Chapter 13 Advanced Linear Programming 13.1 Simplex Method Fundamentals 13.1.1 From Extreme Points to Basic Solutions 13.1.2 Generalized Simplex Tableau in Matrix Form 13.2 Revised Simplex Method 13.2.1 Development of the Optimality and FeasibilityConditions 13.2.2 Revised Simplex Algorithm 13.3 Bounded-Variables Algorithm 13.4 Duality 13.4.1 Matrix Definition of the Dual Problem 13.4.2 Optimal Dual Solution 13.5 Parametric Linear Programming 13.5.1 Parametric Changes in C 13.5.2 Parametric Changes in b References 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 Mean and Variance of 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 References Chapter 15 Probabilistic Inventory Models 15.1 Continuous Review Models 15.1.1 “Probabilitized” EOQ Model 15.1.2 Probabilistic EOQ Model 15.2 Single-Period Models 15.2.1 No-Setup Model (Newsvendor Model) 15.2.2 Setup Model (s-S Policy) 15.3 Multiperiod Model References Chapter 16 Simulation Modeling 16.1 Monte Carlo Simulation 16.2 Types of Simulation 16.3 Elements of Discrete-Event Simulation 16.3.1 Generic Definition of Events 16.3.2 Sampling from Probability Distributions 16.4 Generation of Random Numbers 16.5 Mechanics of Discrete Simulation 16.5.1 Manual Simulation of a Single-Server Model 16.5.2 Spreadsheet-Based Simulation of the Single-Server Model 16.6 Methods for Gathering Statistical Observations 16.6.1 Subinterval Method 16.6.2 Replication Method 16.6.3 Regenerative (Cycle) Method 16.7 Simulation Languages References 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 References Chapter 18 Classical Optimization Theory 18.1 Unconstrained Problems 18.1.1 Necessary and Sufficient Conditions 18.1.2 The Newton-Raphson Method 18.2 Constrained Problems 18.2.1 Equality Constraints 18.2.2 Inequality Constraints-Karush-Kuhn-Tucker (KKT)Conditions References Chapter 19 Nonlinear Progra mming Algorivthms 19.1 Unconstrained Algorithms 19.1.1 Direct Search Method 19.1.2 Gradient Method 19.2 Constrained Algorithms 19.2.1 Separable Programming 19.2.2 Quadratic Programming 19.2.3 Chance-Constrained Programming 19.2.4 Linear Combinations Method References Chapter 20 Additional Network and LP Algorithms 20.1 Minimum-Cost Capacitated Flow Problem 20.1.1 Network Representation 20.1.2 Linear Programming Formulation 20.1.3 Capacitated Network Simplex Algorithm 20.2 Decomposition Algorithm 20.3 Karmarkar Interior-Point Method 20.3.1 Basic Idea of the Interior-Point Algorithm 20.3.2 Interior-Point Algorithm References Chapter 21 Forecasting Models 21.1 Moving Average Technique 21.2 Exponential Smoothing 21.3 Regression References Chapter 22 Probabilistic Dynamic Programming 22.1 A Game of Chance 22.2 Investment Problem 22.3 Maximization of the Event of Achieving a Goal References Chapter 23 Markovian Decision Process 23.1 Scope of the Markovian Decision Problem 23.2 Finite-Stage Dynamic Programming Model 23.3 Infinite-Stage Model 23.3.1 Exhaustive Enumeration Method 23.3.2 Policy Iteration Method Without Discounting 23.3.3 Policy Iteration Method with Discounting 23.4 Linear Programming Solution References Chapter 24 Case Analysis Case 1: Airline Fuel Allocation Using Optimum Tankering Case 2: Optimization of Heart Valves Production Case 3: Scheduling Appointments at Australian Tourist Commission Trade Events Case 4: Saving Federal Travel Dollars Case 5: Optimal Ship Routing and Personnel Assignment for Naval Recruitment in Thailand Case 6: Allocation of Operating Room Time in Mount Sinai Hospital Case 7: Optimizing Trailer Payloads at PFG Building Glass Case 8: Optimization of Crosscutting and Log Allocation at Weyerhaeuser Case 9: Layout Planning for a Computer Integrated Manufacturing (CIM) Facility Case 10: Booking Limits in Hotel Reservations Case 11: Casey's Problem: Interpreting and Evaluating a New Test Case 12: Ordering Golfers on the Final Day of Ryder Cup Matches Case 13: Inventory Decisions in Dell's Supply Chain Case 14: Analysis of an Internal Transport System in a Manufacturing Plant Case 15: Telephone Sales Manpower Planning at Qantas Airways Appendix B Statistical Tables Appendix C Partial Solutions to Answers Problems Appendix D Review of Vectors and Matrices D.1 Vectors D.1.1 Definition of a Vector D.1.2 Addition (Subtraction) of Vectors D.1.3 Multiplication of Vectors by Scalars D.1.4 Linearly Independent Vectors D.2 Matrices D.2.1 Definition of a Matrix D.2.2 Types of Matrices D.2.3 Matrix Arithmetic Operations D.2.4 Determinant of a Square Matrix D.2.5 Nonsingular Matrix D.2.6 Inverse of a Nonsingular Matrix D.2.7 Methods of Computing the Inverse of Matrix D.2.8 Matrix Manipulations Using Excel D.3 Quadratic Forms D.4 Convex and Concave Functions Problems Selected References Appendix E Case Studies
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