are binary variables. What I'm actually trying to do is to charge the ...
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### How to form math model to solve this problem using cplex

Hiring company has the following requirement within a year; week 1 to 5: 20 week 6 to 20: 40 week 21 to 40: 35 week 41 to 60: 55 week 61 to 80:75 week 81 to 100: 60 Training time for an ...
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### How can I find the shortest path for all nodes in a graph from a source $s$?

This is the shortest path problem. I've used a model where we can find the shortest path between the source and a specified destination. The idea behind this model is that we assign a flow of 1 for ...
38 views

### Adding slack nodes to min cost network flows

I have the following question. I want to clarify couple of points. As you can see, total demand and total supply does not match, we do not have enough demand. What I want to ask is: Do we need to ...
197 views

### Is optimal solution to dual not unique if optimal solution to the primal is degenerate?

If optimal solution to the primal is degenerate, does it necessarily follow that optimal solution to dual not unique? That is, is uniqueness an unnecessary assumption? Spin-off from here. In my ...
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### How to deal with the sub-problem with zero reduced cost in D-W decomposition

The specific linear programme has an optimal solution as $x_1 = 0.66$, $x_2 = 1.33$, $x_3 = 12.2$, $x_4 = 0.0$ and the objective value is $33.3$. While the problem is solved by D-W decomposition ...
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### Minimum cost flow problem with negative cost arcs

As far as I know, if there is a directed arc with a negative cost, we change its direction to its opposite and get a positive cost. But in the following question, if we change the direction of the arc ...
39 views

### Multi-objective function normalization

I am trying to solve the multi-objective function of my linear program. Are there another approaches other than the weighted sum approximation?
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### Need help in formulating linear program

Edit: updated my solution for linear programming Can anyone explain the following passage? Both semiconductors and power generation industries also want to buy as many of the remaining units as ...
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### How can I model this Hyperbolic constraint?

In this problem, $\beta_u$, $w_{u,c}$ (a vector of complex elements), $x_u$ are optimization variables. Now, \$||2\sqrt{\frac{\pi_u}{2}}\beta_u; h_{u,c}^{\rm H}w_{u,c}-\frac{1}{2\pi_u}x_u-1||_2\le h_{u,...