Chapter 1: What is Operations Research?
1.1 Operations Research Models
1.2 Solving the OR Model
1.3 Queueing and Simulation Models
1.4 Art of Modeling
1.5 More than Just Mathematics
1.6 Phases of an OR Study
1.7 About this Book
Problems
References
Chapter 2: Modeling with Linear Programming
2.1 Two-Variable LP Model
2.2 Graphical LP Solution
2.3 Selected LP Applications
2.4 Computer Solution with Solver and AMPL
Problems
References
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
3.4 Artificial Starting Solution
3.5 Special Cases in the Simplex Method
3.6 Sensitivity Analysis
Problems
References
Chapter 4: Duality and Post-Optimal Analysis
4.1 Definition of the Dual Problem
4.2 Primal-Dual Relationships
4.3 Economic Interpretation of Duality
4.4 Additional Simplex Algorithms
4.5 Post-Optimal Analysis
Problems
References
Chapter 5: Transportation Model and its Variants
5.1 Definition of the Transportation Model
5.2 Nontraditional Transportation Models
5.3 The Transportation Algorithm
5.4 The Assignment Model
5.5 The Transshipment Model
Problems
References
Chapter 6: Network Models
6.1 Scope and Definition of Network Models
6.2 Minimal Spanning Tree Algorithm
6.3 Shortest-Route Problem
6.4 Maximal Flow Model
6.5 CPM and PERT
Problems
References
Chapter 7: Advanced Linear Programming
7.1 Simplex Method Fundamentals
7.2 Revised Simplex Method
7.3 Bounded Variables Algorithm
7.4 Duality
7.5 Parametric Linear Programming
Problems
References
Chapter 8: Goal Programming
8.1 A Goal Programming Formulation
8.2 Goal Programming Algorithms
Problems
References
Chapter 9: Integer Linear Programming
9.1 Illustrative Applications
9.2 Integer Programming Algorithms
9.3 Traveling Salesperson (TSP) Problem
Problems
References
Chapter 10: Deterministic Dynamic Programming
10.1 Recursive Nature of Computations in DP
10.2 Forward and Backward Recursion
10.3 Selected DP Applications
10.4 Problem of Dimensionality
Problems
References
Chapter 11: Deterministic Inventory Models
11.1 General Inventory Model
11.2 Role of Demand in the Development of Inventory Models
11.3 Static Economic-Order-Quantity (EOQ) Models
11.4 Dynamic EOQ Models
Problems
References
Chapter 12: Review of Basic Probability
12.1 Laws of Probability
12.2 Random Variables and Probability Distributions
12.3 Expectation of a Random Variable
12.4 Four Common Probability Distributions
12.5 Empirical Distributions
Problems
References
Chapter 13: Decision Analysis and Games
13.1 Decision Making under Certainty-Analytic Hierarchy Process (AHP)
13.2 Decision Making under Risk
13.3 Decision under Uncertainty
13.4 Game Theory
Problems
References
Chapter 14: Probabilistic Inventory Models
14.1 Continuous Review Models
14.2 Single-Period Models
14.3 Multiperiod Model
Problems
References
Chapter 15:Queueing Systems
15.1 Why Study Queues?
15.2 Elements of a Queuing Model
15.3 Role of Exponential Distribution
15.4 Pure Birth and Death Models (Relationship between the Exponential and Poisson Distributions)
15.5 Generalized Poisson Queuing Model
15.6 Specialized Poisson Queues
15.7 (M/G/1):(GD/Inf/Inf)-Pollaczek-Khintchine (P-K) Formula
15.8 Other Queuing Models
15.9 Queueing Decision Models
Problems
References
Chapter 16: Simulation Modeling
16.1 Monte Carlo Simulation
16.2 Types of Simulation
16.3 Elements of Discrete-Event Simulation
16.4 Generation of Random Numbers
16.5 Mechanics of Discrete Simulation
16.6 Methods for Gathering Statistical Observations
16.7 Simulation Languages
Problems
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
17.4Steady-State Probabilities and Mean Return Times of Ergodic Chains
17.5 First Passage Time
17.6 Analysis of Absorbing States
Problems
References
Chapter 18: Classical Optimization Theory
18.1 Unconstrained Problems
18.2 Constrained Problems
Problems
References
Chapter 19: Nonlinear Programming Algorithms
19.1 Unconstrained Algorithms
19.2 Constrained Algorithms
Problems
References
Appendix A: AMPL Modeling Language
A.1 Rudimentary AMPL Model
A.2 Components of AMPL Model
A.3 Mathematical Expressions and Computed Parameters
A.4 Subsets and Indexed Sets
A.5 Accessing External Files
A.6 Interactive Commands
A.7 Iterative and Conditional Execution of AMPL Commads
A.8 Sensitivity Analysis Using AMPL
Reference
Appendix B: Statistical Tables
Appendix C: Partial Answers to Selected Problems
Index
On the CD
Chapter 20: Additional Network and LP Algorithms
20.1 Minimim-Cost Capacitated Flow Problem
20.2 Decomposition Alogrithm
20.3 Karmarkar Interior-Point Method
Problems
References
Chapter 21: Forecasting Models
21.1 Moving Average Technique
21.2 Exponential Smoothing
21.3 Maximization of the Event of Achieving a Goal
Problems
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
Problems
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
23.4 Linear Programming Solution
Problems
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 Assignments 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 of 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 D: Review of Vectors and Matrices
D.1 Vectors
D.2 Matrices
D.3 Quadratic Forms
D.4 Convex and Concave Functions
Problems
References
Appendix E: Case Studies
