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Network Model 1 DR Rahma Fitriani, S.Si., M.Sc., Riset Operasi 2011 Semester Genap 2011/2012
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Shortest Path Problem Pengiriman dari titik ke titik Supply, transhipment (substation), dan demand nodes Shortest path problem – Biaya proportional dengan jarak – Masalah pemilihan jarak terpendek (biaya minimum)
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Contoh: 1 3 2 5 4 6 Sumber Tujuan 4 3 3 3 2 2 2
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Algoritma Djikstra Check the file in MS words..
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1 3 2 5 4 6 4 3 3 3 2 2 2
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 ∞∞ ∞ ∞∞ Distance label Temporary ={1, 2, 3, 4, 5, 6} Permanent={ }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 ∞∞ ∞ ∞∞ Distance label Permanen Temporary ={2, 3, 4, 5, 6} Permanent={1 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 ∞∞ ∞ ∞∞ Distance label Permanen Temporary ={2, 3, 4, 5, 6} Permanent={1 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 4∞ ∞ 3∞ Temporary Distance label Permanen Temporary ={2, 3, 4, 5, 6} Permanent={1 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 4∞ ∞ 3∞ Temporary Distance label Permanen Temporary ={2, 4, 5, 6} Permanent={1, 3 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 4∞ ∞ 3∞ Temporary Distance label Permanen Temporary ={2, 4, 5, 6} Permanent={1, 3 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 4∞ ∞ 36 Temporary Distance label Permanen Temporary ={2, 4, 5, 6} Permanent={1, 3 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 4∞ ∞ 36 Temporary Distance label Permanen Temporary ={4, 5, 6} Permanent={1, 2,3 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 4∞ ∞ 36 Temporary Distance label Permanen Temporary ={4, 5, 6} Permanent={1, 2,3 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 ∞ 36 Temporary Distance label Permanen Temporary ={4, 5, 6} Permanent={1, 2,3 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 ∞ 36 Temporary Distance label Permanen Temporary ={4, 5, 6} Permanent={1, 2,3 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 ∞ 36 Temporary Distance label Permanen Temporary ={4, 6} Permanent={1, 2,3, 5 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 8 36 Temporary Distance label Permanen Temporary ={4, 6} Permanent={1, 2,3, 5 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 8 36 Temporary Distance label Permanen Temporary ={4, 6} Permanent={1, 2,3, 5 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 8 36 Temporary Distance label Permanen Temporary ={6} Permanent={1, 2,3, 4, 5 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 Min (9,8)=8 36 Temporary Distance label Permanen Temporary ={6} Permanent={1, 2,3, 4, 5 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 8 36 Temporary Distance label Permanen Temporary ={ } Permanent={1, 2,3, 4, 5, 6 }
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1 3 2 5 4 6 4 3 3 3 2 2 2 0 47 8 36 Temporary Distance label Permanen Shortest path: 1 – 2 – 5 – 6
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Shortest Path sebagai Transhipment Problem Transhipment problem dengan setiap demand dan supply sama dengan 1 Jalur yang tidak terdefinisi dikenai biaya besar Biaya nol untuk jalur dari node i ke node i
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Cost23456Supply 14310000 1 20 32 1 3 0 3 1 4 0 21 5 021 Demand11111 1 3 2 5 4 6 4 3 3 3 2 2 2
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Model LP shortest path sbg transhipment problem
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Solusi optimal Contoh: 1 3 2 5 4 6 Sumber Tujuan 4 2 2 Total distance (cost) = 8
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Max Flow Problem Model network di mana kapasitas jalur diperhitungkan Tujuan: Memaksimumkan jumlah pengiriman dari source ke destination dengan kendala kapasitas setiap jalur
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Contoh: dengan kapasitas setiap jalur S 3 1 2 D 2 3 3 4 1 2 a0 a0 jalur buatan untuk conservation flow, outflow = inflow
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LP untuk max flow problem S 3 1 2 D 2 3 3 4 1 2 a0 See Excell Transhipme nt.xlsx Transhipme nt.xlsx
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Solusi optimal max flow S 3 1 2 D 2(1) 3(2) 3(0) 4(1) 1(1) 2(2) a0 x0xs1xs2x12x13x2dx3d 3120121 Dari Excel
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