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| Review of Calculus and Probability | |
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| Review of Differential Calculus | |
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| Review of Integral Calculus | |
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| Differentiation of Integrals | |
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| Basic Rules of Probability | |
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| Bayes' Rule | |
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| Random Variables | |
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| Mean Variance and Covariance | |
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| The Normal Distribution | |
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| Z-Transforms | |
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| Review Problems | |
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| Decision Making Under Uncertainty | |
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| Decision Criteria | |
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| Utility Theory | |
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| Flaws in Expected Utility Maximization: Prospect Theory and Framing Effects | |
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| Decision Trees | |
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| Bayes' Rule and Decision Trees | |
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| Decision Making with Multiple Objectives | |
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| The Analytic Hierarchy Process | |
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| Review Problems | |
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| Deterministic Eoq Inventory Models | |
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| Introduction to Basic Inventory Models | |
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| The Basic Economic Order Quantity Model | |
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| Computing the Optimal Order Quantity When Quantity Discounts Are Allowed | |
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| The Continuous Rate EOQ Model | |
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| The EOQ Model with Back Orders Allowed | |
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| Multiple Product Economic Order Quantity Models | |
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| Review Problems | |
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| Probabilistic Inventory Models Single Period Decision Models | |
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| The Concept of Marginal Analysis | |
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| The News Vendor Problem: Discrete Demand | |
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| The News Vendor Problem: Continuous Demand | |
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| Other One-Period Models | |
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| The EOQ with Uncertain Demand: the (r, q) and (s, S models) | |
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| The EOQ with Uncertain Demand: The Service Level Approach to Determining Safety Stock Level | |
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| Periodic Review Policy | |
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| The ABC Inventory Classification System | |
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| Exchange Curves | |
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| Review Problems | |
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| Markov Chains | |
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| What is a Stochastic Process | |
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| What is a Markov Chain? N-Step Transition Probabilities | |
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| Classification of States in a Markov Chain | |
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| Steady-State Probabilities and Mean First Passage Times | |
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| Absorbing Chains | |
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| Work-Force Planning Models | |
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| Deterministic Dynamic Programming | |
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| Two Puzzles | |
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| A Network Problem | |
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| An Inventory Problem | |
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| Resource Allocation Problems | |
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| Equipment Replacement Problems | |
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| Formulating Dynamic Programming Recursions | |
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| The Wagner-Whitin Algorithm and the Silver-Meal Heuristic | |
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| Forward Recursions | |
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| Using Spreadsheets to Solve Dynamic Programming Problems | |
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| Review Problems | |
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| Probabilistic Dynamic Programming | |
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| When Current Stage Costs are Uncertain but the Next Period's State is Certain | |
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| A Probabilistic Inventory Model | |
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| How to Maximize the Probability of a Favorable Event Occurring | |
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| Further Examples of Probabilistic Dynamic Programming Formulations | |
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| Markov Decision Processes | |
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| Review Problems | |
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| Queuing Theory | |
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| Some Queuing Terminology | |
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| Modeling Arrival and Service Processes | |
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| Birth-Death Processes | |
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| M/M/1/GD/?V/?V Queuing System and the Queuing Formula L=?? W, The M/M/1/GD/?V Queuing System | |
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| The M/M/S/ GD/?V/?V Queuing System | |
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| The M/G/ ?V/GD/?V?V and GI/G/?V/GD/?V/?VModels | |
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| The M/ G/1/GD/?V/?V Queuing System | |
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| Finite Source Models: The Machine Repair Model | |
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| Exponential Queues in Series and Opening Queuing Networks | |
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| How to Tell whether Inter-arrival Times and Service Times Are Exponential | |
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| The M/G/S/GD/S/?V System (Blocked Customers Cleared) | |
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| Closed Queuing Networks | |
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| An Approximation for the G/G/M Queuing System | |
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| Priority Queuing Models | |
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| Transient Behavior of Queuing Systems | |
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| Review Problems | |
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| Simulation | |
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| Basic Terminology | |
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| An Example of a Discrete Event Simulation | |
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| Random Numbers and Monte Carlo Simulation | |
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| An Example of Monte Carlo Simulation | |
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| Simulations with Continuous Random Variables | |
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| An Example of a Stochastic Simulation | |
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| Statistical Analysis in Simulations | |
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| Simulation Languages | |
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| The Simulation Process | |
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| Simulation With Process Model | |
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| Simulating an M/M/1 Queuing System | |
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| Simulating an M/M/2 System | |
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| A Series System | |
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| Simulating Open Queuing Networks | |
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| Simulating Erlang Service Times | |
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| What Else Can Process Model Do? | |
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| Spreadsheet Simulation With @Risk | |
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| Introduction to @Risk: The Newsperson Problem | |
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| Modeling Cash Flows from a New Product | |
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| Bidding Models | |
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| Reliability and Warranty Modeling | |
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| RISKGENERAL Function | |
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| RISKCUMULATIVE Function | |
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| RISKTRIGEN Function | |
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| Creating a Distribution Based on a Point Forecast | |
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| Forecasting Income of a Major Corporation | |
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| Using Data to Obtain Inputs For New Product Simulations | |
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| Playing Craps with @RISK | |
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| Project Management | |
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| Simulating the NBA Finals | |
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| Spreadsheet Simulation and Optimization with Riskoptimizer | |
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| The Newsperson Problem | |
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| Newsperson Problem with Historical Data | |
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| Manpower Scheduling Under Uncertainty | |
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| Product Mix Problem | |
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| Job Shop Scheduling | |
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| Traveling Salesperson Problem | |
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| Option Pricing and Real Options | |
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| Lognormal Model For Stock Prices | |
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| Option Definitions | |
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| Types of Real Options | |
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| Valuing Options by Arbitrage Methods | |
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| Black-Scholes Option Pricing Formula | |
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| Estimating Volatility | |
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| Risk Neutral Approach to Option Pricing | |
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| Valuing an Internet Start Up and Web TV | |
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| Relation Between Binomial and Lognormal Models | |
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| Pricing American Options with Binomial Trees | |
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| Pricing European Puts and Calls with Simulation | |
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| Using Simulation to Model Real Options | |
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| Portfolio Risk, Optimization and Hedging | |
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| Measuring Value at Risk (VAR) | |
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| Scenario Approach to Portfolio Optimization | |
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| Forecasting | |
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| Moving Average Forecasting Methods | |
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| Simple Exponential Smoothing | |
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| Holt's Method: Exponential Smoothing with Trend | |
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| Winter's Method: Exponential Smoothing with Seasonality | |
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| Ad Hoc Forecasting, Simple Linear Regression | |
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| Fitting Non-Linear Relationships | |
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| Multiple Regression | |
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| Brownian Motion, Stochastic Calculus, and Optimal Control | |
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| What Is Brownian Motion? Derivation of Brownian Motion as a Limit of Random Walks | |
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| Stochastic Differential Equations | |
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| Ito's Lemma | |
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| Using Ito's Lemma to Derive the Black-Scholes Equation | |
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| An Introduction to Stochastic Control. | |