Post-Optimal Analysis in Linear programming / Wissal Sellam

Public ISBD Titre : Post-Optimal Analysis in Linear programming Type de document : texte imprimé Auteurs : Wissal Sellam, Auteur ; Aymen-Charef Eddine Guemmaz ; Amrani, Directeur de thèse Editeur : Setif:UFA Année de publication : 2024 Importance : 1 vol (51 f .) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Informatique Mots-clés : Informatique Post-Optimal Analysis Index. décimale : 004 - Informatique Résumé : Linear programming (LP) is a mathematical optimization technique aimed at maximizing or minimizing a linear function, subject to linear constraints. Its formulation begins with the identification of decision variables, the objective function, and constraints, typically based on goals of profit maximization or cost minimization. Resolution methods, such as the simplex or interior point methods, are then applied to find the optimal solution. Once the optimal solution is obtained, post-optimization analysis is conducted to assess the sensitivity of this solution to changes in model parameters. This includes analyzing the sensitivity of constraints and coefficients of the objective function, identifying available margins of maneuver and critical constraints. By combining precise problem formulation, efficient resolution methods, and rigorous post-optimization analysis, linear programming provides a powerful tool for strategic decision-making in various industrial and commercial domains. Note de contenu : Sommaire Part 01 : ……………………………………………………………………………….…………………... General introduction………...……………………………………………………………….5 Chapter 01 : The Methods of Handling Post-Optimal Analysis 1. Introduction……………………………………………………………………........8 2. formalization of linear programming………………………………………...8 3. The steps in modeling an optimization problem as a linear program………...9 4. The advantages and disadvantages of post-optimal analysis………………..11 5. The methods of handling post-optimal analysis………………………….....12 5.1. Revised Simplex Method………………………………………...…....12 5.2. Decomposition Methods………………………………………………15 5.3. Local Search Methods…………………………………………..….….16 6. Duality…………………………………………………………………....…16 7. Conclusion………………………………………………………………......18 Chapter 02 : Overview of post-optimal analysis in linear programming 1. Introduction……………………………………………………………………....20 2. Basic concepts……………………………………………………………...20 3. Post-Optimization Case Formulation……………………………………....21 4. Example………………………………………………………………….....22 5. Areas of application…………………………………………………….......27 6. Conclusion……………………………………………………………….....28 Part 03 :………………………………………………………………………………………………………… Chapter 03 : application 1. Introduction…………………………………………………………………30 2. Case stady………………………………………………………...................30 3. Presentation of tools ………………………………………………………..32 4. Description of Processing Procedures………………………...35 5. Conclusion……………………………………………………..42 General conclusion …………………………………………………………………………………………………….….44 Bibliographic references…………………………………………………………………………………………46 Côte titre : MAI/0864 Post-Optimal Analysis in Linear programming [texte imprimé] / Wissal Sellam, Auteur ; Aymen-Charef Eddine Guemmaz ; Amrani, Directeur de thèse . - [S.l.] : Setif:UFA, 2024 . - 1 vol (51 f .) ; 29 cm. Langues : Anglais (eng) Catégories : Thèses & Mémoires:Informatique Mots-clés : Informatique Post-Optimal Analysis Index. décimale : 004 - Informatique Résumé : Linear programming (LP) is a mathematical optimization technique aimed at maximizing or minimizing a linear function, subject to linear constraints. Its formulation begins with the identification of decision variables, the objective function, and constraints, typically based on goals of profit maximization or cost minimization. Resolution methods, such as the simplex or interior point methods, are then applied to find the optimal solution. Once the optimal solution is obtained, post-optimization analysis is conducted to assess the sensitivity of this solution to changes in model parameters. This includes analyzing the sensitivity of constraints and coefficients of the objective function, identifying available margins of maneuver and critical constraints. By combining precise problem formulation, efficient resolution methods, and rigorous post-optimization analysis, linear programming provides a powerful tool for strategic decision-making in various industrial and commercial domains. Note de contenu : Sommaire Part 01 : ……………………………………………………………………………….…………………... General introduction………...……………………………………………………………….5 Chapter 01 : The Methods of Handling Post-Optimal Analysis 1. Introduction……………………………………………………………………........8 2. formalization of linear programming………………………………………...8 3. The steps in modeling an optimization problem as a linear program………...9 4. The advantages and disadvantages of post-optimal analysis………………..11 5. The methods of handling post-optimal analysis………………………….....12 5.1. Revised Simplex Method………………………………………...…....12 5.2. Decomposition Methods………………………………………………15 5.3. Local Search Methods…………………………………………..….….16 6. Duality…………………………………………………………………....…16 7. Conclusion………………………………………………………………......18 Chapter 02 : Overview of post-optimal analysis in linear programming 1. Introduction……………………………………………………………………....20 2. Basic concepts……………………………………………………………...20 3. Post-Optimization Case Formulation……………………………………....21 4. Example………………………………………………………………….....22 5. Areas of application…………………………………………………….......27 6. Conclusion……………………………………………………………….....28 Part 03 :………………………………………………………………………………………………………… Chapter 03 : application 1. Introduction…………………………………………………………………30 2. Case stady………………………………………………………...................30 3. Presentation of tools ………………………………………………………..32 4. Description of Processing Procedures………………………...35 5. Conclusion……………………………………………………..42 General conclusion …………………………………………………………………………………………………….….44 Bibliographic references…………………………………………………………………………………………46 Côte titre : MAI/0864

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