Introduction to Operations Research

MATH Mathematical Modeling 2 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.”

MATH Mathematical Modeling 3 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

MATH Mathematical Modeling 4 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

MATH Mathematical Modeling 5 Methodology of Operations Research* The Seven Steps to a Good OR Analysis Feedback loops at all levels! *Adapted from Winston, Wayne L., Operations Research: Applications and Algorithms, 3rd Edition, Duxbury Press, 1994, p. 2. Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Implement and Evaluate Present the Results of the Analysis

MATH Mathematical Modeling 6 Methodology of Operations Research* The Seven Steps to a Good OR Analysis Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Implement and Evaluate Present the Results of the Analysis What are the objectives? Is the proposed problem too narrow? Is it too broad?

MATH Mathematical Modeling 7 Methodology of Operations Research* The Seven Steps to a Good OR Analysis Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Implement and Evaluate Present the Results of the Analysis What data should be collected? How will data be collected? How do different components of the system interact with each other?

MATH Mathematical Modeling 8 Methodology of Operations Research* The Seven Steps to a Good OR Analysis Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Implement and Evaluate Present the Results of the Analysis What kind of model should be used? Is the model accurate? Is the model too complex?

MATH Mathematical Modeling 9 Methodology of Operations Research* The Seven Steps to a Good OR Analysis Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Implement and Evaluate Present the Results of the Analysis Do outputs match current observations for current inputs? Are outputs reasonable? Could the model be erroneous?

MATH Mathematical Modeling 10 Methodology of Operations Research* The Seven Steps to a Good OR Analysis Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Implement and Evaluate Present the Results of the Analysis What if there are conflicting objectives? Inherently the most difficult step. This is where software tools will help us!

MATH Mathematical Modeling 11 Methodology of Operations Research* The Seven Steps to a Good OR Analysis Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Implement and Evaluate Present the Results of the Analysis Must communicate results in layman’s terms. System must be user friendly!

MATH Mathematical Modeling 12 Methodology of Operations Research* The Seven Steps to a Good OR Analysis Identify the Problem or Opportunity Understand the System Formulate a Mathematical Model Verify the Model Select the Best Alternative Implement and Evaluate Present the Results of the Analysis Users must be trained on the new system. System must be observed over time to ensure it works properly.

MATH Mathematical Modeling 13 Successful OR Applications