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Questions tagged [linear-programming]

An optimization technique for minimizing or maximizing a function of several variables in the presence of constraints where all relationships are linear.

Linear Programming is a mathematical optimization technique for minimizing or maximizing a linear function of several variables (called the objective function) subject to several linear constraints. The objective function and the set of constraints are collectively called the Linear Program.

The dual Simplex Method is a commonly used solution technique in Linear Programming. There are several commercial and open-source software packages for solving linear programs.

Brief history:
1939. Production, planning. [Kantorovich]
1947. Simplex algorithm. [Dantzig]
1947. Duality. [von Neumann, Dantzig, Gale-Kuhn-Tucker]
1947. Equilibrium theory. [Koopmans]
1948. Berlin airlift. [Dantzig]
1975. Nobel Prize in Economics. [Kantorovich and Koopmans]
1979. Ellipsoid algorithm. [Khachiyan]
1984. Projective-scaling algorithm. [Karmarkar]
1990. Interior-point methods. [Nesterov-Nemirovskii, Mehorta, ...]

External links:

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Constraints with Binary Variable Resulting in Pyscipopt Breaking

I'm trying to add a series of constraints which make use of an indicator function, but it seems to be breaking the solver. This is the original formulation of the constraint: Which has to be broken down into a form suitable for Pyscipopt: I'm…
Winsor-Mavis
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Python Cplex Ceil() Function

ceil() in the constraint Hello, I am studying a published paper. One of the constraints from this paper(which can be shown in the link) requires the ceil() function. We can use the ceil() function at the OPL but I couldn't find the Python…
Tunahan Bilgiç
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IF, THEN, ELSE Integer Constraint Problem

I've been stuck on formulating this logical constraint for a while. What I'm trying to translate into an integer constraint is: if x1i + x2i + x3i is equal to 3, then yi is equal to 1, else yi is equal to 0. I found out this kind of works: x1i + x2i…
Jihong
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Alternative solution on an assigment problem using PuLP

I'm creating a program to solve assignment problems and so far so good, it works properly and in the end, it solves the problem. I'm using the PuLP library. But I just realized that when the problem has alternative solutions (instead of the unique…
Emico
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Graphing Inequalities in matplotlib python

I'm looking to create a program that will randomly generate lines (that are inequalities) and that will show the area that satisfies the constraints. If possible axes would go from 10 to -10 but I'm not too bothered if this is not possible. I've…
George Alderman
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How to Convert or Solve a Non-Linear Optimization Problem with Non-Linear Objective Function & Constraints

Overview I am working on an order allocation problem with variable and fixed costs. The initial formulation of this problem was a linear optimization, but when fixed and variable costs were introduced, it required the formulation to be non-linear…
Ammaar
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Is there a simple way to reduce the value of positive slack variables in MILP?

Recently, I have been learning optimization, and my optimization problem, (minimization), is encoded in a MILP solver which tells me it's infeasible for my model. Hence, I introduced a few positive/negative slack variables. Now, I get a feasible…
GermanShepherd
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ILP formulation for max-weighted cycle in a directed graph

I am currently trying to find the longest cycle in a !directed! graph G = (V,E). For that, I first want to (have to) formulate an integer linear program (ILP). The objective function is in my opinion quite clear: min sum_{e in E} -w_e * x_e (I…
umhk25
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How to add a PuLP constraint that involves two variables that are subject to be optimized

I am a newbie with PuLP and trying to solve a potentially trivial problem. I have some projects that required employees with a certain skillset per project, defined in a matrix project_skill_demand. The projects demand certain (wo)manpower to be…
TomTom101
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How can i solve some AMPL Syntax problem with my code?

I'm learnig to use AMPL to solve some linear programing related problems; but i have a syntax error with a part of my code, and i dont know how to solve it. #Archivo Mod #Conjuntos set T; #Conjunto Periodos set I; #Conjunto Plantas set J;…
Tomás Sánchez Barry
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How to find the non-zero minimum value in the objective function of a mathematical model

It is a mathematical model. x is the 0-1 decision variable, and c is Non-negative coefficients. The tricky problem I'm facing now is how to find that non-zero minimum value in a series of cx. The objective function is as follows. Now, I want to…
Runfeng Yu
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linear programming, how to define multiple variables have same value?

I am trying to have a constraint in my linear programming. I have 3 factories, and each factory has 3 production lines. I have to make sure that in a factory, all the production lines should work for equal number of hours. and max number of hours…
Kashif Mohammed Abdul
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Which CBC Option to relax the integrality requirements (using Pyomo)

I am using the CBC solver with Pyomo and I have been not been able to get an integer solution within the specified time limit when solving a particular model. Is there an option to pass to CBC that can relax the integrality requirements? I notice…
gbullins
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Setting Integrality tolerance in CPLEX and forcing decision variables to take rounded values

I am currently trying to solve a linear program in CPLEX that has three decision variables, one which is binary and the other two are continuous. The problem I have is that instead of giving results for the continuous variables like '10' or '0' it…
Arctic_Skill
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Assignment Problem for Groups - Convert Brute Force Version to Faster Version

I am writing an algorithm to assign event participants break-out rooms and prioritizing groupings of people that have not met before. The cost matrix is 2D matrix where the number is higher if the two participants matched recently. class Matches { …
Anindha
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