F.S. Hillier & G.T Lierberman Introduction to Operations Research McGraw-Hill, 2004

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1 Recherche opérationnelle. Master 1 - Esa Si vous souhaitez prendre connaissance des questions traitées dans le cours de recherche opérationnelle du Master 1 ESA, je vous recommande cet ouvrage. F.S. Hillier & G.T Lierberman Introduction to Operations Research McGraw-Hill, 2004 Les enseignements de R.O. pour les économistes et économètres de notre UFR sont répartis sur la licence et le M1. Les domaines traités en licence et en M1 sont largement indépendants. Toutefois, pour ceux qui n ont pas suivi le cours de licence, le cours de M1 commence par un rappel (3 heures) des résultats indispensables. Voici la table des matières du manuel de Hiller et Lieberman (7 ème éd., 2001). Vous y trouverez le détail des chapitres abordés en licence et en M1. Je ne saurais mieux recommander aux étudiants entrant en master et n ayant aucune formation initiale en RO d étudier les chapitres ou les paragraphes portant la mention «indispensable». CHAPTER 1 Introduction 1 TABLE OF CONTENTS CHAPTER 2 Overview of the Operations Research Modeling Approach 7 CHAPTER 3 Introduction to Linear Programming 24 CHAPTER 4 Solving Linear Programming Problems: The Simplex Method The Essence of the Simplex Method 109 (indispensable) 4.2 Setting Up the Simplex Method 114 (indispensable) 4.3 The Algebra of the Simplex Method 118 (indispensable) 4.4 The Simplex Method in Tabular Form 123

2 4.5 Tie Breaking in the Simplex Method Adapting to Other Model Forms Postoptimality Analysis Computer Implementation The Interior-Point Approach to Solving Linear Programming Problems Conclusions 168 CHAPTER 5 The Theory of the Simplex Method Foundations of the Simplex Method The Revised Simplex Method 202 (indispensable) 5.3 A Fundamental Insight Conclusions 220 CHAPTER 6 Duality Theory and Sensitivity Analysis The Essence of Duality Theory 231 (indispensable, 6.2 Economic Interpretation of Duality 239 (indispensable, l interprétation économique de la dualité fait l objet d un chapitre du cours de licence) 6.3 Primal-Dual Relationships 242 (indispensable) 6.4 Adapting to Other Primal Forms The Role of Duality Theory in Sensitivity Analysis The Essence of Sensitivity Analysis Applying Sensitivity Analysis Conclusions 284 CHAPTER 7 Other Algorithms for Linear Programming The Dual Simplex Method Parametric Linear Programming The Upper Bound Technique An Interior-Point Algorithm Linear Goal Programming and Its Solution Procedures Conclusions 339 CHAPTER 8 The Transportation and Assignment Problems The Transportation Problem A Streamlined Simplex Method for the Transportation Problem The Assignment Problem Conclusions 391 CHAPTER 9 Network Optimization Models Prototype Example The Terminology of Networks The Shortest-Path Problem The Minimum Spanning Tree Problem The Maximum Flow Problem The Minimum Cost Flow Problem The Network Simplex Method Conclusions 448 CHAPTER 10 Project Management with PERT/CPM A Prototype Example The Reliable Construction Co. Project Using a Network to Visually Display a Project Scheduling a Project with PERT/CPM Dealing with Uncertain Activity Durations 485

3 10.5 Considering Time-Cost Trade-Offs Scheduling and Controlling Project Costs An Evaluation of PERT/CPM Conclusions 512 CHAPTER 11 Dynamic Programming A Prototype Example for Dynamic Programming Characteristics of Dynamic Programming Problems Deterministic Dynamic Programming Probabilistic Dynamic Programming Conclusions 568 CHAPTER 12 Integer Programming Prototype Example Some BIP Applications Innovative Uses of Binary Variables in Model Formulation Some Formulation Examples Some Perspectives on Solving Integer Programming Problems The Branch-and-Bound Technique and Its Application to Binary Integer Programming A Branch-and-Bound Algorithm for Mixed Integer Programming Other Developments in Solving BIP Problems Conclusions 630 (Exemples vus en Master) CHAPTER 13 Nonlinear Programming Sample Applications Graphical Illustration of Nonlinear Programming Problems Types of Nonlinear Programming Problems One-Variable Unconstrained Optimization Multivariable Unconstrained Optimization The Karush-Kuhn-Tucker (KKT) Conditions for Constrained Optimization 679 (indispensable) 13.7 Quadratic Programming Separable Programming Convex Programming Nonconvex Programming 702 CHAPTER 14 Game Theory The Formulation of Two-Person, Zero-Sum Games Solving Simple Games A Prototype Example Games with Mixed Strategies Graphical Solution Procedure Solving by Linear Programming Extensions Conclusions 742 CHAPTER 15 Decision Analysis A Prototype Example Decision Making without Experimentation Decision Making with Experimentation Decision Trees Utility Theory The Practical Application of Decision Analysis Conclusions 781 CHAPTER 16 Markov Chains Stochastic Processes 802

4 16.2 Markov Chains Chapman-Kolmogorov Equations Classification of States of a Markov Chain Long-Run Properties of Markov Chains First Passage Times Absorbing States Continuous Time Markov Chains 822 CHAPTER 17 Queueing Theory Prototype Example Basic Structure of Queueing Models Examples of Real Queueing Systems The Role of the Exponential Distribution The Birth-and-Death Process Queueing Models Based on the Birth-and-Death Process Queueing Models Involving Nonexponential Distributions Priority-Discipline Queueing Models Queueing Networks Conclusions 889 CHAPTER 18 The Application of Queueing Theory Examples Decision Making Formulation of Waiting-Cost Functions Decision Models Some Award-Winning Applications of Queueing Theory Conclusions 926 Selected References 926 CHAPTER 19 Inventory Theory Examples Components of Inventory Models Deterministic Continuous-Review Models A Deterministic Periodic-Review Model A Stochastic Continuous-Review Model A Stochastic Single-Period Model for Perishable Products Stochastic Periodic-Review Models Larger Inventory Systems in Practice Conclusions 987 CHAPTER 20 Forecasting Some Applications of Forecasting Judgmental Forecasting Methods Time Series Forecasting Methods for a Constant-Level Model Incorporating Seasonal Effects into Forecasting Methods An Exponential Smoothing Method for a Linear Trend Model Forecasting Errors Box-Jenkins Method Causal Forecasting with Linear Regression Forecasting in Practice Conclusions 1038 CHAPTER 21 Markov Decision Processes A Prototype Example A Model for Markov Decision Processes Linear Programming and Optimal Policies 1059

5 21.4 Policy Improvement Algorithm for Finding Optimal Policies Discounted Cost Criterion Conclusions CHAPTER 22 Simulation The Essence of Simulation Some Common Types of Applications of Simulation Generation of Random Numbers Generation of Random Observations from a Probability Distribution Outline of a Major Simulation Study Performing Simulations on Spreadsheets Variance-Reducing Techniques Regenerative Method of Statistical Analysis Conclusions 1138 APPENDIXES

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