Introduction to Probability Models Operations Research: Volume Two

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-Period 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=?U 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.