9780534405724

Introduction to Probability Models Operations Research, Volume II (with CD-ROM and InfoTrac)

by
  • ISBN13:

    9780534405724

  • ISBN10:

    053440572X

  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2003-06-05
  • Publisher: Duxbury Press

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Summary

This text, the second volume of Wayne Winston's successful OPERATIONS RESEARCH: APPLICATIONS AND ALGORITHMS, Fourth Edition, covers probability models with recent contributions from financial engineering, computational simulation and manufacturing. The specific attention to probability models with the addition of recent practical breakthroughs makes this the first text to introduce these ideas together at an accessible level. Excellent problem sets abound. The text provides a balanced approach by developing the underlying theory while illustrating them with interesting examples. All of the necessary mathematical requirements are reviewed in Chapter 1.

Table of Contents

1. REVIEW OF CALCULUS AND PROBABILITY
Review of Differential Calculus
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
2. 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
3. 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
4. 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¡XPeriod 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
5. 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
6. 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
7. 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
8. QUEUING THEORY
Some Queuing Terminology
Modeling Arrival and Service Processes
Birth-Death Processes
M/M/1/GD/„V/„V Queuing System and the Queuing Formula L=ƒÜ W, The M/M/1/GD/„V Queuing System
The M/M/S/ GD/„V/„V Queuing System
The M/G/ „V/GD/„V„V and GI/G/„V/GD/„V/„VModels
The M/ G/1/GD/„V/„V 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/„V 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
9. 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
10. 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 Model Do? 11. SPREADSHEET SIMULATION WITH @RISK
Introduction to @RISK: The Newsperson Problem
Modeling Cash Flows from a New Product
Bidding Models
Reliability and Warranty Modeling
RISKGENERAL Function
RISKCUMULATIVE 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
12. SPREADSHEET SIMULATION AND OPTIMIZATION WITH RISKOPTIMIZER
The Newsperson Problem
Newsperson Problem with Historical Data
Manpower Scheduling Under Uncertainty
Product Mix Problem
Job Shop Scheduling
Traveling Salesperson Problem
13. OPTION PRICING AND REAL OPTIONS
Lognormal Model for Stock Prices
Option Definitions
Types of Real Options
Valuing Options by Arbitrage Methods
Black-Scholes Option Pricing Formula
Estimating Volatility
Risk Neutral Approach to Option Pricing
Valuing an Internet Start Up and Web TV
Relation Between Binomial and Lognormal Models
Pricing American Options with Binomial Trees
Pricing European Puts and Calls with Simulation
Using Simulation to Model Real Options
14. PORTFOLIO RISK, OPTIMIZATION AND HEDGING
Measuring Value at Risk (VAR)
Scenario Approach to Portfolio Optimization
15. 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
16. BROWNIAN MOTION, STOCHASTIC CALCULUS, AND OPTIMAL CONTROL
What Is Brownian Motion? Derivation of Brownian Motion as a Limit of Random Walks
Stochastic Differential Equations
Ito's Lemma
Using Ito's Lemma to Derive the Black-Scholes Equation
An Introduction to Stochastic Control

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