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Model Transportasi 2 1. MODI (Modified Distributor) 2. Stepping Stone (Batu Loncatan)

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Presentasi berjudul: "Model Transportasi 2 1. MODI (Modified Distributor) 2. Stepping Stone (Batu Loncatan)"— Transcript presentasi:

1 Model Transportasi 2 1. MODI (Modified Distributor) 2. Stepping Stone (Batu Loncatan)

2 MODI (Modified Distributor) Aturan : 1. Tambahkan variabel Ri dan Ki pada setiap baris dan kolom 2. Hitung semua nilai bukan basis dengan Cij – Ri – Ki 3. Tentukan sel basis dengan memilih sel bukan basis dengan nilai negatif terbesar 4. Tabel optimum akan tercapai jika sel bukan basis memiliki nilai ≥ 0

3 Dari metode NWC P/GABCS P P P D Sel Bukan Basis = P1 – B, P1 – C, P2 – C, P3 - A

4 P1 – A = R1 + K1 = 32 P2 – A = R2 + K1 = 36 P2 – B = R2 + K2 = 42 P3 – B = R3 + K2 = 37 P3 – C = R3 + K3 = 40 Misalkan R1 = 0 R1 + K1 = 32, 0 + K1 = 32, K1 = 32 R2 + K1 = 36, R = 36, R2 = 4 R2 + K2 = 42, 4 + K2 = 42, K2 = 38 R3 + K2 = 37, R = 37, R3 = -1 R3 + K3 = 40, -1 + K3 = 40, K3 = 41

5 Hitung Nilai Sel Bukan Basis P1 – B = C12 – R1 – K2 = 33 – 0 – 38 = -5 P1 – C = C13 – R1 – K3 = 34 – 0 – 41 = -7 P2 – C = C23 – R2 – K3 = 38 – 4 – 41 = - 7 P3 – A = C31 – R3 – K1 = 34 – (-1) – 32 = 3 P/GABCS P P P D

6 P1 – A = R1 + K1 = 32 P2 – A = R2 + K1 = 36 P2 – B = R2 + K2 = 42 P3 – B = R3 + K2 = 37 P1 – C = R1 + K3 = 34 Misalkan R1 = 0 R1 + K1 = 32, 0 + K1 = 32, K1 = 32 R2 + K1 = 36, R = 36, R2 = 4 R2 + K2 = 42, 4 + K2 = 42, K2 = 38 R3 + K2 = 37, R = 37, R3 = -1 R1 + K3 = 34, 0+ K3 = 34, K3 = 34

7 P1 – B = C12 – R1 – K2 = 33 – 0 – 38 = -5 P2 – C = C23 – R2 – K3 = 38 – 4 – 34 = 0 P3 – A = C31 – R3 – K1 = 34 – (-1) – 32 = 3 P3 – C = C33 – R3 – K3 = 40 – (-1) – 34 = 7 P/GABCS P P P D

8 P1 – B = R1 + K2 = 33 P1 – C = R1 + K3 = 34 P2 – B = R2 + K2 = 42 P3 – B = R3 + K2 = 37 P2 – C = R2 + K3 = 36 Misalkan R1 = 0 R1 + K1 = 32, 0 + K1 = 32, K1 = 32 R2 + K1 = 36, R = 36, R2 = 4 R2 + K2 = 42, 4 + K2 = 42, K2 = 38 R3 + K2 = 37, R = 37, R3 = -1 R2 + K3 = 36, 4+ K3 = 36, K3 = 32

9 P1 – B = C12 – R1 – K2 = 33 – 0 – 38 = -5 P1 – C = C13 – R1 – K3 = 34 – 0 – 32 = 2 P3 – A = C31 – R3 – K1 = 34 – (-1) – 32 = 3 P3 – C = C33 – R3 – K3 = 40 – (-1) – 32 = 9 P/GABCS P P P D

10 P1 – A = R1 + K1 = 32 P2 – A = R2 + K1 = 36 P1 – B = R1 + K2 = 33 P3 – B = R3 + K2 = 37 P2 – C = R2 + K3 = 38 Misalkan R1 = 0 R1 + K1 = 32, 0 + K1 = 32, K1 = 32 R2 + K1 = 36, R = 36, R2 = 4 R1 + K2 = 33, 0 + K2 = 33, K2 = 33 R3 + K2 = 37, R = 37, R3 = 4 R2 + K3 = 38, 4+ K3 = 38, K3 = 34

11 P1 – C = C13 – R1 – K3 = 34 – 0 – 34 = 0 P2 – B = C22 – R2 – K2 = 42 – 4 – 33 = 5 P3 – A = C31 – R3 – K1 = 34 – 4 – 32 = -2 P3 – C = C33 – R3 – K3 = 40 – 4 – 34 = 2 P/GABCS P P P D

12 P1 – B = R1 + K2 = 33 P2 – A = R2 + K1 = 36 P2 – C = R2 + K3 = 38 P3 – A = R3 + K1 = 34 P3 – B = R3 + K2 = 37 Misalkan R1 = 0 R1 + K2 = 33, 0 + K2 = 33, K2 = 33 R3 + K2 = 37, R = 37, R3 = 4 R3 + K1 = 34, 4 + K1 = 34, K1 = 30 R2 + K1 = 36, R2+ 30 = 36, R2 = 6 R2 + K3 = 38, 6 + K3 = 38, K3 = 32

13 P1 – A = C11 – R1 – K1 = 32 – 0 – 30 = 2 P1 – C = C13 – R1 – K3 = 34 – 0 – 32 = 2 P2 – B = C22 – R2 – K2 = 42 – 6 – 33 = 3 P3 – C = C33 – R3 – K3 = 40 – 4 – 32 = 4 P/GABCS P P P D Total Biaya = (106.33) + (36.41) + (38.91) + (34.81) + (37.46) =

14 Stepping Stone (Batu Loncatan) Penggunaan Metode Batu loncatan dilakukan dengan cara : a. uji apakah nilai sel bukan basismemiliki nilai ≥ 0. pengujian dilakukan dengan menggunkan jalur tertutup b. Tanda yg digunakan untuk membuat jalur tertutup dimulai dengan tanda positif (+) kemudian negatif sampai ke sel bukan basis semula

15 Contoh Dari metode NWC P/GABCS P P P D Sel Bukan Basis : P1 – B, P1 – C, P2 – C, P3 - A

16 Sel P1 – B P1 – B = 33 – – 42 = -5 P/GAB P132 (-) *(+) P236 (+) (-) 116

17 Sel P1 – C Sel P1 – C = 34 – – – 40 = -7 P/GABC P132 (-) (+) * P236 (+)16 42 (-) 116 P337 (+) (-) 91

18 Sel P2 – C P2 – C = 38 – – 40 = -7 Sel P3 – A P3 – C = 34 – – 36 = 3 P/GBC P242 (-) (+) * P337 (+) (-) 91 P/GAB P236 (-) (+) 116 P334 (+) * 37 (-) 36

19 P/GABCS P P P D Sel bukan Basis : P1 – B, P2 – C, P3 – A, P3 – C

20 Sel P1 – B Hasil = 33 – – 42 = -5 Sel P3 – A Hasil = 34 – – 36 = 3 P/GAB P132 (-) *(+) P236 (+) (-) 25 P/GAB P236 (-) (+) 25 P334 (+) * 37 (-) 127

21 Sel P2 – C Hasil = 38 – – 36 = 0 Sel P3 – C 40 – – – 37 = 7 P/GAC P132 (+) (-) 91 P236 (-) (+) * P/GABC P132 (+)15 34 (-) 91 P236 (-) (+) 25 P337 (-) (+) *

22 Sel Bukan Basis = P1 – A, P2 – C, P3 – A, P3 - C P/GABCS P P P D

23 Sel P1 – A Hasil = 32 – – 33 = 5 Sel P2 – C Hasil = 38 – – 42 = -5 P/GAB P132 (+) * 33 (-) 15 P236 (-) (+) 10 P/GBC P133 (+) (-) 91 P242 (-) (+) *

24 Sel P3 – A Hasil = 34 – – 36 = 3 Sel P3 – C Hasil = 40 – – 37 = 2 P/GAB P236 (-) (+) 10 P334 (+) * 37 (-) 127 P/GBC P133 (+) (-) 91 P337 (-) (+) *

25 Sel bukan basis = P1 – A, P2 – B, P3 – A, P3 - C P/GABCS P P P D

26 Sel P1 – A Hasil = 32 – – 33 = 5 Sel P2 – B Hasil = 42 – – 33 = 5 P/GAB P132 (+) * 33 (-) 15 P236 (-) (+) 10 P/GBC P133 (-) (+) 81 P242 (+) * 38 (-) 10

27 Sel P3 – A Hasil = 34 – – = -2 Sel P3 – C Hasil = 40 – – 37 = 2 P/GABC P133 (+) (-)81 P236 (-) (+)10 P334 (+) * 37 (-) P/GBC P133 (+) (-) 81 P2 P337 (-) (+) *

28 P/GABCS P P P D Hitung sel apakah masih ada yang negatif atau belum P1 – A = 32 – – 33 = 2 P1 – C = 34 – – – 38 = – 2 = 0 P2 – B = 42 – – 37 = 6 – 3 = 3 P3 – C = 40 – – 34 = = 4 Karena tidak ada yang negatif maka : Total Biaya = (34.81) + (37.46) + (33.106) + (38.91) + (36.41) =

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