introduction to operations research. math 327 - mathematical modeling 2 introduction to operations...

Introduction to

Operations Research

MATH 327 - Mathematical Modeling

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Introduction to Operations Research Operations research/management science

– Winston: “a scientific approach to decision making, which seeks to determine how best to design and operate a system, usually under conditions requiring the allocation of scarce resources.”

– Kimball & Morse: “a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control.”


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Introduction to Operations Research

Provides rational basis for decision making– Solves the type of complex problems that turn up

in the modern business environment– Builds mathematical and computer models of

organizational systems composed of people, machines, and procedures

– Uses analytical and numerical techniques to make predictions and decisions based on these models


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Introduction to Operations Research

Draws upon – engineering, management, mathematics

Closely related to the "decision sciences" – applied mathematics, computer science,

economics, industrial engineering and systems engineering


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Methodology of Operations Research*The Seven Steps to a Good OR Analysis

Feedback loopsat all levels!

*Adapted from Winston, Wayne L., Operations Research: Applications and Algorithms, 3rd Edition, Duxbury Press, 1994, p. 2.

Identify the Problemor Opportunity

Understand the System

Formulate a Mathematical Model

Verify the Model

Select the Best Alternative

Implement and Evaluate

Present the Results ofthe Analysis


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Verify the Model




•What are the objectives?

•Is the proposed problem too narrow?

•Is it too broad?


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Verify the Model




•What data should be collected?

•How will data be collected?

•How do different components of the system interact with each other?


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Verify the Model




•What kind of model should be used?

•Is the model accurate?

•Is the model too complex?


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Verify the Model




•Do outputs match current observations for current inputs?

•Are outputs reasonable?

•Could the model be erroneous?


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Verify the Model




•What if there are conflicting objectives?

•Inherently the most difficult step.

•This is where software tools will help us!


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Verify the Model




•Must communicate results in layman’s terms.

•System must be user friendly!


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Verify the Model




•Users must be trained on the new system.

•System must be observed over time to ensure it works properly.


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Successful OR ApplicationsCompany Year Problem Techniques Used Annual Savings

Hewlett Packard 1998Designing buffers into production

lineQueuing models $280 million

Taco Bell 1998 Employee scheduling IP, Forecasting, Simulation $13 million

Proctor & Gamble 1997Redesign production & distributon

systemTransportation models $200 million

Delta Airlines 1994 Assigning planes to routes Integer Programming $100 million

AT&T 1993 Call center designQueuing models,

Simulation$750 million

Yellow Freight Systems, Inc.

1992 Design trucking networkNetwork models,

Forecasting, Simulation$17.3 million

San Francisco Police Dept.

1989 Patrol Scheduling Linear Programming $11 million

Bethlehem Steel 1989 Design an Ingot Mold Stripper Integer Programming $8 million

North American Van Lines

1988 Assigning loads to drivers Network modeling $2.5 million

Citgo Petroleum 1987 Refinery operations & distributionLinear Programming,

Forecasting$70 million

United Airlines 1986 Scheduling reservation personnel LP, Queuing, Forecasting $6 million

Dairyman's Creamery 1985 Optimal production levels Linear Programming $48,000

Phillips Petroleum 1983 Equipment replacement Network modeling $90,000

introduction to operations research. math 327 - mathematical modeling 2 introduction to operations...

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