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

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

Dari metode NWC P/G A B C S P1 32 106 33 34 P2 36 16 42 116 38 132 P3 37 40 91 D 122 152 Sel Bukan Basis = P1 – B, P1 – C, P2 – C, P3 - A

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, R2 + 32 = 36, R2 = 4 R2 + K2 = 42, 4 + K2 = 42, K2 = 38 R3 + K2 = 37, R3 + 38 = 37, R3 = -1 R3 + K3 = 40, -1 + K3 = 40, K3 = 41

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/G A B C S P1 32 15 33 34 91 106 P2 36 107 42 25 38 132 P3 37 127 40 D 122 152

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, R2 + 32 = 36, R2 = 4 R2 + K2 = 42, 4 + K2 = 42, K2 = 38 R3 + K2 = 37, R3 + 38 = 37, R3 = -1 R1 + K3 = 34, 0+ K3 = 34, K3 = 34

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/G A B C S P1 32 33 15 34 91 106 P2 36 92 42 10 38 132 P3 37 127 40 D 122 152

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, R2 + 32 = 36, R2 = 4 R2 + K2 = 42, 4 + K2 = 42, K2 = 38 R3 + K2 = 37, R3 + 38 = 37, R3 = -1 R2 + K3 = 36, 4+ K3 = 36, K3 = 32

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/G A B C S P1 32 81 33 25 34 106 P2 36 41 42 38 91 132 P3 37 127 40 D 122 152

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, R2 + 32 = 36, R2 = 4 R1 + K2 = 33, 0 + K2 = 33, K2 = 33 R3 + K2 = 37, R3 + 33 = 37, R3 = 4 R2 + K3 = 38, 4+ K3 = 38, K3 = 34

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/G A B C S P1 32 33 106 34 P2 36 41 42 38 91 132 P3 81 37 46 40 D 122 152

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, R3 + 33 = 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

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/G A B C S P1 32 33 106 34 P2 36 41 42 38 91 132 P3 81 37 46 40 D 122 152 Total Biaya = (106.33) + (36.41) + (38.91) + (34.81) + (37.46) = 12.888

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

Contoh Dari metode NWC P/G A B C S P1 32 106 33 34 P2 36 16 42 116 132 37 40 91 D 122 152 Sel Bukan Basis : P1 – B, P1 – C, P2 – C, P3 - A

Sel P1 – B P1 – B = 33 – 32 + 36 – 42 = -5 P/G A B P1 32 (-) 106 33 *(+) P2 36 (+) 16 42 (-) 116

Sel P1 – C Sel P1 – C = 34 – 32 + 36 – 42 + 37 – 40 = -7 P/G A B C P1 (-)106 34 (+) * P2 36 (+)16 42 (-) 116 P3 37 (+) 36 40 (-) 91

Sel P2 – C P2 – C = 38 – 42 + 37 – 40 = -7 Sel P3 – A P/G B C P2 42 (-) 116 38 (+) * P3 37 (+) 36 40 (-) 91 P/G A B P2 36 (-) 16 42 (+) 116 P3 34 (+) * 37 (-) 36

Sel bukan Basis : P1 – B, P2 – C, P3 – A , P3 – C P/G A B C S P1 32 15 33 34 91 106 P2 36 107 42 25 38 132 P3 37 127 40 D 122 152 Sel bukan Basis : P1 – B, P2 – C, P3 – A , P3 – C

Sel P1 – B Hasil = 33 – 32 + 36 – 42 = -5 Sel P3 – A P/G A B P1 32 (-) 15 33 *(+) P2 36 (+) 107 42 (-) 25 P/G A B P2 36 (-) 107 42 (+) 25 P3 34 (+) * 37 (-) 127

Sel P2 – C Hasil = 38 – 34 + 32 – 36 = 0 Sel P3 – C 40 – 34 + 32 – 36 + 42 – 37 = 7 P/G A C P1 32 (+) 15 34 (-) 91 P2 36 (-) 107 38 (+) * P/G A B C P1 32 (+)15 34 (-) 91 P2 36 (-)107 42 (+) 25 P3 37 (-) 127 40 (+) *

Sel Bukan Basis = P1 – A , P2 – C, P3 – A, P3 - C P/G A B C S P1 32 33 15 34 91 106 P2 36 122 42 10 38 132 P3 37 127 40 D 152 Sel Bukan Basis = P1 – A , P2 – C, P3 – A, P3 - C

Sel P1 – A Hasil = 32 – 36 + 42 – 33 = 5 Sel P2 – C P/G A B P1 32 (+) * 33 (-) 15 P2 36 (-) 122 42 (+) 10 P/G B C P1 33 (+) 15 34 (-) 91 P2 42 (-) 10 38 (+) *

Sel P3 – A Hasil = 34 – 37 + 42 – 36 = 3 Sel P3 – C P/G A B P2 36 (-) 122 42 (+) 10 P3 34 (+) * 37 (-) 127 P/G B C P1 33 (+) 15 34 (-) 91 P3 37 (-) 127 40 (+) *

Sel bukan basis = P1 – A, P2 – B, P3 – A, P3 - C P/G A B C S P1 32 33 25 34 81 106 P2 36 122 42 38 10 132 P3 37 127 40 D 152 91 Sel bukan basis = P1 – A, P2 – B, P3 – A, P3 - C

Sel P1 – A Hasil = 32 – 36 + 42 – 33 = 5 Sel P2 – B P/G A B P1 32 (+) * 33 (-) 15 P2 36 (-) 122 42 (+) 10 P/G B C P1 33 (-) 25 34 (+) 81 P2 42 (+) * 38 (-) 10

Sel P3 – A Hasil = 34 – 37 + 33 – 34 + 38 - 36 = -2 Sel P3 – C P/G A B C P1 33 (+) 25 34 (-)81 P2 36 (-) 122 38 (+)10 P3 (+) * 37 (-) 127 40 P/G B C P1 33 (+) 25 34 (-) 81 P2 P3 37 (-) 127 40 (+) *

Hitung sel apakah masih ada yang negatif atau belum P/G A B C S P1 32 33 106 34 P2 36 41 42 38 91 132 P3 81 37 46 40 127 D 122 152 Hitung sel apakah masih ada yang negatif atau belum P1 – A = 32 – 34 + 37 – 33 = 2 P1 – C = 34 – 33 + 37 – 34 + 36 – 38 = -1 + 3 – 2 = 0 P2 – B = 42 – 36 + 34 – 37 = 6 – 3 = 3 P3 – C = 40 – 38 + 36 – 34 = 2 + 2 = 4 Karena tidak ada yang negatif maka : Total Biaya = (34.81) + (37.46) + (33.106) + (38.91) + (36.41) = 12.888