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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 |