# Modeling and Solving Linear Programming with R – Free book

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**Modeling and Solving Linear Programming with R (pdf – free download link)**is a book about solving linear programming problems/exercises with R. This book provides a brief introduction to linear programming, an introduction of solving linear programming problems with R and a set of exercises. For each exercise a possible solution through linear programming is introduced together with the code to solve it in R and its numerical solution.

From the back of the book:

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.

Here the main links through everybody can purchase a print copy. Lulu – Amazon.com

But remember that it is an open access book (CC-BY-NC), so that you can download for free from that links: PDF – Google Play – Google Books

Table of content:

1 Introduction 5

2 Solving linear programming 9

2 Solving linear programming 9

2.1 An introduction to linear programming . . . . . . . . . . 9

2.2 Linear programming formulation . . . . . . . . . . . . . 11

2.2.1 The structure of a linear program model . . . . . 11

2.2.2 A simple example of a PL model . . . . . . . . . . 13

2.2.3 A transportation problem . . . . . . . . . . . . . 14

2.2.4 Transformations of elements of a LP . . . . . . . 16

2.2.5 Turning a PL into standard form . . . . . . . . . . 17

2.3 Solving the LP . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Duality in linear programming . . . . . . . . . . . . . . . 19

2.4.1 Obtaining the dual of the LP . . . . . . . . . . . . 20

2.4.2 Properties of the primal-dual relationship . . . . 21

2.5 Integer and mixed integer linear programming . . . . . 22

2.6 Solving linear programming in R . . . . . . . . . . . . . 24

2.6.1 Solving two LPs with the lpSolve package . . . . 25

2.6.2 Syntax to parse LP models . . . . . . . . . . . . . 27

2.2 Linear programming formulation . . . . . . . . . . . . . 11

2.2.1 The structure of a linear program model . . . . . 11

2.2.2 A simple example of a PL model . . . . . . . . . . 13

2.2.3 A transportation problem . . . . . . . . . . . . . 14

2.2.4 Transformations of elements of a LP . . . . . . . 16

2.2.5 Turning a PL into standard form . . . . . . . . . . 17

2.3 Solving the LP . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Duality in linear programming . . . . . . . . . . . . . . . 19

2.4.1 Obtaining the dual of the LP . . . . . . . . . . . . 20

2.4.2 Properties of the primal-dual relationship . . . . 21

2.5 Integer and mixed integer linear programming . . . . . 22

2.6 Solving linear programming in R . . . . . . . . . . . . . 24

2.6.1 Solving two LPs with the lpSolve package . . . . 25

2.6.2 Syntax to parse LP models . . . . . . . . . . . . . 27

3 Modeling linear programming 29

3.1 A production plan with fixed costs . . . . . . . . . . . . 31

3.2 A purchase plan with decreasing unit costs . . . . . . . . 37

3.3 A production plan with extra capacity . . . . . . . . . . 43

3.4 Transportation by trucks . . . . . . . . . . . . . . . . . . 53

3.5 Production of two models of chairs . . . . . . . . . . . . 57

3.6 Hiring and firing . . . . . . . . . . . . . . . . . . . . . . 65

3.7 Planning of shifts through linear programming . . . . . 71

3.8 Assignment maximizing minimal quality . . . . . . . . . 75

3.9 Production of biofuel . . . . . . . . . . . . . . . . . . . . 83

3.10 A finantial optimization problem . . . . . . . . . . . . . 97

3.2 A purchase plan with decreasing unit costs . . . . . . . . 37

3.3 A production plan with extra capacity . . . . . . . . . . 43

3.4 Transportation by trucks . . . . . . . . . . . . . . . . . . 53

3.5 Production of two models of chairs . . . . . . . . . . . . 57

3.6 Hiring and firing . . . . . . . . . . . . . . . . . . . . . . 65

3.7 Planning of shifts through linear programming . . . . . 71

3.8 Assignment maximizing minimal quality . . . . . . . . . 75

3.9 Production of biofuel . . . . . . . . . . . . . . . . . . . . 83

3.10 A finantial optimization problem . . . . . . . . . . . . . 97

4 Bibliography 105

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