Lange Optimal Decisions

Principles of Programming
1. Auflage 2014
ISBN: 978-1-4831-4896-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 302 Seiten, Web PDF

Optimal Decisions: Principles of Programming deals with all important problems related to programming. This book provides a general interpretation of the theory of programming based on the application of the Lagrange multipliers, followed by a presentation of the marginal and linear programming as special cases of this general theory. The praxeological interpretation of the method of Lagrange multipliers is also discussed. This text covers the Koopmans' model of transportation, geometric interpretation of the programming problem, and nature of activity analysis. The solution of the problem by marginal analysis, Hurwitz and the Bayes-Laplace principles, and planning of production under uncertainty are likewise deliberated. This publication is a good source for researchers and specialists intending to acquire knowledge of the principles of programming.

Autoren/Hrsg.

Lange, Oskar

Inhaltsverzeichnis

1;Front Cover;1
2;Optimal Decisions Principles of Programming;4
3;Copyright Page;5
4;Table of Contents;6
5;FOREWORD;10
6;INTRODUCTION PRAXEOLOGY AND THE THEORY OF PROGRAMMING;12
7;CHAPTER 1. TYPICAL MODELS OF PROGRAMMING;18
7.1;1. The routing problem;18
7.2;2. The transportation problem;21
7.3;3. The Koopmans' model of transportation;25
7.4;4. The allocation problem;28
7.5;5. The mix problem;32
7.6;6. A dynamic problem: production and stocks;34
7.7;7. Another dynamic problem: storing of products;39
7.8;8. Investment programming: the choice of investment variants;40
7.9;9. Investment programming: allocation of investment;43
7.10;10. Investment programming: distribution of investment over;49
7.11;11. Classification of programming models;51
8;CHAPTER 2. THE GENERAL PRINCIPLES OF THE THEORY OF PROGRAMMING;53
8.1;1. Mathematical formulation of the general problem of programming;53
8.2;2. Geometric interpretation of the programming problem;57
8.3;3. The method of indeterminate Lagrange multipliers. The dual programme;59
8.4;4. Generalization: the case when the balance relationships are in the form of inequalities;65
9;CHAPTER 3. MARGINAL PROGRAMMING;70
9.1;1. The method and the geometric interpretation of the solution of a marginal programming problem;70
9.2;2. Conditions for the existence of a solution to a marginal programming problem;73
9.3;3. Examples of marginal programmes;75
9.4;4. Programming production when there are n factors of production;89
10;CHAPTER 4. LINEAR PROGRAMMING;95
10.1;1. Mathematical formulation of the problem of linear programming;95
10.2;2. Geometrical interpretation of linear programming. The concept of the simplex method;97
10.3;3, The basic theorem of the theory of linear programming. Duality in linear programming;105
10.4;4. The simplex method;115
10.5;5. Examples of applications of the simplex methods;122
10.6;6. Solution of the dual problem;132
10.7;7. The criterion of optimality of the solution;137
11;CHAPTER 5. ACTIVITY ANALYSIS;143
11.1;1. The nature of activity analysis;143
11.2;2. Maximization of production and minimization of costs;149
11.3;3. The problem of joint production;156
11.4;4. The generalized problem of optimizing production;159
11.5;5. Examples of application of the method of activity analysis;162
12;CHAPTER 6. PROGRAMMING FOR MULTIPLE OBJECTIVES;166
12.1;1. The efficient programme;166
12.2;2. The solution of the problem by marginal analysis;168
12.3;3. Multiple objectives and linear programming;175
13;CHAPTER 7. PROGRAMMING UNDER UNCERTAINTY;179
13.1;1. Optimal allocation of production among different plants;179
13.2;2. The case of limited productive capacity of plants;182
13.3;3. The choice of optimal productive capacity for a new plant;183
13.4;4. Planning of production under uncertainty;188
13.5;5. Planning production when the acceptable risk is limited;194
13.6;6. The neo-classical theory of risk;197
13.7;7. Planning of production on the basis of the neo-classical theory of risk. The choice preference function;202
13.8;8. Criticism of the neo-classical theory. The method of marginal probability;206
14;CHAPTER 8. DYNAMIC PROGRAMMING OF PURCHASES AND STOCKS UNDER CERTAINTY;213
14.1;1. Optimal purchase batch;213
14.2;2. First generalized variant of the problem of purchases and stocks;219
14.3;3. The case when purchases are not necessarily equel;220
14.4;4. The case of restricted warehouse capacity;222
14.5;5. The case when withdrawal from stock is not evenly distributed over;224
15;CHAPTER 9. DYNAMIC PROGRAMMING OF PURCHASES AND STOCKS UNDER UNCERTAINTY;231
15.1;1. The case when the probability of a reserve stock being insufficient (risk-coefficient) is equal to a given value. Normal probability distribution;231
15.2;2. The case when the probability distribution of demand is a Poisson distribution;236
15.3;3. The case when demand has a "rectangular" probability distribution;238
15.4;4. Determining the optimum level of the risk coefficient and of the reserve in relation to the stock-holding cost and the cost of shortage;240
16;CHAPTER 10. DYNAMIC PROGRAMMING OF PRODUCTION UNDER CERTAINTY;249
16.1;1. Determination of optimal production over time by variation calculation;249
16.2;2. An example of dynamic programming of production;258
17;CHAPTER 11. DYNAMIC PROGRAMMING OF PRODUCTION UNDER UNCERTAINTY;262
17.1;1. The case when aggregate demand is a random variable with a known probability distribution;262
17.2;2. Determination of the probability distribution of aggregate demand;266
17.3;3. The solution of the problem of optimal use of sources of electric power;268
18;CHAPTER 12. PROGRAMMING UNDER COMPLETE UNCERTAINTY;276
18.1;1. General remarks on the theory of strategic games;276
18.2;2. Programming under complete uncertainty as a game played by man against nature;282
18.3;3. The Hurwitz and the Bayes-Laplace principles;284
18.4;4. Savage*s principle of the minimax effects of a false decision;287
18.5;5. Determining the optimum stock of raw material on the basis of the theory of strategic games;289
18.6;6. The equivalence of linear programming with the two-person zero-sum game;291
18.7;7. The minimax principle and collective decisions;294
19;BIBLIOGRAPHY;296
20;NDEX;300