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• Table of Contents and Preface
  • Cover Page
  • Title Page
  • Copyright Page
  • About the Authors
  • About the Case Writers
  • Dedication
  • Table of Contents
  • Supplements Available on the Text Website www.mhhe.com/hillier
  • Preface
    • ■ What’s New in this Edition
    • ■ Other Special Features of this Book
    • ■ A Wealth of Software Options
    • ■ The Use of the Book
    • ■ Acknowledgments
• Chapter 1: Introduction
  • 1.1 The Origins of Operations Research
  • 1.2 The Nature of Operations Research
  • 1.3 A Companion Discipline: Analytics
    • The Three Categories of Analytics
    • The Role of Data Science
    • The Role of Machine Learning
    • The Role of Artificial Intelligence
  • 1.4 The Relationship Between Analytics and Operations Research
    • The Increasing Demand for Analytics and Operations Research Professionals
  • 1.5 The Impact of Operations Research
  • 1.6 Some Trends that Should Further Increase the Future Impact of Operations Research
  • 1.7 Algorithms and or Courseware
  • Selected References
  • Problems
• Chapter 2: Overview of How Operations Research and Analytics Professionals Analyze Problems
  • Chapter 2 Introduction
  • 2.1 A Case Study: First Bank Evaluates Applications for Unsecured Loans
  • 2.2 Define the Problem
    • The Complementary Roles of the Study Team and Management
    • Additional Problem Definition Needed for Prescriptive Analytics
    • Returning to the Case Study: Defining the Problem at First Bank
  • 2.3 Performing Descriptive Analytics
    • Returning to the Case Study: Gather and Organize the Relevant Data for First Bank
    • Some Terminology for Descriptive Analytics
    • Returning to the Case Study: Cleaning the Data at First Bank
    • Using Analytic Solver to Explore the Data
    • Returning to the Case Study: Explore the Data at First Bank
    • Explore the Data with Summary Statistics for First Bank
    • Explore the Data with Sorting and Filtering at First Bank
    • Explore the Data Visually at First Bank
  • 2.4 Performing Predictive Analytics
    • Prediction and Classification Models
    • Some Terminology for Prediction and Classification Models
    • Returning to the Case Study: Developing the Model at First Bank
    • Choosing the Variables to Include in the Model at First Bank
    • Choosing the Algorithm for the Model at First Bank
    • Overfitting the Data
    • Partition the Data
    • Returning to the Case Study: Partition the Data at First Bank
    • Returning to the Case Study: Testing the KNN Model at First Bank
    • The Role of Lift Charts in Assessing the Effectiveness of an Algorithm
    • Refining the KNN Model at First Bank
    • Returning to the Case Study: Exploring Several Models and Choosing the Best
    • Returning to the Case Study: Implementing the Model at First Bank
  • 2.5 Using Operations Research to Perform Prescriptive Analytics
    • Returning to the Case Study: Formulating a Decision Model for First Bank
  • 2.6 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
    • 2.S1. Category D Loan Applicants at First Bank
  • Problems
  • Case
    • Case 2.1 Vacations at Vegas Villas
• Chapter 3: Introduction to Linear Programming
  • Chapter 3 Introduction
  • 3.1 Prototype Example
    • Formulation as a Linear Programming Problem
    • Graphical Solution
    • Conclusions
    • Continuing the Learning Process with Your OR Courseware
  • 3.2 The Linear Programming Model
    • A Standard Form of the Model
    • Other Forms
    • Terminology for Solutions of the Model
  • 3.3 Assumptions of Linear Programming
    • Proportionality
    • Additivity
    • Divisibility
    • Certainty
    • The Assumptions in Perspective
  • 3.4 Additional Examples
    • Design of Radiation Therapy
    • Controlling Air Pollution
    • Distributing Goods through a Distribution Network
  • 3.5 Formulating and Solving Linear Programming Models on a Spreadsheet
    • Formulating the Model on a Spreadsheet
    • Using Solver to Solve the Model
  • 3.6 Using Modeling Languages to Formulate Very Large Linear Programming Models
    • Modeling Languages
    • The Application of AMPL and Gurobi to the Original Wyndor Model
    • Using Indexing for Larger Versions of the Wyndor Model
    • A Really Big Production Planning Example
    • The LINGO Modeling Language
  • 3.7 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 3.1 Reclaiming Solid Wastes
  • Previews of Added Cases on Our Website
    • Case 3.2 Cutting Cafeteria Costs
    • Case 3.3 Staffing a Call Center
    • Case 3.4 Promoting a Breakfast Cereal
    • Case 3.5 Auto Assembly
• Chapter 4: Solving Linear Programming Problems: The Simplex Method
  • Chapter 4 Introduction
  • 4.1 The Essence of the Simplex Method
    • Solving the Example
    • The Key Solution Concepts
  • 4.2 Setting Up the Simplex Method
  • 4.3 The Algebra of the Simplex Method
    • Initialization
    • Optimality Test
    • Determining the Direction of Movement (Step 1 of an Iteration)
    • Determining Where to Stop (Step 2 of an Iteration)
    • Solving for the New BF Solution (Step 3 of an Iteration)
    • Optimality Test for the New BF Solution
    • Iteration 2 and the Resulting Optimal Solution
  • 4.4 The Simplex Method in Tabular Form
    • Summary of the Simplex Method (and Iteration 1 for the Example)
    • Iteration 2 for the Example and the Resulting Optimal Solution
  • 4.5 Tie Breaking in the Simplex Method
    • Tie for the Entering Basic Variable
    • Tie for the Leaving Basic Variable—Degeneracy
    • No Leaving Basic Variable—Unbounded Z
    • Multiple Optimal Solutions
  • 4.6 Reformulating Nonstandard Models to Prepare for Applying the Simplex Method
    • Conceptual Procedure for Dealing with Nonstandard Linear Programming Models
    • Equality Constraints
    • Negative Right-Hand Sides
    • Functional Constraints in ≥ Form
    • Variables Allowed to Be Negative
  • 4.7 The Big M Method for Helping to Solve Reformulated Models
  • 4.8 The Two-Phase Method is an Alternative to the Big M Method
    • No Feasible Solutions
  • 4.9 Postoptimality Analysis
    • Reoptimization
    • Shadow Prices
    • Sensitivity Analysis
    • Using Excel to Generate Sensitivity Analysis Information
    • Parametric Linear Programming
  • 4.10 Computer Implementation
    • Implementation of the Simplex Method
    • Linear Programming Software Featured in This Book
    • Available Software Options for Linear Programming
  • 4.11 The Interior-Point Approach to Solving Linear Programming Problems
    • The Key Solution Concept
    • Comparison with the Simplex Method
    • Sizes of Linear Programming Models That Can Be Solved
  • 4.12 Conclusions
  • Appendix 4.1: Introduction to Using LINGO + Classic LINDO
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 4.1 Fabrics and Fall Fashions
  • Previews of Added Cases on Our Website
    • Case 4.2 New Frontiers
    • Case 4.3 Assigning Students to Schools
• Chapter 5: The Theory of the Simplex Method
  • Chapter 5 Introduction
  • 5.1 Foundations of the Simplex Method
    • Terminology
    • Adjacent CPF Solutions
    • Properties of CPF Solutions
    • Extensions to the Augmented Form of the Problem
  • 5.2 The Simplex Method in Matrix Form
    • Solving for a Basic Feasible Solution
    • Matrix Form of the Current Set of Equations
    • Summary of the Matrix Form of the Simplex Method
    • Final Observations
  • 5.3 A Fundamental Insight
    • Adapting to Other Model Forms
    • Applications
  • 5.4 The Revised Simplex Method
  • 5.5 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
• Chapter 6: Duality Theory
  • Chapter 6 Introduction
  • 6.1 The Essence of Duality Theory
    • Origin of the Dual Problem
    • Summary of Primal-Dual Relationships
    • Applications
  • 6.2 Primal-Dual Relationships
    • Complementary Basic Solutions
    • Relationships between Complementary Basic Solutions
  • 6.3 Adapting to Other Primal Forms
    • The SOB Method for Determining the Form of Constraints in the Dual2
  • 6.4 The Role of Duality Theory in Sensitivity Analysis
    • Changes in the Coefficients of a Nonbasic Variable
    • Introduction of a New Variable
    • Other Applications
  • 6.5 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
• Chapter 7: Linear Programming under Uncertainty
  • Chapter 7 Introduction
  • 7.1 The Essence of Sensitivity Analysis
  • 7.2 Applying Sensitivity Analysis
    • Case 1—Changes in b i
    • Case 2a—Changes in the Coefficients of a Nonbasic Variable
    • Case 2b—Introduction of a New Variable
    • Case 3—Changes in the Coefficients of a Basic Variable
    • Case 4—Introduction of a New Constraint
  • 7.3 Performing Sensitivity Analysis on a Spreadsheet
    • Checking Individual Changes in the Model
    • Checking Two-Way Changes in the Model
    • Using the Sensitivity Report to Perform Sensitivity Analysis
    • Other Types of Sensitivity Analysis
  • 7.4 Robust Optimization
    • Robust Optimization with Independent Parameters
    • Extensions
  • 7.5 Chance Constraints
    • The Form of a Chance Constraint
  • 7.6 Stochastic Programming with Recourse
    • Some Typical Applications
  • 7.7 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 7.1 Controlling Air Pollution
  • Previews of Added Cases on Our Website
    • Case 7.2 Farm Management
    • Case 7.3 Assigning Students to Schools, Revisited
    • Case 7.4 Writing a Nontechnical Memo
• Chapter 8: Other Algorithms for Linear Programming
  • Chapter 8 Introduction
  • 8.1 The Dual Simplex Method
    • Summary of the Dual Simplex Method
    • An Example
  • 8.2 Parametric Linear Programming
    • Systematic Changes in the c j Parameters
    • Summary of the Parametric Linear Programming Procedure for Systematic Changes in the c j Parameters
    • Systematic Changes in the b i Parameters
    • Summary of the Parametric Linear Programming Procedure for Systematic Changes in the b i Parameters
  • 8.3 The Upper Bound Technique
  • 8.4 An Interior-Point Algorithm
    • The Relevance of the Gradient for Concepts 1 and 2
    • Using the Projected Gradient to Implement Concepts 1 and 2
    • A Centering Scheme for Implementing Concept 3
    • Summary and Illustration of the Algorithm
    • Summary of the Interior-Point Algorithm
  • 8.5 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
• Chapter 9: The Transportation and Assignment Problems
  • Chapter 9 Introduction
  • 9.1 The Transportation Problem
    • Prototype Example
    • The Transportation Problem Model
    • Using Excel to Formulate and Solve Transportation Problems
    • Generalizations of the Transportation Problem
  • 9.2 A Streamlined Simplex Method for the Transportation Problem
    • Setting Up the Transportation Simplex Method
    • Initialization
    • Optimality Test
    • An Iteration
    • Summary of the Transportation Simplex Method
    • Special Features of This Example
  • 9.3 The Assignment Problem
    • Prototype Example
    • The Assignment Problem Model
    • Solution Procedures for Assignment Problems
  • 9.4 A Special Algorithm for the Assignment Problem
    • The Role of Equivalent Cost Tables
    • Application to the Job Shop Co. Problem
    • Application to the Better Products Co. Problem
    • Summary of the Hungarian Algorithm
  • 9.5 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 9.1 Shipping Wood to Market
  • Previews of Added Cases on Our Website
    • Case 9.2 Continuation of the Texago Case Study
    • Case 9.3 Project Pickings
• Chapter 10: Network Optimization Models
  • Chapter 10 Introduction
  • 10.1 Prototype Example
  • 10.2 The Terminology of Networks
  • 10.3 The Shortest-Path Problem
    • Algorithm for the Shortest-Path Problem
    • Applying This Algorithm to the Seervada Park Shortest-Path Problem
    • Using Excel to Formulate and Solve Shortest-Path Problems
    • Other Applications
  • 10.4 The Minimum Spanning Tree Problem
    • Some Applications
    • An Algorithm for Constructing a Minimum Spanning Tree
    • Outline of This Algorithm
    • Applying This Algorithm to the Seervada Park Minimum Spanning Tree Problem
  • 10.5 The Maximum Flow Problem
    • Some Applications
    • An Algorithm
    • The Augmenting Path Algorithm for the Maximum Flow Problem1
    • Applying This Algorithm to the Seervada Park Maximum Flow Problem
    • Finding an Augmenting Path
    • Using Excel to Formulate and Solve Maximum Flow Problems
  • 10.6 The Minimum Cost Flow Problem
    • Some Applications
    • Formulation of the Model
    • Using Excel to Formulate and Solve Minimum Cost Flow Problems
    • Special Cases
  • 10.7 The Network Simplex Method
    • Incorporating the Upper Bound Technique
    • Correspondence between BF Solutions and Feasible Spanning Trees
    • Selecting the Entering Basic Variable
    • Finding the Leaving Basic Variable and the Next BF Solution
  • 10.8 A Network Model for Optimizing a Project’s Time-Cost Trade-Off
    • A Prototype Example—the Reliable Construction Co. Problem
    • Project Networks
    • The Critical Path
    • Time-Cost Trade-Offs for Individual Activities
    • Which Activities Should Be Crashed?
    • Using Linear Programming to Make Crashing Decisions
  • 10.9 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 10.1 Money in Motion
  • Previews of Added Cases on Our Website
    • Case 10.2 Aiding Allies
    • Case 10.3 Steps to Success
• Chapter 11: Dynamic Programming
  • Chapter 11 Introduction
  • 11.1 A Prototype Example for Dynamic Programming
  • 11.2 Characteristics of Dynamic Programming Problems
  • 11.3 Deterministic Dynamic Programming
    • A Prevalent Problem Type—The Distribution of Effort Problem
  • 11.4 Probabilistic Dynamic Programming
  • 11.5 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
• Chapter 12: Integer Programming
  • Chapter 12 Introduction
  • 12.1 Prototype Example
    • The BIP Model
    • Software Options for Solving Such Models
  • 12.2 Some BIP Applications
    • Investment Analysis
    • Site Selection
    • Designing a Production and Distribution Network
    • Dispatching Shipments
    • Scheduling Interrelated Activities
    • Airline Applications
  • 12.3 Using Binary Variables to Deal with Fixed Charges
  • 12.4 A Binary Representation of General Integer Variables
  • 12.5 Some Perspectives on Solving Integer Programming Problems
  • 12.6 The Branch-and-Bound Technique and its Application to Binary Integer Programming
    • Branching
    • Bounding
    • Fathoming
    • Summary of the BIP Branch-and-Bound Algorithm
    • Completing the Example
    • Other Options with the Branch-and-Bound Technique
  • 12.7 A Branch-and-Bound Algorithm for Mixed Integer Programming
    • Summary of the MIP Branch-and-Bound Algorithm
  • 12.8 The Branch-and-Cut Approach to Solving Pure BIP Problems
    • Background
    • Automatic Problem Preprocessing for Pure BIP
    • Generating Cutting Planes for Pure BIP
  • 12.9 The Incorporation of Constraint Programming
    • The Nature of Constraint Programming
    • The Potential of Constraint Programming
    • The All-Different Constraint
    • The Element Constraint
  • 12.10 Extensions of Integer Linear Programming
    • An Example of Linearizing a Nonlinear Model
    • An Example of Linearizing a Constraint in a Nonlinear Model
    • Some Options for Formulating and Solving Integer Nonlinear Programming (INLP) Models
    • Convex Problems
    • Nonconvex Problems
    • Computational Experience When Applying AMPL/Gurobi to INLP Problems
    • Factors Affecting the Speed of Solving MIQP and MIQCP Models
  • 12.11 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 12.1 Capacity Concerns
  • Previews of Added Cases on Our Website
    • Case 12.2 Assigning Art
    • Case 12.3 Stocking Sets
    • Case 12.4 Assigning Students to Schools, Revisited Again
• Chapter 13: Nonlinear Programming
  • Chapter 13 Introduction
  • 13.1 Sample Applications
    • The Product-Mix Problem with Price Elasticity
    • The Transportation Problem with Volume Discounts on Shipping Costs
    • Portfolio Selection with Risky Securities
  • 13.2 Graphical Illustration of Nonlinear Programming Problems
  • 13.3 Types of Nonlinear Programming Problems
    • Unconstrained Optimization
    • Linearly Constrained Optimization
    • Quadratic Programming
    • Convex Programming
    • Separable Programming
    • Nonconvex Programming
    • Geometric Programming
    • Fractional Programming
    • The Complementarity Problem
  • 13.4 One-Variable Unconstrained Optimization
    • The Bisection Method
    • Summary of the Bisection Method
    • Newton’s Method
    • Summary of Newton’s Method
  • 13.5 Multivariable Unconstrained Optimization
    • The Gradient Search Procedure
    • Summary of the Gradient Search Procedure
    • Newton’s Method
  • 13.6 The Karush-Kuhn-Tucker (KKT) Conditions for Constrained Optimization
  • 13.7 Quadratic Programming
    • The KKT Conditions for Quadratic Programming
    • The Modified Simplex Method
    • Some Software Options
  • 13.8 Separable Programming
    • Reformulation as a Linear Programming Problem
    • Extensions
  • 13.9 Convex Programming
    • A Sequential Linear Approximation Algorithm (Frank-Wolfe)
    • Summary of the Frank-Wolfe Algorithm
    • Some Other Algorithms
    • Sequential Unconstrained Minimization Technique (SUMT)
    • Summary of SUMT
    • Some Software Options for Convex Programming
  • 13.10 Nonconvex Programming (with Spreadsheets)
    • The Challenge of Solving Nonconvex Programming Problems
    • Using Solver to Find Local Optima
    • A More Systematic Approach to Finding Local Optima
    • Evolutionary Solver
  • 13.11 Formulating and Solving Nonlinear Programming Problems with AMPL and Gurobi
    • Portfolio Selection with a Quadratic Objective Function
    • Portfolio Selection with Quadratic Constraints
    • Portfolio Selection with Binary Variables and a Quadratic Objective Function
    • Computational Experience When Solving Large Problems with Gurobi
  • 13.12 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 13.1 Savvy Stock Selection
  • Previews of Added Cases on Our Website
    • Case 13.2 International Investments
    • Case 13.3 Promoting a Breakfast Cereal, Revisited
• Chapter 14: Metaheuristics
  • Chapter 14 Introduction
  • 14.1 The Nature of Metaheuristics
    • An Example: A Nonlinear Programming Problem with Multiple Local Optima
    • An Example: A Traveling Salesman Problem
    • The Sub-Tour Reversal Algorithm
  • 14.2 Tabu Search
    • Basic Concepts
    • Outline of a Basic Tabu Search Algorithm
    • A Minimum Spanning Tree Problem with Constraints
    • The Traveling Salesman Problem Example
  • 14.3 Simulated Annealing
    • Basic Concepts
    • Outline of a Basic Simulated Annealing Algorithm
    • The Traveling Salesman Problem Example
    • The Nonlinear Programming Example
  • 14.4 Genetic Algorithms
    • Basic Concepts
    • Outline of a Basic Genetic Algorithm
    • The Integer Version of the Nonlinear Programming Example
    • The Traveling Salesman Problem Example
    • Procedure for Generating a Child
  • 14.5 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
• Chapter 15: Game Theory
  • Chapter 15 Introduction
  • 15.1 The Formulation of Two-Person, Zero-Sum Games
  • 15.2 Solving Simple Games—A Prototype Example
    • Formulation as a Two-Person, Zero-Sum Game
    • Variation 1 of the Example
    • Variation 2 of the Example
    • Variation 3 of the Example
  • 15.3 Games with Mixed Strategies
  • 15.4 Graphical Solution Procedure
  • 15.5 Solving by Linear Programming
    • The Linear Programming Formulation
    • Application to Variation 3 of the Political Campaign Problem
  • 15.6 Extensions
  • 15.7 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
• Chapter 16: Decision Analysis
  • Chapter 16 Introduction
  • 16.1 A Prototype Example
  • 16.2 Decision Making without Experimentation
    • Formulation of the Prototype Example in This Framework
    • The Maximin Payoff Criterion
    • The Maximum Likelihood Criterion
    • Bayes’ Decision Rule2
    • Sensitivity Analysis with Bayes’ Decision Rule
  • 16.3 Decision Making with Experimentation
    • Continuing the Prototype Example
    • Posterior Probabilities
    • The Value of Experimentation
  • 16.4 Decision Trees
    • Constructing the Decision Tree
    • Performing the Analysis
  • 16.5 Utility Theory
    • Utility Functions for Money
    • Equivalent Lottery Method
    • Applying Utility Theory to the Full Goferbroke Co. Problem
    • Another Approach for Estimating U(M)
    • Using a Decision Tree to Analyze the Goferbroke Co. Problem with Utilities
  • 16.6 The Practical Application of Decision Analysis
  • 16.7 Multiple Criteria Decision Analysis, Including Goal Programming
    • Goal Programming
    • Prototype Example for Nonpreemptive Goal Programming
    • Dealing with Nonnumerical and Less Tangible Goals
  • 16.8 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 16.1 Brainy Business
  • Preview of Added Cases on Our Website
    • Case 16.2 Smart Steering Support
    • Case 16.3 Who Wants to Be a Millionaire?
    • Case 16.4 University Toys and the Engineering Professor Action Figures
• Chapter 17: Queueing Theory
  • Chapter 17 Introduction
  • 17.1 Prototype Example
  • 17.2 Basic Structure of Queueing Models
    • The Basic Queueing Process
    • Input Source (Calling Population)
    • Queue
    • Queue Discipline
    • Service Mechanism
    • An Elementary Queueing Process
    • Terminology and Notation
    • Relationships between L, W, L q , and W q
  • 17.3 Some Common Types of Real Queueing Systems
  • 17.4 The Role of the Exponential Distribution
  • 17.5 The Birth-and-Death Process
    • Analysis of the Birth-and-Death Process
    • Results for the Birth-and-Death Process
  • 17.6 Queueing Models Based on the Birth-and-Death Process
    • The M/M/s Model
    • The Finite Queue Variation of the M/M/s Model (Called the M/M/s/K Model)
    • The Finite Calling Population Variation of the M/M/s Model
  • 17.7 Queueing Models Involving Nonexponential Distributions
    • The M/G/1 Model
    • The M/D/s Model
    • The M/Ek/s Model
    • Models without a Poisson Input
    • Other Models
  • 17.8 Priority-Discipline Queueing Models
    • The Models
    • Results for the Nonpreemptive Priorities Model
    • A Single-Server Variation of the Nonpreemptive Priorities Model
    • Results for the Preemptive Priorities Model
  • 17.9 Queueing Networks
    • Infinite Queues in Series
    • Jackson Networks
  • 17.10 The Application of Queueing Theory
    • How Many Servers Should Be Provided?
    • Other Issues
  • 17.11 Behavioral Queueing Theory
  • 17.12 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 17.1 Reducing In-Process Inventory
  • Preview of an Added Case on Our Website
    • Case 17.2 Queueing Quandary
• Chapter 18: Inventory Theory and Revenue Management
  • Chapter 18 Introduction
• Chapter 19: Markov Decision Processes
  • Chapter 19 Introduction
  • 19.1 A Prototype Example
  • 19.2 A Model for Markov Decision Processes
    • Solving the Prototype Example by Exhaustive Enumeration
  • 19.3 Linear Programming and Optimal Policies
    • Randomized Policies
    • A Linear Programming Formulation
    • Solving the Prototype Example by Linear Programming
  • 19.4 Markov Decision Processes in Practice
    • When Is Approximate Dynamic Programming Needed?
    • Early Examples of Markov Decision Processes in Practice
    • More Recent Applications
  • 19.5 Approximate Dynamic Programming
    • The Bellman Equation
    • The Essence of the ADP Framework
    • Using the Prototype Example in Section 19.1 to Illustrate the ADP Framework
    • A Large Application: Freight Consolidation
    • The Post-Decision State
    • Approximate Linear Programming (ALP): An Alternative to Simulating Sample Paths
    • ADP in Practice
  • 19.6 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
• Chapter 20: Simulation
  • Chapter 20 Introduction
  • 20.1 The Essence of Simulation
    • The Role of Simulation in Operations Research Studies
    • Discrete-Event versus Continuous Simulation
    • More Examples in Your OR Courseware
  • 20.2 Some Common Types of Applications of Simulation
    • Design and Operation of Queueing Systems
    • Managing Inventory Systems
    • Estimating the Probability of Completing a Project by the Deadline
    • Design and Operation of Manufacturing Systems
    • Design and Operation of Distribution Systems
    • Financial Risk Analysis
    • Health Care Applications
    • Applications to Other Service Industries
    • Military Applications
    • New Applications
  • 20.3 Generation of Random Numbers
    • Characteristics of Random Numbers
    • Congruential Methods for Random Number Generation
  • 20.4 Generation of Random Observations from a Probability Distribution
    • Simple Discrete Distributions
    • The Inverse Transformation Method
    • Summary of Inverse Transformation Method
    • Exponential and Erlang Distributions
    • Normal and Chi-Square Distributions
    • The Acceptance-Rejection Method
  • 20.5 Simulation Optimization
    • A Small State Space
    • Bechhofer’s Ranking and Selection Procedure for Small State Spaces
    • Other Ranking and Selection Procedures for Small State Spaces
    • A Large Discrete State Space
    • A Continuous State Space
    • Software for Simulation Optimization
  • 20.6 Outline of a Major Simulation Study
    • Step 1: Formulate the Problem and Plan the Study
    • Step 2: Collect the Data and Formulate the Simulation Model
    • Step 3: Check the Accuracy of the Simulation Model
    • Step 4: Select the Software and Construct a Computer Program
    • Step 5: Test the Validity of the Simulation Model
    • Step 6: Plan the Simulations to Be Performed
    • Step 7: Conduct the Simulation Runs and Analyze the Results
    • Step 8: Present Recommendations to Management
  • 20.7 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 20.1 Reducing In-Process Inventory, Revisited
  • Previews of Added Cases on Our Website
    • Case 20.2 Planning Planers
    • Case 20.3 Pricing under Pressure
• Appendixes
  • Appendix 1 Documentation for the OR Courseware
    • OR Tutor
    • IOR Tutorial
    • Excel Files
    • AMPL/Gurobi
    • LINGO/LINDO Files
    • Updates
  • Appendix 2 Convexity
    • Convex or Concave Functions of a Single Variable
    • Convex or Concave Functions of Several Variables
    • Convex Sets
  • Appendix 3 Classical Optimization Methods
    • Unconstrained Optimization of a Function of a Single Variable
    • Unconstrained Optimization of a Function of Several Variables
    • Constrained Optimization with Equality Constraints
    • The Derivative of a Definite Integral
  • Appendix 4 Matrices and Matrix Operations
    • Matrix Operations
    • Special Kinds of Matrices
    • Vectors
    • Some Properties of Matrices
  • Appendix 5 Table for a Normal Distribution
  • Appendix 6 Simultaneous Linear Equations
• Partial Answers to Selected Problems
  • Partial Answers to Selected Problems
• Author Index
  • Author Index
• Subject Index
  • Subject Index
• Online Chapter 18: Inventory Theory and Revenue Management
  • Chapter 18 Introduction
  • 18.1 Examples
  • 18.2 Components of Inventory Models
  • 18.3 Deterministic Continuous-Review Models
    • The Basic EOQ Model
    • The EOQ Model with Planned Shortages
    • The EOQ Model with Quantity Discounts
    • Some Useful Excel Templates
    • Observations about EOQ Models
    • Different Types of Demand for a Product
    • The Role of Just-In-Time (JIT) Inventory Management
  • 18.4 A Deterministic Periodic-Review Model
    • An Algorithm
    • Application of the Algorithm to the Example
  • 18.5 Deterministic Multiechelon Inventory Models for Supply Chain Management
    • A Model for a Serial Two-Echelon System
    • Rounding Procedure for n *
    • A Model for a Serial Multiechelon System
    • Assumptions for Serial Multiechelon Model
    • Outline of Phase 1 (Solve the Relaxation)
    • Outline of Phase 2 (Solve the Revised Problem)
    • Extensions of These Models
  • 18.6 A Stochastic Continuous-Review Model
    • The Assumptions of the Model
    • Choosing the Order Quantity Q
    • Choosing the Reorder Point R
  • 18.7 A Stochastic Single-Period Model for Perishable Products
    • Some Types of Perishable Products
    • The Assumptions of the Model
    • Analysis of the Model with No Initial Inventory ( I = 0 ) and No Setup Cost ( K = 0 )
    • Analysis of the Model with Initial Inventory ( I > 0 ) but No Setup Cost ( K = 0 )
    • Optimal Inventory Policy with I > 0 and K > 0
    • Analysis of the Model with a Setup Cost ( K > 0 )
    • Optimal Inventory Policy with I ≥ 0 and K > 0
    • An Approximate Solution for the Optimal Policy When the Demand Has an Exponential Distribution
  • 18.8 Revenue Management
    • A Model for Capacity-Controlled Discount Fares
    • An Overbooking Model
    • Other Models
  • 18.9 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 18.1 Brushing Up on Inventory Control
  • Previews of Added Cases on Our Website
    • Case 18.2 Dealing with a Perishable Product
    • Case 18.3 Jettisoning Surplus Stock
• Additional Cases: Chapter 3
  • Case 3.2 Cutting Cafeteria Costs
  • Case 3.3 Staffing a Call Center
  • Case 3.4 Promoting a Breakfast Cereal
  • Case 3.5 Auto Assembly
• Additional Cases: Chapter 20
  • Case 20.2 Planning Planers
  • Case 20.3 Pricing Under Pressure
• Supplement to Chapter 6
  • Supplement to Chapter 6: An Economic Interpretation of the Dual Problem and the Simplex Method
    • Interpretation of the Dual Problem
    • Interpretation of the Simplex Method
  • Problem
• Supplement to Chapter 9
  • Supplement 1 to Chapter 9: A Case Study with Many Transportation Problems
    • Background
    • Gathering the Necessary Data
    • Analysis (Six Applications of a Transportation Problem)
    • The Message to Management
  • Supplement 2 to Chapter 9: The Construction of Initial BF Solutions for Transportation Problems
  • Problems
• Supplement to Chapter 12
  • Supplement to Chapter 12: Some Innovative Uses of Binary Variables in Model Formulation
    • Either-Or Constraints
    • K out of N Constraints Must Hold
    • Functions with N Possible Values
  • Problems
• Supplement to Chapter 16
  • Supplement to Chapter 16: Preemptive Goal Programming and Its Solution Procedures
    • The Sequential Procedure for Preemptive Goal Programming
    • The Streamlined Procedure for Preemptive Goal Programming
  • Problems
  • Cases
    • Case 16S-1  A Cure for Cuba
    • Case 16S-2  Airport Security
• Supplement to Chapter 18
  • Supplement to Chapter 18: Stochastic Periodic-Review Models
    • A Stochastic Two-Period Model with No Setup Cost
    • Optimal Inventory Policy for Period 2
    • Optimal Inventory Policy for Period 1
    • Stochastic Multiperiod Models—An Overview
    • Optimal Inventory Policy
    • Optimal Inventory Policy
  • Learning Aids for this Supplement on this Website
  • Problems
• Supplement to Chapter 19
  • Supplement 1 to Chapter 19: A Policy Improvement Algorithm for Finding Optimal Policies
    • Preliminaries
    • The Policy Improvement Algorithm1
    • Summary of the Policy Improvement Algorithm
    • Solving the Prototype Example by the Policy Improvement Algorithm
  • Learning Aids for this Supplement on this Website
  • Problems
  • Supplement 2 to Chapter 19: A Discounted Cost Criterion
    • A Policy Improvement Algorithm
    • Summary of the Policy Improvement Algorithm (Discounted Cost Criterion)
    • Linear Programming Formulation
    • Finite-Period Markov Decision Processes and the Method of Successive Approximations
    • Solving the Prototype Example by the Method of Successive Approximations
  • Learning Aids for this Supplement on this Website
  • Problems
• Supplement to Chapter 20
  • Supplement 1 to Chapter 20: Variance-Reducing Techniques
    • Stratified Sampling
    • Method of Complementary Random Numbers
    • Conclusions
  • Problems
  • Supplement 2 to Chapter 20: Regenerative Method of Statistical Analysis
    • Traditional Methods and Their Shortcomings
    • The Regenerative Method Approach
    • Statistical Formulas
    • Application of the Statistical Formulas to the Example
  • Problems
• Online Chapter 21: The Art of Modeling with Spreadsheets
  • Chapter 21 Introduction
  • 21.1 A Case Study: The Everglade Golden Years Company Cash Flow Problem
  • 21.2 Overview of the Process of Modeling with Spreadsheets
    • Plan: Define the Problem and Gather the Data
    • Plan: Visualize Where You Want to Finish
    • Plan: Do Some Calculations by Hand
    • Plan: Sketch Out a Spreadsheet
    • Build: Start with a Small Version of the Spreadsheet
    • Test: Test the Small Version of the Model
    • Build: Expand the Model to Full-Scale Size
    • Test: Test the Full-Scale Version of the Model
    • Analyze: Analyze the Model
    • Conclusion of the Case Study
  • 21.3 Some Guidelines for Building “Good” Spreadsheet Models
    • Enter the Data First
    • Organize and Clearly Identify the Data
    • Enter Each Piece of Data into One Cell Only
    • Separate Data from Formulas
    • Keep it Simple
    • Use Range Names
    • Use Relative and Absolute Referencing to Simplify Copying Formulas
    • Use Borders, Shading, and Colors to Distinguish between Cell Types
    • Show the Entire Model on the Spreadsheet
    • A Poor Spreadsheet Model
  • 21.4 Debugging a Spreadsheet Model
  • 21.5 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 21.1 Prudent Provisions for Pensions
  • Acknowledgment
• Online Chapter 22: Project Management with PERT/CPM
  • Chapter 22 Introduction
  • 22.1 A Prototype Example—The Reliable Construction Co. Project
  • 22.2 Using a Network to Visually Display a Project
    • Project Networks
  • 22.3 Scheduling a Project with PERT/CPM
    • The Critical Path
    • Scheduling Individual Activities
    • Identifying Slack in the Schedule
    • Review
  • 22.4 Dealing with Uncertain Activity Durations
    • The PERT Three-Estimate Approach
    • Three Simplifying Approximations
    • Probability Distribution of Project Duration
    • Approximating the Probability of Meeting the Deadline
  • 22.5 Considering Time-Cost Trade-Offs
    • Time-Cost Trade-Offs for Individual Activities
    • Which Activities Should Be Crashed?
    • Using Linear Programming to Make Crashing Decisions
    • Mr. Perty’s Conclusions
  • 22.6 Scheduling and Controlling Project Costs
    • Scheduling Project Costs
    • Controlling Project Costs
  • 22.7 An Evaluation of PERT/CPM
    • The Value of PERT/CPM
    • Using the Computer
    • Approximating the Means and Variances of Activity Durations
    • Approximating the Probability of Meeting the Deadline
    • Dealing with Overlapping Activities
    • Incorporating the Allocation of Resources to Activities
    • The Future
  • 22.8 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 22.1 “School’s Out Forever . . .” Alice Cooper
• Online Chapter 23: Additional Special Types of Linear Programming Problems
  • Chapter 23 Introduction
  • 23.1 The Transshipment Problem
    • Prototype Example
    • General Features
  • 23.2 Multidivisional Problems
    • Prototype Example
    • Important Special Cases
  • 23.3 The Decomposition Principle for Multidivisional Problems
    • A Useful Reformulation (Decomposition) of the Problem
    • The Algorithm Based on This Decomposition
  • 23.4 Multitime Period Problems
    • Prototype Example
  • 23.5 Multidivisional Multitime Period Problems
  • 23.6 Conclusions
  • Selected References
  • Problems
• Online Chapter 24: Probability Theory
  • Chapter 24 Introduction
  • 24.1 Sample Space
  • 24.2 Random Variables
  • 24.3 Probability and Probability Distributions
  • 24.4 Conditional Probability and Independent Events
  • 24.5 Discrete Probability Distributions
    • Binomial Distribution
    • Poisson Distribution
    • Geometric Distribution
  • 24.6 Continuous Probability Distributions
    • The Exponential Distribution
    • The Gamma Distribution
    • The Beta Distribution
    • The Normal Distribution
  • 24.7 Expectation
  • 24.8 Moments
  • 24.9 Bivariate Probability Distribution
  • 24.10 Marginal and Conditional Probability Distributions
  • 24.11 Expectations for Bivariate Distributions
  • 24.12 Independent Random Variables and Random Samples
  • 24.13 Law of Large Numbers
    • Law of Large Numbers
  • 24.14 Central Limit Theorem
    • Central Limit Theorem
  • 24.15 Functions of Random Variables
  • Selected References
  • Problems
• Online Chapter 25: Reliability
  • Chapter 25 Introduction
  • 25.1 Structure Function of a System
    • Series System
    • Parallel System
    • k Out of n System
  • 25.2 System Reliability
    • Reliability of Series Systems
    • Reliability of Parallel Systems
    • Reliability of k Out of n Systems
  • 25.3 Calculation of Exact System Reliability
  • 25.4 Bounds on System Reliability
  • 25.5 Bounds on Reliability Based upon Failure Times
    • Bounds for IFR Distributions
    • Increasing Failure Rate Average
  • 25.6 Conclusions
  • Selected References
  • Problems
• Online Chapter 26: The Application of Queueing Theory
  • Chapter 26 Introduction
  • 26.1 Examples
  • 26.2 Decision Making
  • 26.3 Formulation of Waiting-Cost Functions
    • The g(N) Form
    • The h(𝒲) Form
  • 26.4 Decision Models
    • Model 1—Unknown s
    • Formulation of Model 1
    • Model 2—Unknown μ and s
    • Formulation of Model 2
    • Model 3—Unknown λ and s
    • Formulation of Model 3
  • 26.5 The Evaluation of Travel Time
    • A Basic Travel-Time Model
  • 26.6 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
• Online Chapter 27: Forecasting
  • Chapter 27 Introduction
  • 27.1 Some Applications of Forecasting
    • Sales Forecasting
    • Forecasting the Need for Spare Parts
    • Forecasting Production Yields
    • Forecasting Economic Trends
    • Forecasting Staffing Needs
    • Other
  • 27.2 Judgmental Forecasting Methods
  • 27.3 Time Series
  • 27.4 Forecasting Methods for a Constant-Level Model
    • Last-Value Forecasting Method
    • Averaging Forecasting Method
    • Moving-Average Forecasting Method
    • Exponential Smoothing Forecasting Method
  • 27.5 Incorporating Seasonal Effects into Forecasting Methods
    • The Seasonally Adjusted Time Series
    • The General Procedure
  • 27.6 An Exponential Smoothing Method for a Linear Trend Model
    • Adapting Exponential Smoothing to This Model
    • Application of the Method to the CCW Example
    • Forecasting More Than One Time Period Ahead
  • 27.7 Forecasting Errors
  • 27.8 The ARIMA Method
  • 27.9 Causal Forecasting with Linear Regression
    • Causal Forecasting
    • Linear Regression
    • Method of Least Squares
    • Confidence Interval Estimation of E ( Y | x = x * )
    • Predictions
  • 27.10 Conclusions
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
  • Cases
    • Case 27.1 Finagling the Forecasts
• Online Chapter 28: Markov Chains
  • Chapter 28 Introduction
  • 28.1 Stochastic Processes
    • A Weather Example
    • An Inventory Example
  • 28.2 Markov Chains
    • Formulating the Weather Example as a Markov Chain
    • Formulating the Inventory Example as a Markov Chain
    • Additional Examples of Markov Chains
  • 28.3 Chapman-Kolmogorov Equations
    • n-Step Transition Matrices for the Weather Example
    • n-Step Transition Matrices for the Inventory Example
    • Unconditional State Probabilities
  • 28.4 Classification of States of a Markov Chain
    • Recurrent States and Transient States
    • Periodicity Properties
  • 28.5 Long-Run Properties of Markov Chains
    • Steady-State Probabilities
    • Expected Average Cost per Unit Time
    • Expected Average Cost per Unit Time for Complex Cost Functions
  • 28.6 First Passage Times
  • 28.7 Absorbing States
  • 28.8 Continuous Time Markov Chains
    • Formulation
    • Some Key Random Variables
    • Steady-State Probabilities
  • Selected References
  • Learning Aids for this Chapter on Our Website
  • Problems
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  • A Decision Tree with the Blank Nodes, Probabilities Text Alternative (Chapter 16)
  • A Decision Tree with the Blank Nodes, Probabilities Text Alternative (Chapter 16)
  • Figure 17.1 Text Alternative (Chapter 17)
  • Figure 17.2 Text Alternative (Chapter 17)
  • Figure 17.3 Text Alternative (Chapter 17)
  • Figure 17.4 Text Alternative (Chapter 17)
  • Figure 17.5 Text Alternative (Chapter 17)
  • Figure 17.6 Text Alternative (Chapter 17)
  • Figure 17.7 Text Alternative (Chapter 17)
  • Figure 17.8 Text Alternative (Chapter 17)
  • Figure 17.9 Text Alternative (Chapter 17)
  • Figure 17.10 Text Alternative (Chapter 17)
  • Figure 17.11 Text Alternative (Chapter 17)
  • Figure 17.12 Text Alternative (Chapter 17)
  • Figure 17.13 Text Alternative (Chapter 17)
  • Figure 17.14 Text Alternative (Chapter 17)
  • An Illustration Shows the Conventional Labeling Text Alternative (Chapter 17)
  • The States 0, 1, 2, and 3 Along Text Alternative (Chapter 17)
  • Figure 18.1 Text Alternative (Chapter 18)
  • Figure 18.2 Text Alternative (Chapter 18)
  • Figure 18.3 Text Alternative (Chapter 18)
  • Figure 18.4 Text Alternative (Chapter 18)
  • Figure 18.5 Text Alternative (Chapter 18)
  • Figure 18.6 Text Alternative (Chapter 18)
  • Figure 18.7 Text Alternative (Chapter 18)
  • Figure 18.8 Text Alternative (Chapter 18)
  • Figure 18.9 Text Alternative (Chapter 18)
  • Figure 18.10 Text Alternative (Chapter 18)
  • Figure 18.11 Text Alternative (Chapter 18)
  • Figure 18.12 Text Alternative (Chapter 18)
  • Figure 18.13 Text Alternative (Chapter 18)
  • Figure 18.14 Text Alternative (Chapter 18)
  • Figure 18.15 Text Alternative (Chapter 18)
  • The Graph Plots Inventory Level Versus Text Alternative (Chapter 18)
  • A Matrix with the Columns Representing Decision Text Alternative (Chapter 19)
  • A Matrix with the Columns Represents Decision Text Alternative (Chapter 19)
  • Figure 20.1 Text Alternative (Chapter 20)
  • Figure 20.2 Text Alternative (Chapter 20)
  • Figure 20.3 Text Alternative (Chapter 20)
  • Figure 20.4 Text Alternative (Chapter 20)
  • Figure 20.5 Text Alternative (Chapter 20)
  • Figure 20.7 Text Alternative (Chapter 20)
  • A Line Graph Plots for CDF Versus Text Alternative (Chapter 20)
  • Figure 21.1 Text Alternative (Chapter 21)
  • Figure 21.2 Text Alternative (Chapter 21)
  • Figure 21.3 Text Alternative (Chapter 21)
  • Figure 21.4 Text Alternative (Chapter 21)
  • Figure 21.5 Text Alternative (Chapter 21)
  • Figure 21.6 Text Alternative (Chapter 21)
  • Figure 21.7 Text Alternative (Chapter 21)
  • Figure 21.8 Text Alternative (Chapter 21)
  • Figure 21.9 Text Alternative (Chapter 21)
  • Figure 21.10 Text Alternative (Chapter 21)
  • A Spreadsheet Formulation for Wyndor Glass Text Alternative (Chapter 21)
  • Figure 22.1 Text Alternative (Chapter 22)
  • Figure 22.2 Text Alternative (Chapter 22)
  • Figure 22.3 Text Alternative (Chapter 22)
  • Figure 22.4 Text Alternative (Chapter 22)
  • The Notation of Start and Finish Time Text Alternative (Chapter 22)
  • Figure 22.5 Text Alternative (Chapter 22)
  • Figure 22.6 Text Alternative (Chapter 22)
  • Figure 22.7 Text Alternative (Chapter 22)
  • Figure 22.8 Text Alternative (Chapter 22)
  • Figure 22.9 Text Alternative (Chapter 22)
  • Figure 22.10 Text Alternative (Chapter 22)
  • Figure 22.11 Text Alternative (Chapter 22)
  • Figure 22.12 Text Alternative (Chapter 22)
  • Figure 22.13 Text Alternative (Chapter 22)
  • Figure 22.14 Text Alternative (Chapter 22)
  • Figure 22.15 Text Alternative (Chapter 22)
  • A Project Network with 14 Activities Text Alternative (Chapter 22)
  • A Project Network with 10 Activities Text Alternative (Chapter 22)
  • A Project Network with 6 Activities Text Alternative (Chapter 22)
  • Project Network Consists of 10 Activities, A, B, C, D, E, F, G, H, I, and J Text Alternative (Chapter 22)
  • Network with 6 Activities Text Alternative (Chapter 22)
  • Table 23.1 Text Alternative (Chapter 23)
  • Figure 23.1 Text Alternative (Chapter 23)
  • Figure 23.2 Text Alternative (Chapter 23)
  • A Network with 4 Nodes Text Alternative (Chapter 23)
  • Table 23.4 Text Alternative (Chapter 23)
  • Table 23.5 Text Alternative (Chapter 23)
  • Table 23.6 Text Alternative (Chapter 23)
  • Table 23.7 Text Alternative (Chapter 23)
  • Figure 23.3 Text Alternative (Chapter 23)
  • Figure 23.4 Text Alternative (Chapter 23)
  • Table 23.8 Text Alternative (Chapter 23)
  • Table 23.9 Text Alternative (Chapter 23)
  • Table 23.11 Text Alternative (Chapter 23)
  • Table 23.12 Text Alternative (Chapter 23)
  • Table of Constraint Coefficients Text Alternative (Chapter 23)
  • Linear Programming Problem with 7 Entries Text Alternative (Chapter 23)
  • Linear Programming Problem with 10 Entries Text Alternative (Chapter 23)
  • Figure 24.1 Text Alternative (Chapter 24)
  • Figure 24.2 Text Alternative (Chapter 24)
  • Figure 24.3 Text Alternative (Chapter 24)
  • Figure 24.4 Text Alternative (Chapter 24)
  • Figure 24.5 Text Alternative (Chapter 24)
  • Figure 24.6 Text Alternative (Chapter 24)
  • Figure 24.7 Text Alternative (Chapter 24)
  • Figure 24.8 Text Alternative (Chapter 24)
  • Figure 24.9 Text Alternative (Chapter 24)
  • Figure 24.10 Text Alternative (Chapter 24)
  • Figure 24.11 Text Alternative (Chapter 24)
  • Figure 24.12 Text Alternative (Chapter 24)
  • Figure 24.13 Text Alternative (Chapter 24)
  • Figure 24.14 Text Alternative (Chapter 24)
  • Graphical Representation of a Triangular Text Alternative (Chapter 24)
  • Figure 25.1 Text Alternative (Chapter 25)
  • Figure 25.2 Text Alternative (Chapter 25)
  • Figure 25.3 Text Alternative (Chapter 25)
  • Figure 25.4 Text Alternative (Chapter 25)
  • A Network with 4 Components, 1, 2, 3, and 4 Text Alternative (Chapter 25)
  • A Network with 4 Components, 1, 2, 3, 4, and 5 Text Alternative (Chapter 25)
  • A Network with 4 Components, 1, 2,and 3 Text Alternative (Chapter 25)
  • A Network with 4 Components, 1, 2, 3, 4, 5, and 6 Text Alternative (Chapter 25)
  • Figure 26.1 Text Alternative (Chapter 26)
  • Figure 26.2 Text Alternative (Chapter 26)
  • Figure 26.3 Text Alternative (Chapter 26)
  • Figure 26.4 Text Alternative (Chapter 26)
  • Figure 26.5 Text Alternative (Chapter 26)
  • Figure 26.6 Text Alternative (Chapter 26)
  • Figure 26.7 Text Alternative (Chapter 26)
  • Figure 26.8 Text Alternative (Chapter 26)
  • Figure 26.9 Text Alternative (Chapter 26)
  • Figure 26.10 Text Alternative (Chapter 26)
  • Figure 26.11 Text Alternative (Chapter 26)
  • Figure 26.12 Text Alternative (Chapter 26)
  • Graphical Representation Text Alternative (Chapter 26)
  • Figure 27.1 Text Alternative (Chapter 27)
  • Figure 27.2 Text Alternative (Chapter 27)
  • Figure 27.3 Text Alternative (Chapter 27)
  • Figure 27.4 Text Alternative (Chapter 27)
  • Figure 27.5 Text Alternative (Chapter 27)
  • Figure 27.6 Text Alternative (Chapter 27)
  • Figure 27.7 Text Alternative (Chapter 27)
  • Figure 28.1 Text Alternative (Chapter 28)
  • Figure 28.2 Text Alternative (Chapter 28)
  • Figure 28.3 Text Alternative (Chapter 28)
  • Figure 28.4 Text Alternative (Chapter 28)
  • Figure 28.5 Text Alternative (Chapter 28)
  • Figure A2.1 Text Alternative (Chapter Appendix)
  • Figure A2.2 Text Alternative (Chapter Appendix)
  • Figure A2.3 Text Alternative (Chapter Appendix)
  • Figure A2.4 Text Alternative (Chapter Appendix)
  • Figure A2.5 Text Alternative (Chapter Appendix)
  • Figure A2.6 Text Alternative (Chapter Appendix)
  • Figure A2.7 Text Alternative (Chapter Appendix)
  • Figure A2.8 Text Alternative (Chapter Appendix)
  • Figure A2.9 Text Alternative (Chapter Appendix)
  • Figure A2.10 Text Alternative (Chapter Appendix)
  • Figure A2.11 Text Alternative (Chapter Appendix)
  • Figure A3.1 Text Alternative (Chapter Appendix)
  • A Graph Plots X Text Alternative (Chapter Answer)
  • A Flowchart for Winning Text Alternative (Chapter Answer)
  • A Network with 4 Nodes 0, 1, 2, 3 Text Alternative (Chapter Answer)
  • Figure 1 Text Alternative (Supplement 1 to Chapter 9)
  • Figure 2 Text Alternative (Supplement 1 to Chapter 9)
  • Figure 3 Text Alternative (Supplement 1 to Chapter 9)
  • Figure 4 Text Alternative (Supplement 1 to Chapter 9)
  • Figure 5 Text Alternative (Supplement 1 to Chapter 9)
  • Figure 6 Text Alternative (Supplement 1 to Chapter 9)
  • Figure 7 Text Alternative (Supplement 1 to Chapter 9)
  • Figure 8 Text Alternative (Supplement 1 to Chapter 9)
  • Table 1 Text Alternative (Supplement 2 to Chapter 9)
  • Table 2 Text Alternative (Supplement 2 to Chapter 9)
  • Figure 1 Text Alternative (Supplement to Chapter 12)
  • A Network with Six Nodes Text Alternative (Supplement to Chapter 12)
  • A Graph Plots Text Alternative (Supplement to Chapter 18)
  • Figure 1 Text Alternative (Supplement 1 to Chapter 20)
  • Figure 1(a) Text Alternative (Supplement 2 to Chapter 20)
  • Figure 1(b) Text Alternative (Supplement 2 to Chapter 20)

  UM RAFBÆKUR Á HEIMKAUP.IS

  Bókahillan þín er þitt svæði og þar eru bækurnar þínar geymdar. Þú kemst í bókahilluna þína hvar og hvenær sem er í tölvu eða snjalltæki. Einfalt og þægilegt!
  
  Rafbók til eignar
  Rafbók til eignar þarf að hlaða niður á þau tæki sem þú vilt nota innan eins árs frá því bókin er keypt.
  
  Þú kemst í bækurnar hvar sem er
  Þú getur nálgast allar raf(skóla)bækurnar þínar á einu augabragði, hvar og hvenær sem er í bókahillunni þinni. Engin taska, enginn kyndill og ekkert vesen (hvað þá yfirvigt).
  
  Auðvelt að fletta og leita
  Þú getur flakkað milli síðna og kafla eins og þér hentar best og farið beint í ákveðna kafla úr efnisyfirlitinu. Í leitinni finnur þú orð, kafla eða síður í einum smelli.
  
  Glósur og yfirstrikanir
  Þú getur auðkennt textabrot með mismunandi litum og skrifað glósur að vild í rafbókina. Þú getur jafnvel séð glósur og yfirstrikanir hjá bekkjarsystkinum og kennara ef þeir leyfa það. Allt á einum stað.
  
  Hvað viltu sjá? / Þú ræður hvernig síðan lítur út
  Þú lagar síðuna að þínum þörfum. Stækkaðu eða minnkaðu myndir og texta með multi-level zoom til að sjá síðuna eins og þér hentar best í þínu námi.
  
  
  
  Fleiri góðir kostir
  - Þú getur prentað síður úr bókinni (innan þeirra marka sem útgefandinn setur)
  - Möguleiki á tengingu við annað stafrænt og gagnvirkt efni, svo sem myndbönd eða spurningar úr efninu
  - Auðvelt að afrita og líma efni/texta fyrir t.d. heimaverkefni eða ritgerðir
  - Styður tækni sem hjálpar nemendum með sjón- eða heyrnarskerðingu