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Applications of LP/ILP Models

Applications of LP/ILP Models. Tran Van Hoai Faculty of Computer Science & Engineering HCMC University of Technology. Evolution of LP/ILP. Millions USD saved from applying LP/ILP to business/government Motivated by Simplex Digital computers Applied to. Building good LP/ILP models.

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Applications of LP/ILP Models

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  1. Applications of LP/ILP Models Tran Van HoaiFaculty of Computer Science & Engineering HCMC University of Technology Tran Van Hoai

  2. Evolution of LP/ILP • Millions USD saved from applying LP/ILP to business/government • Motivated by • Simplex • Digital computers • Applied to Tran Van Hoai

  3. Building good LP/ILP models • Familiarity • Limited resources • Overall (tradeoff) objective • Different perspectives • Simplification • Models always simplify real-life, but which is simplified is important • Clarity • Model must be clear What constitutes the proper simplification is subject to individual judgment and experience (George Dantzig) Tran Van Hoai

  4. Summation variables/constraints • Introduce new variables to be easier to understand/debug • Summation of variables/constraints • Production of 3 TV models • resource: 7000 pounds plastic • 2 pounds/TV1, 3 pounds/TV2, 4 pounds/TV3 • profit: • $23/TV1, $34/TV2, $45/TV3 • management constraint: not any TV model exceed 40% total production Tran Van Hoai

  5. First model Not management constraint anymore No meaning as natural input (especially on spreadsheet) Tran Van Hoai

  6. Revised model • Define summation variable X4 = total production of TVs • Add summation constraint X1 + X2 + X3 - X4 = 0 Clarity (although more variables/constraints) Summation constraint Summation variable Tran Van Hoai

  7. Applications of LP/ILP • More realistic example • Reduced version in different practical applications • Portfolio model Tran Van Hoai

  8. Financial portfolio model • Consider return projections of investment • Measure of risk, volatility, liquidity, short/long term • Highly nonlinear in nature, but we consider a linear case Tran Van Hoai

  9. Jones investment service(advise clients on investment) • Problem summary • Determine amount to be placed in each investment • Minimize total risk • Invest all $100,000 • Meet the goals developed with client • annual return at least 7% • at least 50% in A-rated investments • at least 40% in immediately liquid investments • no more $30,000 in savings and deposit Tran Van Hoai

  10. LP model Tran Van Hoai

  11. Analysis (1) • Binding constraints • What exceed minimum requirements • Investment Tran Van Hoai

  12. Analysis (2) • Reduced costs: in order to be included, risk factor must be lowered • Optimality range • Shadow price: risk increased by Tran Van Hoai

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