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IE 302 Recitation 3

IE 302 Recitation 3. Distance Measures. Rectilinear distance (L 1 norm) d(X, P i ) = |x - a i | + |y - b i | Straight line or Euclidean distance (L 2 norm) d(X, P i ) = Tchebyshev distance (L  norm) d(X, P i ) = max{|x - a i |, |y - b i |}. P i = (a i , b i ). X = (x, y).

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IE 302 Recitation 3

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  1. IE 302Recitation 3

  2. Distance Measures • Rectilinear distance (L1 norm) • d(X, Pi) = |x - ai| + |y - bi| • Straight line or Euclidean distance (L2 norm) • d(X, Pi) = • Tchebyshev distance (L norm) • d(X, Pi) = max{|x - ai|, |y - bi|} Pi = (ai, bi) X = (x, y) Pi = (ai, bi) X = (x, y) Pi = (ai, bi) X = (x, y)

  3. Rectilinear Minisum Euclidean Tchebyshev Single- Facility Rectilinear Minimax Euclidean Tchebyshev Facility Location Rectilinear Minisum Euclidean Tchebyshev Multi- Facility Rectilinear Minimax Euclidean Tchebyshev Classification of Planar Facility Location Problems # of facilities Objectives Distance measures

  4. Discrete or continuous? Example for discrete case Example for continuous case M1 M2 M3 M1, m2, m3 existing facilities No restricted location sites M1, m2, m3 existing facilities 1, 2, 3 possible location sites

  5. Minimax or minisum? Where to locate?

  6. Minimax or minisum? 5 5 5 25 Total distance: 40 units Max distance: 25 units

  7. Minimax or minisum? 15 15 15 15 Total distance: 60 units Max distance: 15 units Justice!

  8. Q1 • A new back up powe generator is to be located to serve a total of six precision machines in a manufacturing facility. Seperate electrical cables are to be run from the generator o each machine. The locations of the six machines are given in the table. Determine ehe location for the generator that will minimize the total required length of electrical cable. (Assume rectiliniar distance.)

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