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Operations Research Applications

IEEM 5170作業研究應用

授課教師: 陳茂生

Course Description:

介紹作業研究各種應用,學生將熟悉作業研究常用之電腦套

裝軟體,經由案例學習,強調資料收集、資料分析過程以及決

策表達。

This course surveys various models and techniques in operations research, with emphasis on applications. It focuses on: (1) datacollection for analysis (2) data analysis process (3) the development of modeling skills (4) sensitivity analysis and computer supporting systems (5) the interpretation of results. Topics include linear, integer and network optimization models. Simulation analysis and other topics in stochastic processes arealso included.

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Deterministic Models in Operations Researchdecisions making under certainty

Probabilistic Models in Operations Researchdecisions making under uncertainty

Dynamic Programming11.

Nonlinear Programming10.

Integer Programming9.

Network Optimization Models8.

Incorporating Uncertainty into a Linear Program7.

Multiple Criteria Decision Making and Goal Programming6.

Duality Theory and Sensitivity Analysis & Data Envelop Analysis 5.

Solving Linear Programming4.

Introduction to Linear Programming, Portfolio Optimization and Case Study3.

Modeling Approach of Operations Research2.

Introduction to Operations Research: History of OR etc.1.

Course Contents:

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Text Books & References:

1. Frederick S. Hillier and Gerald J. Lieberman, Introduction to Operations Research, 8th ed. McGraw Hill, New York 2005.

2. Lecture Notes, Case Problems.3. Selected literatures in Omega, Interface, Decision Science, OR/MS Today

etc.4. Computer Software: LINGO, Microsoft Project 2000, STORM, LINDO,

GINO, . . . , etc..5. 網路資源World-Wide-Web

Course Homepage: http://chern.ie.nthu.edu.tw/ora/ora.htm

Grading: Assignments 10%, Mid-Term 25%, Attendance 10% Case Report & Presentation 65%

Case Problems

NetworkThe Federal Power Commission Transport of Alaskan Natural Gas

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NetworkAluminum Products International9.

NetworkBay Area Bakery Company8.

Linear ProgrammingAvis Rent a Car system, Inc.7.

Linear ProgrammingScott Paper Company6.

Linear ProgrammingLowell Steel Corporation5.

Linear ProgrammingKrebs Wire Company4.

Linear ProgrammingDelta Oil Refinery3.

Linear ProgrammingGenessee Wire and Cable2.

Linear ProgrammingKuwait’s al-Manakh Stock Market1.

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Integer ProgrammingSectoral Planning for the Indian Concrete Industry

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Integer ProgrammingThe Bubble19.

Integer ProgrammingHunt-Wesson Foods, Inc.18.

Integer ProgrammingAgua del Pueblo, Inc.17.

integer programmingStocking Sets16.

Project ManagementSchool’s Out Forever15.

Project ManagementSteps to Success14.

Data Envelopment AnalysisFinancial Institution (1) (2)13.

NetworkAiding Allies12

NetworkChrysler Corporation Plant Loading Model

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A, B (Linear Programming)C (Multiple Criteria Decision Making)

Mitchell Enterprises (A) (B) (C)27.

A(Integer Programming)B(Nonlinear programming)

New York City Environmental Protection Administration (A)

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Nonlinear ProgrammingCity of Centerville(A) (B)25.

Nonlinear ProgrammingThe Netherlands Dairy Fund24.

Probabilistic Linear Programming

Carnation International23.

Probabilistic Linear Programming

Agricultural Chemical International22.

A (Linear Programming)B (Integer Programming)

Assigning Students to School & Revisited A, B

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宏觀的思維與觀察:

微觀 ( Micro - ) 宏觀 (Macro - )

見樹不見林lose the forest for the trees

Butterfly Effect (蝴蝶效應)

Chapter 1 Introduction

History of Operations Research:

Research on Radar: This work involved the closest possible cooperation between the scientists and the officers and men of the (English) Royal Air Force, so that the best tactical operations of both equipment and men, air and ground crews, could be achieved.

1935 - 1937

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1938A.P. Rowe was in charge of the scientific group at Bawdsey, refereed to it as "Operational Research". (Bawdsey is the birthplace of Operations Research.)

1942 U.S. captain W. D. Baker, an anti-submarine warfare officer with Atlantic Fleet, requested the establishment of an Anti-Submarine Warfare Operations Research Group(ASWORG). To lead ASWORG, later named Operations Research Group and attached to the Headquarters of the Commander-in-Chief, U.S. Navy. Philip, M. Morse, a physicist, was recruited from

military operations

Massachusetts Institute of Technology to be project supervisor, and William Bradford Shockley, later to win a Nobel Prize for his work on the transistor, was brought from the Bell Laboratories to be director of research.

Blackett early 1941 memorandum emphasized that the work of operational research was the “ scientific analysis of operations". Its objective is to assist the finding of means to improve the efficiency of air operations in progress or planned for the future. To do this, past operations are studied to determine the facts; theories are elaborated to explain the facts; and finally the facts and theories are used to make predictions about future operations . . .

William B. Skockley

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After the 2nd World War, the success of OR in the war effort spurred interest in applying OR outside the military as well. As the industrial boom, the problems caused by the increasing complexity and specialization in organizations were coming to the forefront. By the early 1950s, these who served on or with the OR team had introduced the use of OR to a variety of organizations in business, industry, and government. The rapid spread of OR soon followed.

At least two other factors played a key role in the rapid growth of OR. One is the substantial progress that was made early in improving the techniques of OR. A second factor is the computer revolution. This brought the use of OR within the easy reach of much larger number of people.

(Operations Research Society of America)

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Research on (military) operations, 1935Management Sciences (synonym)System Sciences

What is Operations Research/ Management Sciences?

1. The focus of the Operations Research is on applications of mathematics and logic in research and decision-making on operations, as well as problem solving in all types of public and private organization business, industry, government and state enterprises in order to bring about optimal outcomes in organizational operations.

Scientific Methods

2. “Scientific approach to decision making that involves the operations for organized systems. O.R. is concerned with optimal decision making in and modeling of deterministic and probabilistic systems that originate from real life,” – Hillier & Lieberman, Introduction to Operations Research, 8th Ed., Holden-Day, 2005.

3. “Operations Research is the application of scientific methods to decision problems. It has found wide use and acceptance in all areas of business, government and industry.” – Saul L. Gass, College of Business & Management, University of Maryland, 1979.

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4. “The use of analytic methods adapted from mathematics for solving operational and business problems” –Computer Dictionary, Charles J. Sippl and Charles P. Sippl, Howard W. Sams & Co., Inc., Indianapolis, 1978.

5. “A scientific method of providing executive department with a quantitative basis for decisions making operations under their control.” – Morse & Kimball, Methods of Operations Research, Columbia University Press for office of Naval Research, 1943 (9th printing, 1963).

6. “A branch of applied mathematics wherein the application is to the decision making process,” –Donald Gross, Department of Operations Research, The George Washington University, 1979.

7. Operations research employs mathematical models to suggest how best to operate and coordinate the activities within an organization. The tools of operations research are applied in industry, commerce, government, the military, education, health - in fact in virtually any area of human activity.

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8. Operations Research (OR) is the study of how to form mathematical models of complex engineering and management problems and how to analyze them to gain insight about possible solutions. - Ronald L. Rardin, Optimization in Operations Research, prentice-Hall, Inc., 1998

The Origins of Operations Research:1. The World War II; Its object is to assist the finding of

means to improve the war operations in progress or planned for the future. To do this past studied to determine the facts; theories are elaborated to explain finally the facts and theories are used to make predictions about future operations.

2. Industrial revolution - increasing complexity (size) and specification in (creating new problems)

3. Computer Revolution

4. OR is applied to problems that concern how to conduct and coordinate the activities within an organization.

5. Scientific method; scientific research into the fundamental properties of practical management of the organization; OR uses the method of understand and explain phenomena of operating system.

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The Impact of Operations Research:

4. International Federation of Operations Research Societies (IFORS) -more than 30 countries, January,1, 1959.

2. Operations Research Society of America ORSA, founded May 26-27, 1952.

3. The Institute of Management Sciences TIMS, founded 1953.

5. The Institute of Operations Research and Management Sciences INFORMS: ORSA and TIMS are merged in 1995.

1. Operational Research Quarterly (Journal of Operational Research Society), the appearing in March 1950.

6. Operations Research Society of Taiwan, founded 2003.

Applications of Operations Research (case studies):

Team approach

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問題模式

理論

資料結構

演算法

程式

問題OR模式

理論

資料結構

演算法

程式

台灣數學建模與創意學會

http://model.chiuchang.com.tw/model/

Problem Solving Procedure:

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Research on Problem Solving:

Modeling

Theory Algorithms(methodologies)

Problems ApplicationsProblems Modeling Applications

Theory Algorithms(Methodologies)

WASSILY LEONTIEF1973 Nobel Laureate in Economicsfor the development of the input-output method and for its application to important economic problems. BackgroundBorn: 1906Place of Birth: St. Petersburg, RussiaResidence: U.S.A.Affiliation: Harvard University, Cambridge, MA

Nobel Laureates and Operations Research:

KENNETH J. ARROW1972 Nobel Laureate in Economicsfor their pioneering contributions to general economic equilibrium theory and welfare theory. BackgroundBorn: 1921Residence: U.S.A.Affiliation: Harvard University, Cambridge, MA

Nobel e-museum http://nobelprize.org/index.html

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LEONID VITALIYEVICH KANTOROVICH1975 Nobel Laureate in Economicsfor their contributions to the theory of optimum allocation of resources. Background1912-1986Residence: USSRAffiliation: Academy of Sciences, Moscow

TJALLING C. KOOPMANS1975 Nobel Laureate in Economicsfor their contributions to the theory of optimum allocation of resources. Background1910-1985Place of Birth: s'Graveland, the NetherlandsResidence: U.S.A.Affiliation: Yale University, New Haven,

HARRY M. MARKOWITZ1990 Nobel Laureate in Economicsfor their pioneering work in the theory of financial economics. BackgroundBorn: 1927Residence: U.S.A.Affiliation: City University of New York, NY

JOHN F. NASH1994 Nobel Laureate in Economicsfor their pioneering analysis of equilibria in the theory of non-cooperative games. Background

•Born: June 13, 1928 •Place of birth: Bluefield, West Virginia •Affiliation: Princeton University, NJ •Education:

•Carnegie Mellon University, B.S., M.S. 1948 •Princeton University, Ph. D. 1950 •Massachusetts Institute of Technology, C. L. E. Moore Instructor 1951-1959

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ROBERT J. AUMANN2005 Nobel Laureate in Economicsfor having enhanced our understanding of conflict and cooperation through game-theory analysis. • Background•Born: June 8, 1930•Residence: ISRAELAffiliation: Hebrew University of Jerusalem, Israel

•Education: City College of New York, B.S., Mathematics, 1950 Massachusetts Institute of Technology, S.M.,

Mathematics, 1952 Massachusetts Institute of Technology, Ph.D.,

Mathematics, 1955

THOMAS C. SCHELLING2005 Nobel Laureate in Economicsfor having enhanced our understanding of conflict and cooperation through game-theory analysis. Background

•Born: 1921•Place of birth: Oakland, CA, USA•Affiliation: Department of Economics and School of Public Policy, University of Maryland, College Park, MD, USA , NJ •Education:

•University of California, A.B.,Economics, 1944 •Harvard University, Ph.D., Economics, 1951

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Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, 2002-03 Edition, Operations Research Analysts

Operations research and management science are terms that are used interchangeably to describe the discipline of applying advanced analytical techniques to help make better decisions andto solve problems. The procedures of operations research gave effective assistance during World War II in missions such as deploying radar, searching for enemy submarines, and getting supplies where they were most needed. Following the war, new analytical methods were developed and numerous peacetime applications emerged, leading to the use of operations research in many industries and occupations.

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The prevalence of operations research in the Nation's economy reflects the growing complexity of managing large organizations that require the effective use of money, materials, equipment, and people. Operations research analysts help determine better ways to coordinate these elements by applying analytical methods from mathematics, science, and engineering. They solve problems in different ways and propose alternative solutions to management, which then chooses the course of action that best meets the organization's goals. In general, operations research analysts may be concerned with diverse issues such as top-level strategy, planning, forecasting, resource allocation, performance measurement, scheduling, design of production facilities and systems, supply chain management, pricing, transportation and distribution, and analysis of data in large databases.

The duties of the operations research analyst vary according to the structure and management philosophy of the employer or client. Some firms centralize operations research in one department; others use operations research in each division. Operations research analysts also may work closely with senior managers to identify and solve a variety of problems. Some organizations contract operations research services with a consulting firm. Economists, systems analysts, mathematicians, industrial engineers, and others also may apply operations research techniques to address problems in their respective fields. (These occupations are discussed elsewhere in the Handbook.)

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Operations research analysts also must be able to think logically and work well with people, and employers prefer workers with good oral and written communication skills.

Because computers are the most important tools for in-depth analysis, training and experience in programming are required. Operations research analysts typically need to be proficient in database collection and management, programming, and in the development and use of sophisticated software programs.

Many jobs in operations research have other titles such as operations analyst, management analyst, systems analyst, or policy analyst. Individuals who hold a master's or Ph.D. degree in operations research, management science, or a closely related field should find good job opportunities as the number of openings generated by employment growth and the need to replace those leaving the occupation is expected to exceed the number of persons graduating with these credentials.

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Opportunities for operations research analysts exist in almost every industry because of the diversity of applications for their work. However, opportunities should be especially good in highly competitive industries, such as manufacturing, transportation, and telecommunications, and finance. As businesses and government agencies continue to contract out jobs to cut costs, many operations research analysts also will find opportunities as consultants, either working for a consulting firm or setting up their own practice. Opportunities in the military also exist, but will depend on the size of future military budgets. As the military develops new weaponssystems and strategies, military leaders will rely on operations research analysts to test and evaluate their accuracy and effectiveness.

THE DISCIPLINES THE METHODS AND THEORIESPhysical ScienceMathematicsPolitical SciencesSocial Sciences Business Administration Industrial Engineering Behavior Science Economics Computer Science

. . .

Mathematical Programming, Scheduling Theory, Inventory Theory, Network Theory, Layout and Location Theory, Game Theory, Decision Theory,Probability& Statistics, Stochastic Process, Reliability Theory, Queuing Theories, Simulation, Decision Theory, . . .

↘ ↙Operations Research

↓

The Applications↓

Education, Manufacturing, Engineering Design, Heath, Finance, Energy and Utilities, Transportation, Environmental, Military, Forest Management, Financial Engineering . . .

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1. 作業研究(Operations Research OR)與管理科學 (ManagementScience)是否不相同?

Summary

Operations Research 這個名稱的來源如何?為何會有 OR 這個領域產生?OR的發源地在那裡?OR 的技術為何會愈來愈重要(需求愈來愈多)?OR與電腦科學的發展有什麼關連性?

2. 解釋什麼是”作業研究”。3. ”作業研究”有那些領域?4. 列舉一些”作業研究”的應用。5. 應用”作業研究”技術來解決案例問題時, 應有什麼態度? 應注意些什麼事項?

OR 的理論與技術是否發展愈來愈多,應用範圍愈來愈廣?