Efnisyfirlit

• Title Page
• Copyright Page
• Contents
• What’s New in the Tenth Edition
• Acknowledgments
• About the Author
• Trademarks
• Chapter 1 What is Operations Research?
  • 1.1 Introduction
  • 1.2 Operations Research Models
  • 1.3 Solving the OR Model
  • 1.4 Queuing and Simulation Models
  • 1.5 Art of Modeling
  • 1.6 More than Just Mathematics
  • 1.7 Phases of an OR Study
  • 1.8 About this Book
  • Bibliography
  • Problems
• Chapter 2 Modeling with Linear Programming
  • 2.1 Two-Variable LP Model
  • 2.2 Graphical LP Solution
    • 2.2.1 Solution of a Maximization Model
    • 2.2.2 Solution of a Minimization Model
  • 2.3 Computer Solution with Solver and AMPL
    • 2.3.1 LP Solution with Excel Solver
    • 2.3.2 LP Solution with AMPL
  • 2.4 Linear Programming Applications
    • 2.4.1 Investment
    • 2.4.2 Production Planning and Inventory Control
    • 2.4.3 Workforce Planning
    • 2.4.4 Urban Development Planning
    • 2.4.5 Blending and Refining
    • 2.4.6 Additional LP Applications
  • Bibliography
  • Problems
• Chapter 3 The Simplex Method and Sensitivity Analysis
  • 3.1 LP Model in Equation Form
  • 3.2 Transition from Graphical to Algebraic Solution
  • 3.3 The Simplex Method
    • 3.3.1 Iterative Nature of the Simplex Method
    • 3.3.2 Computational Details of the Simplex Algorithm
    • 3.3.3 Summary of the Simplex Method
  • 3.4 Artificial Starting Solution
    • 3.4.1 M-Method
    • 3.4.2 Two-Phase Method
  • 3.5 Special Cases in the Simplex Method
    • 3.5.1 Degeneracy
    • 3.5.2 Alternative Optima
    • 3.5.3 Unbounded Solution
    • 3.5.4 Infeasible Solution
  • 3.6 Sensitivity Analysis
    • 3.6.1 Graphical Sensitivity Analysis
    • 3.6.2 Algebraic Sensitivity Analysis—Changes in the Right-Hand Side
    • 3.6.3 Algebraic Sensitivity Analysis—Objective Function
    • 3.6.4 Sensitivity Analysis With Tora, Solver, and AMPL
  • 3.7 Computational Issues In Linear Programming
    • 3.7 Computational Issues In Linear Programming13
      • 3.7 Computational Issues In Linear Programming13
  • Bibliography
  • Problems
• Chapter 4 Duality and Post-Optimal Analysis
  • 4.1 Definition of the Dual Problem
  • 4.2 Primal–Dual Relationships
    • 4.2.1 Review of Simple Matrix Operations
    • 4.2.2 Simplex Tableau Layout
    • 4.2.3 Optimal Dual Solution
    • 4.2.4 Simplex Tableau Computations
  • 4.3 Economic Interpretation of Duality
  • 4.3.1 Economic Interpretation of Dual Variables
  • 4.3.2 Economic Interpretation of Dual Constraints
  • 4.4 Additional Simplex Algorithms
    • 4.4.1 Dual Simplex Algorithm
    • 4.4.2 Generalized Simplex Algorithm
  • 4.5 Post-Optimal Analysis
    • 4.5.1 Changes Affecting Feasibility
    • 4.5.2 Changes Affecting Optimality
  • Bibliography
  • Problems
• Chapter 5 Transportation Model and Its Variants
  • 5.1 Definition of the Transportation Model
  • 5.2 Nontraditional Transportation Models
  • 5.3 The Transportation Algorithm
    • 5.3.1 Determination of the Starting Solution
    • 5.3.2 Iterative Computations of the Transportation Algorithm
    • 5.3.3 Simplex Method Explanation of the Method of Multipliers
  • 5.4 The Assignment Model
    • 5.4.1 The Hungarian Method
    • 5.4.2 Simplex Explanation of the Hungarian Method
  • Bibliography
  • Problems
• Chapter 6 Network Model
  • 6.1 Scope and Definition of Network Models
  • 6.2 Minimal Spanning Tree Algorithm
  • 6.3 Shortest-route Problem
    • 6.3.1 Examples of the Shortest-Route Applications
    • 6.3.2 Shortest-Route Algorithms
    • 6.3.3 Linear Programming Formulation of the Shortest-Route Problem
  • 6.4 Maximal Flow Model
    • 6.4.1 Enumeration of Cuts
    • 6.4.2 Maximal Flow Algorithm
    • 6.4.3 Linear Programming Formulation of Maximal Flow Mode
  • 6.5 CPM and Pert
    • 6.5.1 Network Representation
    • 6.5.2 Critical Path Method (CPM) Computations
    • 6.5.3 Construction of the Time Schedule
    • 6.5.4 Linear Programming Formulation of CPM
    • 6.5.5 Pert Networks
  • Bibliography
  • Problems
• Chapter 7 Advanced Linear Programming
  • 7.1 Simplex Method Fundamentals
    • 7.1.1 From Extreme Points to Basic Solutions
    • 7.1.2 Generalized Simplex Tableau in Matrix Form
  • 7.2 Revised Simplex Method
    • 7.2.1 Development of the Optimality and Feasibility Conditions
    • 7.2.2 Revised Simplex Algorithm
    • 7.2.3 Computational Issues in the Revised Simplex Method
  • 7.3 Bounded-Variables Algorithm
  • 7.4 Duality
    • 7.4.1 Matrix Definition of the Dual Problem
    • 7.4.2 Optimal Dual Solution
  • 7.5 Parametric Linear Programming
    • 7.5.1 Parametric Changes in C
    • 7.5.2 Parametric Changes in B
  • 7.6 More Linear Programming Topics
  • Bibliography
  • Problems
• Chapter 8 Goal Programming
  • 8.1 A Goal Programming Formulation
  • 8.2 Goal Programming Algorithms
    • 8.2.1 The Weights Method
    • 8.2.2 The Preemptive Method
  • Bibliography
  • Case Study: Allocation of Operating Room Time in Mount Sinai Hospital
  • Problems
• Chapter 9 Integer Linear Programming
  • 9.1 Illustrative Applications
    • 9.1.1 Capital Budgeting
    • 9.1.2 Set-Covering Problem
    • 9.1.3 Fixed-Charge Problem
    • 9.1.4 Either-Or and If-Then Constraints
  • 9.2 Integer Programming Algorithms
    • 9.2.1 Branch-and-Bound (B&B) Algorithm
    • 9.2.2 Cutting-Plane Algorithm
  • 9.2 Integer Programming Algorithms
  • Bibliography
  • Problems
• Chapter 10 Heuristic Programming
  • 10.1 Introduction
  • 10.2 Greedy (Local Search) Heuristics
    • 10.2.1 Discrete Variable Heuristic
    • 10.2.2 Continuous Variable Heuristic
  • 10.3 Metaheuristic
    • 10.3.1 Tabu Search Algorithm
    • 10.3.2 Simulated Annealing Algorithm
    • 10.3.3 Genetic Algorithm
  • 10.4 Application of Metaheuristics to Integer Linear Programs
    • 10.4.1 ILP Tabu Algorithm
    • 10.4.2 ILP Simulated Annealing Algorithm
    • 10.4.3 ILP Genetic Algorithm
  • 10.5 Introduction To Constraint Programming (CP)
  • Bibliography
  • Problems
• Chapter 11 Traveling Salesperson Problem (TSP)
  • 11.1 Scope of the TSP
  • 11.2 TSP Mathematical Model
  • 11.3 Exact TSP Algorithms
    • 11.3.1 B&B Algorithm
    • 11.3.2 Cutting-Plane Algorithm
  • 11.4 Local Search Heuristics
    • 11.4.1 Nearest-Neighbor Heuristic
    • 11.4.2 Reversal Heuristic
  • 11.5 Metaheuristics
    • 11.5.1 TSP Tabu Algorithm
    • 11.5.2 TSP Simulated Annealing Algorithm
    • 11.5.3 TSP Genetic Algorithm
  • Bibliography
  • Problems
• Chapter 12 Deterministic Dynamic Programming
  • 12.1 Recursive Nature of Dynamic Programming (DP) Computations
  • 12.2 Forward and Backward Recursion
  • 12.3 Selected DP Applications
    • 12.3.1 Knapsack/Fly-Away Kit/cargo-Loading Model
    • 12.3.2 Workforce Size Model
    • 12.3.3 Equipment Replacement Model
    • 12.3.4 Investment Model
    • 12.3.5 Inventory Models
  • 12.4 Problem of Dimensionality
  • Bibliography
  • Case Study: Optimization of Crosscutting and Log Allocation at Weyerhaeuser
  • Problems
• Chapter 13 Inventory Modeling (with Introduction to Supply Chains)
  • 13.1 Inventory Problem: A Supply Chain Perspective
    • 13.1.1 An Inventory Metric in Supply Chains
    • 13.1.2 Elements of the Inventory Optimization Model
  • 13.2 Role of Demand In the Development of Inventory Models
  • 13.3 Static Economic-Order-Quantity Models
    • 13.3.1 Classical EOQ Model
    • 13.3.2 EOQ with Price Breaks
    • 13.3.3 Multi-Item EOQ With Storage Limitation
  • 13.4 Dynamic EOQ Models
    • 13.4.1 No-Setup EOQ Model
    • 13.4.2 Setup EOQ Model
  • 13.5 Sticky Issues in Inventory Modeling
  • Bibliography
  • Case Study: Kroger Improves Pharmacy Inventory Management
  • Problems
• Chapter 14 Review of Basic Probability
  • 14.1 Laws of Probability
    • 14.1.1 Addition Law of Probability
    • 14.1.2 Conditional Law of Probability
  • 14.2 Random Variables and Probability Distributions
  • 14.3 Expectation of a Random Variable
    • 14.3.1 Mean and Variance (Standard Deviation) of a Random Variable
    • 14.3.2 Joint Random Variables
  • 14.4 Four Common Probability Distributions
    • 14.4.1 Binomial Distribution
    • 14.4.2 Poisson Distribution
    • 14.4.3 Negative Exponential Distribution
    • 14.4.4 Normal Distribution
  • 14.5 Empirical Distributions
  • Bibliography
  • Problems
• Chapter 15 Decision Analysis and Games
  • 15.1 Decision Making Under Certainty—Analytic Hierarchy Process (AHP)
  • 15.2 Decision Making Under Risk
    • 15.2.1 Decision Tree–Based Expected Value Criterion
    • 15.2.2 Variants of the Expected Value Criterion
  • 15.3 Decision Under Uncertainty
  • 15.4 Game Theory
    • 15.4.1 Optimal Solution of Two-Person Zero-Sum Games
    • 15.4.2 Solution of Mixed Strategy Games
  • Bibliography
  • Case Study: Booking Limits in Hotel Reservations
  • Problems
• Chapter 16 Probabilistic Inventory Models
  • 16.1 Continuous Review Models
    • 16.1.1 “Probabilitized” EOQ Model
    • 16.1.2 Probabilistic EOQ Model
  • 16.2 Single-Period Models
    • 16.2.1 No-Setup Model (Newsvendor Model)
    • 16.2.2 Setup Model (s-S Policy)
  • 16.3 Multiperiod Model
  • Bibliography
  • Problems
• Chapter 17 Markov Chains
  • 17.1 Definition of a Markov Chain
  • 17.2 Absolute and n-Step Transition Probabilities
  • 17.3 Classification of the States in a Markov Chain
  • 17.4 Steady-State Probabilities and Mean Return Times of Ergodic Chains
  • 17.5 First Passage Time
  • 17.6 Analysis of Absorbing States
  • Bibliography
  • Problems
• Chapter 18 Queuing Systems
  • 18.1 Why Study Queues?
  • 18.2 Elements of a Queuing Model
  • 18.3 Role of Exponential Distribution
  • 18.4 Pure Birth and Death Models (Relationship Between the Exponential and Poisson Distributions)
    • 18.4.1 Pure Birth Model
    • 18.4.2 Pure Death Model
  • 18.5 General Poisson Queuing Model
  • 18.6 Specialized Poisson Queues
    • 18.6.1 Steady-State Measures of Performance
    • 18.6.2 Single-Server Models
    • 18.6.3 Multiple-Server Models
    • 18.6.4 Machine Servicing Model—(M/M/R):(GD/K/K), R<K
  • 18.7 (M/G/1):(GD/∞/∞)—Pollaczek–Khintchine (P–K) Formula
  • 18.8 Other Queuing Models
  • 18.9 Queuing Decision Models
    • 18.9.1 Cost Models
    • 18.9.2 Aspiration Level Model
  • Bibliography
  • Case Study: Analysis of an Internal Transport System in a Manufacturing Plant
  • Problems
• Chapter 19 Simulation Modeling
  • 19.1 Monte Carlo Simulation
  • 19.2 Types of Simulation
  • 19.3 Elements of Discrete Event Simulation
    • 19.3.1 Generic Definition of Events
    • 19.3.2 Sampling From Probability Distributions
  • 19.4 Generation of Random Numbers
  • 19.5 Mechanics of Discrete Simulation
    • 19.5.1 Manual Simulation of a Single-Server Model
    • 19.5.2 Spreadsheet-Based Simulation of the Single-Server Model
  • 19.6 Methods for Gathering Statistical Observations
    • 19.6.1 Subinterval Method
    • 19.6.2 Replication Method
  • 19.7 Simulation Languages
  • Bibiliography
  • Problems
• Chapter 20 Classical Optimization Theory
  • 20.1 Unconstrained Problems
    • 20.1.1 Necessary and Sufficient Conditions
    • 20.1.2 The Newton–Raphson Method
  • 20.2 Constrained Problems
    • 20.2.1 Equality Constraints
    • 20.2.2 Inequality Constraints—Karush–Kuhn–Tucker (KKT) Conditions
  • Bibliography
  • Problems
• Chapter 21 Nonlinear Programming Algorithms
  • 21.1 Unconstrained Algorithms
    • 21.1.1 Direct Search Method
    • 21.1.2 Gradient Method
  • 21.2 Constrained Algorithms
    • 21.2.1 Separable Programming
    • 21.2.2 Quadratic Programming
    • 21.2.3 Chance-Constrained Programming
    • 21.2.4 Linear Combinations Method
    • 21.2.5 Sumt Algorithm
  • Bibliography
  • Problems
• Appendix A Statistical Tables
• Appendix B Partial Answers to Selected Problems
• Index

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