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 can I formulate an LP or heuristic solution for this problem?

[I welcome any alternate or simplified formulation of my problem] I have an optimization problem. See the attached figure which is self explanatory. The solid line is intended signal, the dashed lines ...
46 views

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 ...
57 views

Maximum bipartite matching with breakpoints in edge weight function

I am looking for an analogy to the problem I am facing or better yet a paper or even code. I have: Nodes from set A and B. Edges are from a single A to many B. I am framing a max bipartite matching ...
162 views

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 ...
100 views

Obtaining the system of irredundant inequalities from a set of inequalities using CPLEX

Given a linear system of inequalities $Ax \geq b$, I would ideally like to compute the irredundant set for those set of inequalities. I know how to do so mathematically, but I was wondering if there ...
3k views

Is there a Linear Programming Library that natively supports fractions instead of floating point arithmetic?

If one recalls how the Simplex method is taught by hand in most LP classes it takes place entirely in $\mathbb{Q}$. All operations yield exact fractions. For this reason I'm looking for linear ...
44 views

Simplex method on graphs: How do I find a basic solution using the Ford-Fulkerson algorithm?

I'm tasked with solving a minimal cost flow problem. I'm asked to first use the Ford-Fulkerson algorithm on my graph to find a basic solution that will then be used to do the simplex method on that ...
53 views

Estimating multistop routing costs

In many OR problems, it is sometimes a good idea (or necessary) to relax routing constraints. An example of this occurs in the classical facility location problem, where a warehouse can send out a ...
154 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 ...
74 views

How to linearize $f(x,y) = (ax+by)/(x+y)$?

I have a problem which is mainly linear but it has a non-linear component. The objective function is obj = Linear_term + $c*f(x,y)$ where, $f(x,y) = (G_1 x_1 + G_2 x_2)/(x_1 + x_2)$. The decision ...
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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 ...
74 views

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 ...