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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