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• 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
• 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