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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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is there a way in OPL to maximize the minimun of a list of decision variables?

I want to do something like this: dvar Q [1..10]; maximize min(i in 1..10) Q[i] ; Q has 10 different values which i don´t know, i want that the minimun of all those values be as high as possible But this doesn´t allow me to use Q which is a…
user16555238
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Identifying column and row clusters with linear programming

I believe that the question Is there a good way to do this type of mining? could be solved using linear programming techniques. But I am completely new to this and do not know the best way to frame this as a minimization. Would the following…
andrew cooke
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Pyomo Error: No value for uninitialized NumericValue object Variable

I have built a multiobjective model and I am solving this with an augmented epsilon method package for pyomo, which is available in Github. The model gives me the objective values, but when I try to print out some individual values of variables, it…
Lily Cole
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R Manipulating List of Lists With Conditions / Joining Data

I have the following data showing 5 possible kids to invite to a party and what neighborhoods they live in. I have a list of solutions as well (binary indicators of whether the kid is invited or not; e.g., the first solution invites Kelly, Gina, and…
Kathy
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Adding decision variables in gurobi

I am new to gurobipy and I am trying to model this linear program the objective value and constraints are seen in this picture: This is the code I have written for the objective function and constraints #objective function obj_fn = -…
imsorry
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Linear Optimization in R using lpSolve Package

I am learning about linear optimization in R using the lpSolve package. I am wondering if the lp() function in R can sometimes find a solution that is a saddle point and not the true min/max. I have looked at the documentation of the package and I…
Jason
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Is this optimization algorithm a linear programming problem?

I am trying to solve a variant of the multidimensional multiple knapsack problem which tries to optimize the values in each knapsack so that a percentage of each of them can be “taken” and added to create a “final knapsack” with the ideal values.…
imsorry
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How to use nested IF-THEN constraints in DOCPLEX (Python)?

I am modeling the situation I want using python cplex. While using it, a few questions arose, and these are: Can I use nested IF-THEN constraints in CPLEX? First, I could find below how to use the basic IF-THEN constraint. How to use Continuous…
pioneer
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function for ```model += constraint_lhs == constraint_rhs``` in pulp python

I'm solving an LP using pulp. I want to add constraints to my model. Most friendly way is : model += lhs == rhs When we want to add constraints using apply method in pandas.DataFrame, since lambda methods don't take += sign in them, we need to do…
mufassir
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Scipy Linear Programming returns False for success

I am working on a project about Transportation Network Analysis. My network contains data such as nodes, edges, free-flow travel times, capacity, etc. I need to find the volume of edges (links) by using the Frank-Wolf algorithm. I used…
Mohammad Rahmani
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Pulp Solver always returning "Optimal" with elastic constraints

I am currently developing a solver to return an optimized set of questions based off of an item response theory 3pl equation. Initially I developed this without any "elasticity" in the constraints, to meet specific targets. However I found the…
jshbrmn
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How can I check if a solution of an LP is unique?

I want to check if my linear program has just one solution or infinite ones. How can I do that using PuLP?
prince99
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Pyomo mapping sets

I am new to Pyomo and python and am currently trying to build a MILP model. It'd be great if someone can help me out on this. So in my production model, I have packing families,pf, and a packing line,l, can handle a packing family at a time. I also…
Lily Cole
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Implementing binary constraint in PuLP Objective Function

I'm trying to determine the maximum revenue that can be earned from a battery connected to the grid using linear programming. The battery can earn revenues in two markets, the energy market and the frequency market. My model is throwing an error…
sharkdawg
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How to encourage a balanced solution in ojAlgo ExpressionBasedModel

I have the following model: ExpressionsBasedModel model = new ExpressionsBasedModel(); Variable va = model.addVariable("va") .lower(0); Variable vb = model.addVariable("vb") .lower(0); …
elcheapogary
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