交通大學開放式課程─作業研究(二)

課程目標/概述  

This is the second course that introduces deterministic and probabilistic optimization models such as dynamic programming, integer programming, nonlinear programming, Markov chain and queueing theory. This course focuses on modeling approaches, fundamental solution methodologies and their applications to the real world.

課程章節  

課程章節
單元主題
第10章
 Dynamic Programming
  10.1  A Prototype Example for Dynamic Programming
10.2 Characteristics of Dynamic Programming Problems
10.3 Deterministic Dynamic Programming ─ Example 4改為簡單案例
10.4 Probabilistic Dynamic Programming ─ 僅教Example 6
第11章
 Integer Programming
  11.1 Prototype Example
11.2 Some BIP Applications
11.3 Innovative Uses of Binary Variables in Model Formulation
11.4 Some Formulation Examples
11.5 Some Perspectives on Solving Integer Programming Problem
11.6 The Branch-and-Bound Technique and its Application to Binary integer Programming
11.7 A Branch-and-Bounds Algorithm for the Mixed Integer Programming
第12章
 Review of basic probability
  Review Calculus
12.1 Sample applications
12.2 Graphical Illustration of Nonlinear Programming Problems
12.3 Types of Nonlinear Programming Problems
12.4 One-Variable Unconstrained Optimization
Appendix 3: Constrained Optimization with Equality Constraints
12.5 Multivariable Unconstrained Optimization
12.6 The Karush-Kuhn-Tucker(KKT) Conditions for Constrained Optimization
12.7 Quadratic Programming
第16章
 Probabilistic Inventory Models
  Review Probability Theory
16.1 Stochastic Processes
16.2 Markov Chains
16.3 Chapman-Kolmogorov Equations　
16.4 Classification of States of a Markov Chain
16.5 Long-Run Properties of A Markov Chain
16.6 First Passage Times
16.7 Absorbing States
第17章
  Queueing Theory
  17.1 Prototype Example
17.2 Basic Structure of Queuing Models
17.3 Examples of Real Queuing Systems
17.4 The Role of the Exponential Distribution
17.5 The Birth-and-Death Process
17.6 Queuing Models Based on the Birth-and-Death Process
17.7 Queuing Models involving Nonexponential Distributions
17.8 Priority-Discipline Queuing Models
17.9 Queuing Networks
17.10 The Application of Queuing Theory
第20章
 Simulation (option)
  20.1 Simulations
20.2 Simulations
20.3 Simulations
20.4 Simulations

課程書目

F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, 8th edition, 2005, McGraw-Hill Inc.

 

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