Programación lineal : métodos cuantitativos para la toma de decisiones

Citación

Suñe Torrents, Albert; Fonollosa Guardiet, Juan Bautista; Fernández Alarcón, Vicenç; Sallán Leyes, José M. (2016). Programación lineal : métodos cuantitativos para la toma de decisiones. Iniciativa Digital Politècnica.

Abstract

Esta obra es el primer volumen de una colección en que se presentan las técnicas y las aplicaciones de los métodos cuantitativos para la toma de decisiones. Cada volumen desarrolla un método específico para resolver una tipología de problemas. Este volumen pretende introducir al lector en el uso de la programación lineal para resolver problemas de gestión de recursos escasos. Se dedica especialmente a la resolución de problemas propios de las empresas industriales y de servicios. Su propósito principal es capacitar al lector para elaborar modelos de programación lineal, así como utilizar herramientas informáticas para la resolución y la explotación de estos modelos. Los contenidos del volumen introducen la técnica de la programación lineal de forma didáctica y con una orientación práctica con vistas a su aplicación profesional. Son especialmente indicados para estudiantes de grado o máster de ingeniería industrial o de organización.

Disponibilitat

Disponible en https://upcommons.upc.edu/handle/2117/89074

Modeling and Solving Linear Programming with R

Citation

Sallan, Jose M.; Lordan, Oriol; Fernandez, Vicenc (2015). Modeling and Solving Linear Programming with R. Omniascience.

Abstract

Linear programming is one of the most extensively used techniques in the toolbox of quantitative methods of optimization. One of the reasons of the popularity of linear programming is that it allows to model a large variety of situations with a simple framework. Furthermore, a linear program is relatively easy to solve. The simplex method allows to solve most linear programs efficiently, and the Karmarkar interior-point method allows a more efficient solving of some kinds of linear programming. The power of linear programming is greatly enhanced when came the opportunity of solving integer and mixed integer linear programming. In these models all or some of the decision variables are integers, respectively.

In this book we provide a brief introduction to linear programming, together with a set of exercises that introduce some applications of linear programming. We will also provide an introduction to solve linear programming in R. For each problem a possible solution through linear programming is introduced, together with the code to solve it in R and its numerical solution.

Availability

Please see Omniascience website for details, and the repository containing the code used in the book.

Also available through UPCommons in this direction.

A list of linear programming solvers

Here is a list of software available to solve linear programming (LP) models, focused on free software with an R implementation. Most of this software is also able to solve integer linear programming (ILP) and mixed integer linear programming (MILP) models. The list is intended to be extended and more extensively annotated in the future. Don't hesitate to comment below if you see how this list can be extended or enhanced.

lp_solve

lp_solve is a MILP solver, that runs in a large variety of languages. Models can be passed via input files, an API (application programming interface) or an IDE (integrated development environment). It is also embedded into R via the lp_solve and lp_solveAPI packages. The reference guide is quite exhaustive, and a good place to start using this software.

lp_solve reference guide
lp_solve FAQ (MIT)
R package lp_solve
R package lp_solveAPI

GLPK

GLPK stands for GNU Linear Programming Kit. It is a set of callable libraries written in C intended to solve large scale LP, ILP and MILP models. It is developed by Andrei Makhorin, of the Moscow Aviation Institute. GLPK contains an standalone solver, glpsol, that can be called from the command line. It can read models written in a variety of languages, among them CPLEX, convenient for relatively small problems and GNU MathProg, a standard based on the AMPL format adequate to write large models with regular structure.

GLPK can be used in R via the Rglpk package. For windows users is available GUSEK, an IDE running the GLPK libraries.

GLPK homepage
R package Rglpk
GUSEK IDE

SYMPHONY

Symphony is an open-source solver of MILP problems written in C. It is an initiative of the COIN-OR project. It can read problems written in MPS and MathProg formats. It is also implemented in R through the Rsymphony package.

SYMPHONY homepage
SYMPHONY user's manual
R package Rsymphony

linprog

A library for solving linear programming models, quite popular in MATLAB. There is also a R package available. This library does not solve ILP/MILP models.

linprog in MATLAB
linprog R package