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IE 302 Recitation 3

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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 |} X = (x, y) P i = (a i, b i ) X = (x, y)

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Classification of Planar Facility Location Problems Facility Location Single- Facility Multi- Facility Minisum Minimax Rectilinear Euclidean Tchebyshev Rectilinear Euclidean Tchebyshev Rectilinear Euclidean Tchebyshev Rectilinear Euclidean Tchebyshev Minisum Minimax # of facilitiesObjectives Distance measures

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Discrete or continuous? M12 M3 3 M2 1 Example for discrete case M1, m2, m3 existing facilities 1, 2, 3 possible location sites Example for continuous case M1 M2 M3 M1, m2, m3 existing facilities No restricted location sites

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Minimax or minisum? Where to locate?

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Minimax or minisum? Total distance: 40 units Max distance: 25 units

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

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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.) Existing facility (a i,b i )WiWi 1(0,0)1 2(30,90)1 3(60,20)1 4(20,80)1 5(70,70)1 6(90,40)1

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