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Introduction to Linear Programming and Standardization: Week IV Overview

This week focuses on the introduction of Linear Programming (LP) concepts, particularly LP standardization. We will review the general and standard forms of LP, dive into definitions, basic assumptions, and explore various modeling examples including the server problem. Additionally, we'll tackle the time assignment problem, optimizing total cost under given constraints, and illustrate these concepts with LINGO programming. By the end of this week, you will have a solid understanding of LP's foundational elements and their applications in problem-solving.

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Introduction to Linear Programming and Standardization: Week IV Overview

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  1. Agenda of Week IV. LPII Objective : • Understanding the introduction of LP 1 2 Week 3 LP Standardization • LP introduction • General form • Standard form

  2. Review of Week 3 Objective : • Understanding the introduction of LP • Understanding LP 2 3 1 LP intro LP Standardization Solving • General form • How to get… • Definition • Basic assumptions • Example

  3. Modeling Examples of LP • Example 3-2 • Server problem: p.113 • Lingo program • Example 3-3 • P.126 • Lingo program

  4. LP Standard from of LP

  5. Transformation • Minimization • Multiply -1 to obj. func. • Non nonnegativity • Decompose variable x into 2 variables • Give nonnegativity to both variables • Equality constraint • Decompose it into 2 constraints with ‘>=‘ and ‘<=‘ • Multiply -1 to constraint with ‘>=‘

  6. Examples of LP Standard Form • Example 3-2 • Server problem: p.113 • Lingo program • Example 3-3 • P.126 • Lingo program

  7. Week 4 Summary Example • Time assignment problem • Total 80 hours for a week • Alternatives: study, date, Alcohol, exercise, idle • Utility/hour: 6, 18, 12, 11, 7 • Cost/hour: 1000, 2200, 1800, 1500, 1200 • Minimum utility:800 • Minimization of total cost

  8. Week 4 Summary Example

  9. Week 4 Summary Example

  10. LINGO Illustration • Time assignment problem • Modeling the minimization problem • Transformation to standard form • Solution

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