The market-leading textbook for the course, Winston's OPERATIONS
RESEARCH owes much of its success to its practical orientation and
consistent emphasis on model formulation and model building. It moves
beyond a mere study of algorithms without sacrificing the rigor that
faculty desire. As in every edition, Winston reinforces the book's
successful features and coverage with the most recent developments in
the field.
Benefits:
NEW!-This edition places greater emphasis on spreadsheets, with more examples and instructions appearing throughout the text.
NeuralWorks Predict, DecisionTools Suite (@RISK, PrecisionTree, and BestFit), StatPro, and ProcessModel.
NEW!-Over 200 new exercises have been added, and hundreds have been revised.
NEW!-The text now includes output and instructions for using
ProcessModel and @Risk, two popular professional simulation software
packages.
NEW!-Many new examples are taken from hot emerging disciplines such as financial engineering.
The book's emphasis on model formulation and model building throughout reinforces the practical approach taken by this text.
The rich and thorough examples and exercises offer excellent applications to industry.
Table of Contents
1. INTRODUCTION TO MODEL BUILDING.
Introduction to Modeling. The Seven-Step Model-Building Process. Examples.
2. BASIC LINEAR ALGEBRA.
Matrices and Vectors. Matrices and Systems of Linear Equations. The Gauss-Jordan Method for Solving Systems
of Linear Equations. Linear Independence and Linear Dependence. The Inverse of a Matrix. Determinants.
3. INTRODUCTION TO LINEAR PROGRAMMING.
What is a Linear Programming Problem? The Graphical Solution of Two-Variable Linear Programming Problems. Special
Cases. A Diet Problem. A Work-Scheduling Problem. A Capital Budgeting Problem. Short-term Financial Planning. Blending
Problems. Production Process Models. Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory
Model. Multiperiod Financial Models. Multiperiod Work Scheduling.
4. THE SIMPLEX ALGORITHM AND GOAL PROGRAMMING.
How to Convert an LP to Standard Form. Preview of the Simplex Algorithm. The Simplex Algorithm. Using the Simplex
Algorithm to Solve Minimization Problems. Alternative Optimal Solutions. Unbounded LPs. The LINDO Computer Package.
Matrix Generators, LINGO, and Scaling of LPs. Degeneracy and the Convergence of the Simplex Algorithm. The Big
M Method. The Two-Phase Simplex Method. Unrestricted-in-Sign Variables. Karmarkar's Method for Solving LPs. Multiattribute
Decision-Making in the Absence of Uncertainty: Goal Programming. Solving LPs with Spreadsheets.
5. SENSITIVITY ANALYSIS: AN APPLIED APPROACH.
A Graphical Introduction to Sensitivity Analysis. The Computer and Sensitivity Analysis. Managerial Use of Shadow
Prices. What Happens to the Optimal z-value if the Current Basis is No Longer Optimal?
6. SENSITIVITY ANALYSIS AND DUALITY.
A Graphical Introduction to Sensitivity Analysis. Some Important Formulas. Sensitivity Analysis. Sensitivity
Analysis When More Than One Parameter is Changed: The 100% Rule. Finding the Dual of an LP. Economic Interpretation
of the Dual Problem. The Dual Theorem and Its Consequences. Shadow Prices. Duality and Sensitivity Analysis.
7. TRANSPORTATION, ASSIGNMENT, AND TRANSSHIPMENT PROBLEMS.
Formulating Transportation Problems. Finding Basic Feasible Solutions for Transportation Problems. The Transportation
Simplex Method. Sensitivity Analysis for Transportation Problems. Assignment Problems. Transshipment Problems.
8. NETWORK MODELS.
Basic Definitions. Shortest Path Problems. Maximum Flow Problems. CPM and PERT. Minimum Cost Network Flow Problems.
Minimum Spanning Tree Problems. The Network Simplex Method.
9. INTEGER PROGRAMMING.
Introduction to Integer Programming. Formulation Integer Programming Problems. The Branch-and-Bound Method for
Solving Pure Integer Programming Problems. The Branch-and-Bound Method for Solving Mixed Integer Programming Problems.
Solving Knapsack Problems by the Branch-and-Bound Method. Solving Combinatorial Optimization Problems by the Branch-and-Bound
Method. Implicit Enumeration. The Cutting Plane Algorithm.
10. ADVANCED TOPICS IN LINEAR PROGRAMMING.
The Revised Simplex Algorithm. The Product Form of the Inverse. Using Column Generation to Solve Large-Scale
LPs. The Dantzig-Wolfe Decomposition Algorithm. The Simplex Methods for Upper-Bounded Variables. Karmarkar's Method
for Solving LPs.
11. NONLINEAR PROGRAMMING.
Review of Differential Calculus. Introductory Concepts. Convex and Concave Functions. Solving NLPs with One
Variable. Golden Section Search. Unconstrained Maximization and Minimization with Several Variables. The Method
of Steepest Ascent. Lagrange Multiples. The Kuhn-Tucker Conditions. Quadratic Programming. Separable Programming.
The Method of Feasible Directions. Pareto Optimality and Tradeoff Curves.
12. REVIEW OF CALCULUS AND PROBABILITY.
Review of Integral Calculus. Differentiation of Integrals. Basic Rules of Probability. Bayes' Rule. Random Variables.
Mean Variance and Covariance. The Normal Distribution. Z-Transforms. Review Problems.
13. DECISION MAKING UNDER UNCERTAINTY.
Decision Criteria. Utility Theory. Flaws in Expected Utility Maximization: Prospect Theory and Framing Effects.
Decision Trees. Bayes' Rule and Decision Trees. Decision Making with Multiple Objectives. The Analytic Hierarchy
Process. Review Problems.
14. GAME THEORY.
Two-Person Zero-Sum and Constant-Sum Games: Saddle Points. Two-Person Zero-Sum Games: Randomized Strategies,
Domination, and Graphical Solution. Linear Programming and Zero-Sum Games. Two-Person Nonconstant-Sum Games. Introduction
to n-Person Game Theory. The Core of an n-Person Game. The Shapley Value.
15. DETERMINISTIC EOQ INVENTORY MODELS.
Introduction to Basic Inventory Models. The Basic Economic Order Quantity Model. Computing the Optimal Order
Quantity When Quantity Discounts Are Allowed. The Continuous Rate EOQ Model. The EOQ Model with Back Orders Allowed.
Multiple Product Economic Order Quantity Models. Review Problems.
16. PROBABILISTIC INVENTORY MODELS.
Single Period Decision Models. The Concept of Marginal Analysis. The News Vendor Problem: Discrete Demand. The
News Vendor Problem: Continuous Demand. Other One--Period Models. The EOQ with Uncertain Demand: the (r, q) and
(s,S models). The EOQ with Uncertain Demand: the Service Level Approach to Determining Safety Stock Level. Periodic
Review Policy. The ABC Inventory Classification System. Exchange Curves. Review Problems.
17. MARKOV CHAINS.
What is a Stochastic Process. What is a Markov Chain? N-Step Transition Probabilities. Classification of States
in a Markov Chain. Steady-State Probabilities and Mean First Passage Times. Absorbing Chains. Work-Force Planning
Models.
18.DETERMINISTIC DYNAMIC PROGRAMMING.
Two Puzzles. A Network Problem. An Inventory Problem. Resource Allocation Problems. Equipment Replacement Problems.
Formulating Dynamic Programming Recursions. The Wagner-Whitin Algorithm and the Silver-Meal Heuristic. Forward
Recursions. Using Spreadsheets to Solve Dynamic Programming Problems. Review Problems.
19. PROBABILISTIC DYNAMIC PROGRAMMING.
When Current Stage Costs are Uncertain but the Next Period's State is Certain. A Probabilistic Inventory Model.
How to Maximize the Probability of a Favorable Event Occurring. Further Examples of Probabilistic Dynamic Programming
Formulations. Markov Decision Processes. Review Problems.
20. QUEUING THEORY.
Some Queuing Terminology. Modeling Arrival and Service Processes. Birth-Death Processes. M/M/1/GD/o/o Queuing
System and the Queuing Formula L=o W, The M/M/1/GD/o Queuing System. The M/M/S/ GD/o/o Queuing System. The M/G/
o/GD/oo and GI/G/o/GD/o/oModels. The M/ G/1/GD/o/o Queuing System. Finite Source Models: The Machine Repair Model.
Exponential Queues in Series and Opening Queuing Networks. How to Tell whether Inter-arrival Times and Service
Times Are Exponential. The M/G/S/GD/S/o System (Blocked Customers Cleared). Closed Queuing Networks. An Approximation
for the G/G/M Queuing System. Priority Queuing Models. Transient Behavior of Queuing Systems. Review Problems.
21.SIMULATION.
Basic Terminology. An Example of a Discrete Event Simulation. Random Numbers and Monte Carlo Simulation. An
Example of Monte Carlo Simulation. Simulations with Continuous Random Variables. An Example of a Stochastic Simulation.
Statistical Analysis in Simulations. Simulation Languages. The Simulation Process.
22.SIMULATION WITH PROCESS MODEL.
Simulating an M/M/1 Queuing System. Simulating an M/M/2 System. A Series System. Simulating Open Queuing Networks.
Simulating Erlang Service Times. What Else Can Process Models Do?
23. SPREADSHEET SIMULATION WITH @RISK
Introduction to @RISK: The Newsperson Problem. Modeling Cash Flows From A New Product. Bidding Models. Reliability
and Warranty Modeling. Risk General Function. Risk Cumulative Function. Risktrigen Function. Creating a Distribution
Based on a Point Forecast. Forecasting Income of a Major Corporation. Using Data to Obtain Inputs For New Product
Simulations. Playing Craps with @RISK. Project Management. Simulating the NBA Finals.
24. FORECASTING.
Moving Average Forecasting Methods. Simple Exponential Smoothing. Holt's Method: Exponential Smoothing with
Trend. Winter's Method: Exponential Smoothing with Seasonality. Ad Hoc Forecasting, Simple Linear Regression. Fitting
Non-Linear Relationships. Multiple Regression.