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

by Winston, Wayne L.

• ISBN13: 9780534405724
• ISBN10: 053440572X
• Edition: 4th
• Format: Hardcover
• Copyright: 2003-06-05
• Publisher: Duxbury Press

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