456556 Introduction to Operations Research

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456/556 Introduction to Operations Research

• Chapter 1 Introduction
• Chapter 2 Overview of the Operations Research
  Modeling Approach

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Origins of Operations Research

• Operations Research (OR) or Management Science
  can be defined as the use of quantitative methods
  to assist analysts and decision makers in
  designing, analyzing, and improving the
  performance or operations of systems.
• OR is a branch of mathematics that grew out of
  the need during WWII to allocate scarce resources
  to various military operations in an effective
  manner.

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Origins of Operations Research (cont.)

• Examples include
• The development and use of radar for detecting
  and tracking aircraft.
• Allocation of scarce resources (raw materials,
  parts, time, people) to problems such as
• Producing high octane fuel,
• Developing systems for detection of submarines
  and aircraft,
• Strategic and tactical planning in order to
  achieve military and industrial goals.

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Origins of Operations Research (cont.)

• After WWII, an industrial boom led to increasing
  complexity and specialization in organizations.
• Typical problems that needed to be solved
• How to get various components of a company
  working at cross purposes to work together.
• How to allocate limited resources in the most
  effective way.

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Origins of Operations Research (cont.)

• People who had worked on OR problems for the
  military realized that these new problems were
  basically the same as those faced by the military
  in a different context.
• Two factors that have played a key role in the
  growth of OR are
• The development of powerful techniques for
  solving OR problems such as the simplex method
  developed by George Dantzig in 1947.
• The digital computer - large scale OR problems
  are solvable and anyone with a personal computer
  can solve OR problems with software such as
  Excel.

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The Nature of Operations Research

• Operations research is applied to problems that
  deal with how to conduct and coordinate the
  operations (or activities) within an
  organization.
• Some of the areas where OR has been applied
• Manufacturing
• Transportation
• Construction
• Telecommunications
• Financial Planning
• Health care
• Military
• Public services
• See Table 1.1 (p. 4) in our textbook for some
  actual problems solved by OR techinques!
• Some specific examples follow!

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Reengineering IBMs Global Supply Chain

• In 1994, IBM began to reengineer its global
  supply chain.
• It wanted to achieve quick responsiveness to
  customers with minimal inventory.
• To support this effort, an extended-enterprise
  supply-chain analysis tool, the Asset Management
  Tool (AMT) was developed.
• AMT integrates graphical process modeling,
  analytical performance optimization, simulation,
  activity-based costing, and enterprise database
  connectivity into a system that allows
  quantitative analysis of extended supply chains.
• IBM has used AMT to study such issues as
  inventory budgets, turnover objectives,
  customer-service targets, and new-product
  introductions.
• It has been implemented at a number of IBM
  business units and their channel partners.
• AMT benefits include over 750 million in
  material costs and price-protection expenses
  saved in 1998.
• INTERFACES 30 1 JanuaryFebruary 2000 (pp. 725)

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Nuclear Weapons Dismantlement, Evaluation, and
Maintenance

• The end of the Cold War changed the missions of
  facilities in the US nuclear weapons complex.
• They ceased production of new weapons and focused
  on dismantling old weapons and maintaining the
  safety, security, and reliability of those
  remaining.
• The Pantex Plant, operated for the US Department
  of Energy (DOE) by the Mason and Hanger
  Corporation, is the sole assembly and disassembly
  facility for dismantlement, evaluation, and
  maintenance activities for the US nuclear
  stockpile.
• A decision support tool, the Pantex Process Model
  (PPM), was developed to help Pantex plan capacity
  and deploy resources to meet its new
  requirements.
• Using the PPM, Pantex has provided critical input
  to help the US form and defend positions during
  arms-control-treaty negotiations.
• It has changed the way Pantex and the DOE
  evaluate resource requirements in planning future
  workloads.
• It has also led to an innovative cooperative
  agreement among Pantex, the Transportation
  Safeguards Division of DOE, and the Department of
  Defense (DOD) that resulted in Pantex exceeding
  weapon dismantlement goals.
• INTERFACES 30 1 JanuaryFebruary 2000 (pp. 5782)

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Optimized Crew Scheduling at Air New Zealand

• The aircrew-scheduling problem consists of two
  important subproblems
• The tours-of-duty planning problem to generate
  minimum-cost tours of duty (sequences of duty
  periods and rest periods) to cover all scheduled
  flights
• The rostering problem to assign tours of duty to
  individual crew members.
• Between 1986 and 1999, Air New Zealand staff and
  consultants in collaboration with the University
  of Auckland have developed eight
  application-specific optimization-based computer
  systems to solve all aspects of the tours-of-duty
  planning and rostering processes for Air New
  Zealands national and international operations.
• These systems have saved NZ15,655,000 per year
  while providing crew rosters that better respect
  crew members preferences.
• INTERFACES 31 1 JanuaryFebruary 2001 (pp. 3056)

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Characterization of Operations Research

• The scientific method is used to investigate
  problems to be solved.
• OR is concerned with practical management of an
  organization.
• OR must provide positive, understandable
  conclusions to decision makers when they are
  needed!
• OR takes a broad viewpoint
• OR attempts to resolve conflicts of interest
  among components of an organization in a way that
  is best for the organization as a whole.

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Characterization of Operations Research (cont.)

• The goal of OR is to find a best (optimal)
  solution.
• Usually, the problems in OR need to be solved
  with a team of people with a collective expertise
  in
• Mathematics
• Statistics and probability theory
• Economics
• Business administration
• Computer science
• Physical sciences
• Behavioral sciences
• Special techniques of OR

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Overview of the OR Modeling Approach

• An OR study usually consists of the following
  (overlapping) phases
• 1. Define the problem of interest and gather
  relevant data.
• 2. Formulate a mathematical model to represent
  the problem.
• 3. Develop a computer-based procedure for
  deriving solutions to the problem from the model.
• 4. Test the model and refine it as needed.
• 5. Prepare for the ongoing application of the
  model as prescribed by management.
• 6. Implement.

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Modeling Process in General
Real World Problem
Mathematical Model
Solve Mathematical Model
Compare Model Solution to Real World
Refine Model
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Homework

• Read Chapters 1 and 2 in our textbook.
• Read INTERFACES journal articles on three
  specific applications of OR discussed above.
• Read the article History in the Making  INFORMS
  celebrates 50 years of problems, solutions,
  anecdotes and achievement  (http//www.lionhrtpub
  .com/orms/orms-10-02/frhistory.html)
• p. 7 1.3-2 (apply to three applications of OR
  discussed above).

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References

• Operations Research A Practical Introduction by
  Michael W. Carter and Camille C. Price, CRC
  Press, 2001.
• Introduction to Operations Research (8th ed) by
  Frederick S. Hiller and Gerald J. Lieberman,
  McGraw Hill, 2005.
• Interfaces Journal, Jan. - Feb. Issues, Volumes
  30 and 31 (http//interfaces.pubs.informs.org/)