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7-Introduction to Linear Optimization

# Origin of optimization 1940s application of

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Unformatted text preview: ond) starts the calculation from the Big Bang of the universe (15 billion years ago), •  Will it Finish by Year 2012? •  How about switching to a super computer that runs at 1 billion computations per second? •  How about we Fill the whole earth with super computers all running in parallel? •  Actually, we will need 1040 earths full of such super computers to run from the Big Bang until the Sun cools down … –  With modern optimization software, it takes less than a second to solve! Origin of Optimization (1940’s) Application of Optimization •  Military – logistics planning •  Business – manufacturing, Finance, marketing, transportation, communication, … •  Engineering – design of products, data analysis, … •  Science – medicine, biology, geometry, chemistry, physics, … •  … •  Games – Sudoku Key components in optimization modeling •  Decision variables –  What are the possible alternatives? •  Objective –  What do you want to achieve? •  Constraints –  What limit your choices? Example 2: A Transportation Problem •  Microsoft has three plants (1, 2, and 3) with monthly production capacity of 1,700, 2,000, and 1,700 units, respectively. •  Their XBoxes are sold through four retail outlets (A, B, C, and D) with monthly orders of 1,700, 1,000, 1,500, and 1,200 units, respectively. •  Transportation costs are as follows: Shipping costs cij (\$/unit) A B C D 1 5 3 2 6 2 7 7 8 10 3 6 5 3 8 Example 2: A Transportation Problem •  The network A 1 B 2 C 3 D Example 2: A Transportation Problem •  Task: C...
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