作業研究（二）

Abstract

本課程是由交通大學 運輸與物流管理學系提供。

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

章節名稱 章節名稱

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 nonlinear programming

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

Markov Chain

Review Probability Theory 16.1 Stochastic Processes 16.2 Markov Chains 16.3 Chapman-Kolmogorov Equations 16.4 Classification of States of a Markov Chan 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.

評分標準

項目 百分比

3次期中考試(每次各佔25%) 75%

作業、隨堂小考、隨堂表現、出席率 25%

期中、期末考試依院方規定統一安排會考：預定利用4/9、5/14、6/25星期四傍晚(考試時間17:30-19:30, YI )進行會考，請依院方公告時間為主。

授課對象：大學二年級學生

預備知識：Calculus 與Probability Theory