Data Preparation in Problem Formulation
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Questions and Answers

What is the objective of the mathematical model in Iron Works, Inc?

  • Maximize the total monthly production
  • Minimize the total amount of steel used
  • Maximize the total monthly profit (correct)
  • Minimize the total monthly profit

    • What is the constraint on the total amount of steel used?

  • a1x1 + a2x2 > b
  • a1x1 + a2x2 < b (correct)
  • a1x1 + a2x2 = b
  • a1x1 + a2x2 ≥ b

    • What is the minimum monthly production level of product 1?

  • x1 > m
  • x1 > 60
  • x1 ≥ 60 (correct)
  • x1 > 0

    • What is the maximum monthly production level of product 2?

    <p>x2 &lt; 720</p> Signup and view all the answers

    What is the profit per unit of product 1?

    <p>100</p> Signup and view all the answers

    What is the amount of steel required per unit of product 2?

    <p>3</p> Signup and view all the answers

    What is the total monthly profit function?

    <p>p1x1 + p2x2</p> Signup and view all the answers

    What is the rewritten model with the given specific values?

    <p>Max 100x1 + 200x2</p> Signup and view all the answers

    What was the issue Continental Airlines faced before September 11, 2001?

    <p>Recovering from limited and massive weather delays</p> Signup and view all the answers

    How many daily flights did Continental Airlines need to accommodate?

    <p>1,400 daily flights</p> Signup and view all the answers

    What was the result of Continental Airlines' project?

    <p>Millions of dollars and thousands of hours saved for the airline and its passengers</p> Signup and view all the answers

    What was Merrill Lynch's problem?

    <p>Dealing with online investment firms</p> Signup and view all the answers

    What was the objective of Merrill Lynch's project?

    <p>Evaluating new products and pricing options</p> Signup and view all the answers

    What was CALEB Technologies' role in Continental Airlines' project?

    <p>Developing an optimization model</p> Signup and view all the answers

    What was special about Continental Airlines' response to 9/11?

    <p>It was the first airline to resume normal operations</p> Signup and view all the answers

    What is the name of the website for more information on these successful stories?

    <p><a href="http://www.scienceofbetter.org">www.scienceofbetter.org</a></p> Signup and view all the answers

    What is the primary focus of the data preparation step in problem formulation?

    <p>Collecting and organizing data to minimize errors</p> Signup and view all the answers

    What is the outcome of a well-formulated problem statement?

    <p>A clear definition of variables and constraints</p> Signup and view all the answers

    What is the primary purpose of a mathematical model?

    <p>To evaluate and delimit allowable actions</p> Signup and view all the answers

    What is the result of a model with 50 decision variables and 25 constraints?

    <p>A large number of data elements</p> Signup and view all the answers

    What is the role of information systems specialists in data preparation?

    <p>To assist in collecting and organizing data</p> Signup and view all the answers

    What is the goal of the problem formulation step?

    <p>To translate verbal statements into logical models</p> Signup and view all the answers

    What is the relationship between a logical model and a computer program?

    <p>A logical model is often embodied in a computer program</p> Signup and view all the answers

    What is the purpose of defining relationships between individual nurse assignments and preference violations?

    <p>To evaluate and delimit allowable actions</p> Signup and view all the answers

    What is the age deduction per year in the Austin Auto Auction model?

    <p>$800</p> Signup and view all the answers

    What is the mileage deduction per mile in the Austin Auto Auction model?

    <p>$0.025</p> Signup and view all the answers

    What is the expression for the expected winning bid in terms of the car's original price, current age, and mileage?

    <p>P - 800(A) - .025(M)</p> Signup and view all the answers

    What is the assumption underlying the Austin Auto Auction model regarding the factors that influence a car's value?

    <p>Only age and mileage affect a car's value.</p> Signup and view all the answers

    What is the unit profit for product 1 in the Iron Works, Inc. example?

    <p>p1</p> Signup and view all the answers

    What is the restriction on the production level of product 1 in the Iron Works, Inc. example?

    <p>At least m units of product 1</p> Signup and view all the answers

    What are the variables x1 and x2 in the Iron Works, Inc. example?

    <p>The production levels of products 1 and 2</p> Signup and view all the answers

    What is the expression for the starting bid in the Austin Auto Auction model?

    <p>B = .7(P) - 560(A) - .0175(M)</p> Signup and view all the answers

    What was the main objective of Ford Motor's Prototype Optimization Model?

    <p>To reduce the number of prototype vehicles</p> Signup and view all the answers

    What was the outcome of Ford's Prototype Optimization Model?

    <p>Reduced annual prototype costs by $250 million</p> Signup and view all the answers

    What was the main challenge facing Procter & Gamble's supply chain?

    <p>Eliminating duplication and non-value-added costs</p> Signup and view all the answers

    What was the goal of Procter & Gamble's operations research department?

    <p>To create decision-making models and software</p> Signup and view all the answers

    What was the approach used by the P&G operations research department to solve the supply chain problem?

    <p>Solving two easier-to-handle subproblems</p> Signup and view all the answers

    What was the outcome of Procter & Gamble's Strengthening Global Effectiveness effort?

    <p>Saved $200 million a year before tax</p> Signup and view all the answers

    What was the main advantage of increasing prototype usage at Ford Motor?

    <p>Reducing idle time of prototypes</p> Signup and view all the answers

    What was the collaboration between Ford Motor and Wayne State University?

    <p>Developing a Prototype Optimization Model</p> Signup and view all the answers

    Study Notes

    Problem Formulation

    • A problem situation involves defining variables, boundaries, assumptions, and performance measures.
    • A problem statement translates the problem from verbal to logical, quantitative terms.
    • Data preparation is a crucial step that requires a significant amount of time and may require information systems specialists.

    Data Preparation

    • Data preparation involves collecting and preparing data elements, which can be a time-consuming process prone to errors.
    • A large database may be required, and the process may need expertise from information systems specialists.

    Constructing a Model

    • A model is a representation of a real object or situation.
    • A logical model consists of a series of rules, usually embodied in a computer program.
    • A mathematical model is a collection of functional relationships that delimit and evaluate allowable actions.

    Model Development

    • Models can be developed to represent real objects or situations, such as the Austin Auto Auction example.
    • The example shows how to develop a mathematical model to determine the starting bid for a car based on its original price, age, and mileage.

    Mathematical Modeling

    • Mathematical models can be used to solve real-world problems, such as the Iron Works, Inc. example.
    • The example shows how to develop a mathematical model to maximize profit for a company that manufactures two products made from steel.

    Case Studies

    • Several case studies are presented, including:
      • Continental Airlines, which used optimization models to plan recovery from potential disasters.
      • Merrill Lynch, which evaluated new products and pricing options using mathematical models.
      • Ford Motor, which developed a prototype optimization model to reduce the number of prototype vehicles.
      • Procter & Gamble, which used decision-making models to improve its supply chain and streamline work processes.

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    Learn about the importance of data preparation in problem formulation, including defining variables, setting boundaries, and preparing data elements. Understand the process and potential pitfalls of data preparation.

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