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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. | |