Математическое программирование и моделирование экономических процессов. Коробов П.Н. - 8 стр.

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СПбГЛТУ | Санкт-Петербург

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8
CONTENTS
Page
FOREWORD……………………………………………………………………….…5
INTRODUCTION. OBJECTIVE NECESSITY OF IMPROVING THE SCIENTIFIC LEVEL OF
ECONOMIC SOLUTIONS……………………………………………...7
ALPHABET……………………………………………………………………….…13
MATHEMATICAL PROGRAMMING
Chapter 1. ECONOMIC AND MATHEMATICAL MODELLING OF MATHEMATICAL
PROGRAMMING TYPICAL PROBLEMS………………….14
1.1. Principles of economical and mathematical modeling………………….14
1.2. Setting of standard problem of linear programming at maximum target
function………………………………………………………………….16
1.3. Setting of standard problem of linear programming at minimum target
function………………………………………………………………….21
1.4. Economic content and mathematical setting of transportation problem..25
1.5. Setting of dynamic programming problem……………………………..29
Chapter 2. ELEMENTS OF LINEAR ALGEBRA AND LINEAR PROGRAMMING
THEORY……………………………………………………………………………..31
2.1. Elements of linear algebra……………………………………………….31
2.1.1. Matrix and operations on them………………………………………...31
2.1.2. Vectors and operations on them……………………………………….33
2.1.3. Linear dependence of vectors………………………………………….35
2.1.4. System of vectors class and basis……………………………………...36
2.1.5. Single basis. Vector chart in relation to the single basis………………38
2.1.6. One-time substitution operation……………………………………….39
2.1.7. Vector expansion in terms of undegenerated matrix columns………...46
2.1.8. Linear equations’ system………………………………………………48
2.1.9. Basic solutions…………………………………………………………50
2.1.10. Reference solutions…………………………………………………...56
Part 2. Linear Programming Theory Elements……………………………………….60
2.2.1. Different forms of linear programming problems and putting them in canonical and standard
form………………………………………………………….60
2.2.2. Dual or intermating pairs of linear programming problems…………...67
2.2.3. Reference solutions’ theorem…………………………………………..75
2.2.4. Linear programming geometrical interpretation……………………….78
Chapter 3. SIMPLEX METHOD……………………………………………………..93
3.1. Simplex method basic algorithm…………………………………………93
3.2. Simplex method in solving problems with conditions in the form of equations and inequalities
with the sign (the method of artificial basis)……………..107
3.3. Dual problems of linear programming and application of the duality
theory………………………………………………………………………...123
3.4. Concept of degeneration………………………………………………...133
3.5. Detection of intractability of linear programming problems……………136
Chapter 4. TRANSPORTATION ALGHORITHMS. THEIR ESSENCE IN SOLVING
PROBLEMS………………………………………………………………………….141
4.1. Distributive method……………………………………………………….142
4.2. Method of potentials………………………………………………………154
4.3. Method of differential rents……………………………………………….160
Chapter 5. COMPLICATED AND MODIFIED SETTINGS OF TRANSPORTATION
PROBLEM…………………………………………………………………………….172
5.1. Transportation problem with degenerated reference plan………………...172
5.2. Open models of transportation problem…………………………………..174
5.3. Transportation problem with limited capabilities of transportation means and
communications………………………………………………………………..178
5.4. Non-linear model of transportation problem……………………………...181
5.5. Lambda-problem and Malkov method in its solving……………………...184
Chapter 6. ELEMENTS OF NON-LINEAR PROGRAMMING……………………...199

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