l8printrolinpgm

l8printrolinpgm - Introduction to Linear Programming Eric...

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Introduction to Linear Programming Eric Feron (updated Sommer Gentry) (updated by Paul Robertson) 16.410/16.413 Historical aspects Historical contributor: G. Dantzig, late 1940’s (Now at Stanford University). Realize many real-world design problems can be formulated as linear programs and solved efficiently. Finds algorithm, the Simplex method to solve LP’s. As of 1997, still best algorithm for most applications. So important for world economy that any new algorithmic development on LP’s is likely to make the Front Page of major newspapers (e.g. NY times, Wall Street Journal). Example: 1979 L. Khachyan’s adaptation of ellipsoid algorithm, N. Karmarkar’s new interior-point algorithm. A remarkably practical and theoretical framework: LPs eat a large chunk of total scientific computational power expended today. It is crucial for economic success of most distribution/transport industries and to manufacturing. Now becomes suitable for real-time applications . Examples of Linear programs 1
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Example 2: Resource Allocation • An aircraft company makes two aircraft engines. Engine parts are made at three plants: A, B, C. – Engine 1 is made of elements produced in A and C – Engine 2 is made of elements of B and C • Plants A, B, C have limited throughput • What mix of product 1 and 2 will bring maximum profit? Another resource allocation problem.
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l8printrolinpgm - Introduction to Linear Programming Eric...

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