Introduction to Probability Models

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.

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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-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=? 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.
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