Formulasi Fungsi Pencapaian Formulasi Fungsi Model Goal Programming 1. Variabel Keputusan

Keuntungan dapat dilihat pada Tabel 5.7. dihitung dengan proyeksi bahwa seluruh produk laku terjual,maka perhitungan keuntungan adalah Keuntungan = Rp. 1.508 x 176.606 + Rp. 1.240 x 272.108 = Rp. 266.234.001 + Rp. 337.413.300 = Rp. 603.647.301 Berdasarkan proyeksi keuntungan tersebut dapat dirumuskan formulasinya adalah 1.508X 1 + 1.240X 2 ≥ 603.647.301 Berdasarkan fungsi sasaran ini diharapkan keuntungan yang diperoleh lebih besar maka deviasi negatif tidak diharapkan terjadi Fungsi matematis untuk bulan Januari adalah 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 603.647.301 Sehingga Min Z = d 15 -

5.2.4.4. Formulasi Fungsi Pencapaian

Fungsi pencapaian disusun berdasarkan sasaran yang ingin dicapai, maka formulasi untuk bulan Januari 2016 adalah Universitas Sumatera Utara Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 176606 X 2 + d 12 - - d 12 + = 272108 X 1 + d 13 - - d 13 + = 138531 X 2 + d 14 - - d 14 + = 242463 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 603.647.301 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 17640 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + , d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + ,d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Formulasi fungsi pencapaian untuk Februari- Desember 2016 dapat dilihat pada Tabel 5.36. Universitas Sumatera Utara Tabel 5.36. Formulasi Fungsi Pencapaian Februari– Desember 2016 Periode Fungsi Februari Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 181959 X 2 + d 12 - - d 12 + = 194489 X 1 + d 13 - - d 13 + = 154057 X 2 + d 14 - - d 14 + =221571 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 515470467 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 15960 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Universitas Sumatera Utara Tabel 5.36. Formulasi Fungsi Pencapaian Februari– Desember 2016 Lanjutan Periode Fungsi Maret Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 198316 X 2 + d 12 - - d 12 + = 219771 X 1 + d 13 - - d 13 + = 164667 X 2 + d 14 - - d 14 + =207294 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 571476450 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 17640 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 April Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 209318 X 2 + d 12 - - d 12 + = 297389 X 1 + d 13 - - d 13 + = 144912 X 2 + d 14 - - d 14 + =233877 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 684310001 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 15960 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Universitas Sumatera Utara Tabel 5.36. Formulasi Fungsi Pencapaian Februari– Desember 2016 Lanjutan Periode Fungsi Mei Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 203965 X 2 + d 12 - - d 12 + = 272108 X 1 + d 13 - - d 13 + = 149898 X 2 + d 14 - - d 14 + =227168 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 644890835 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 16800 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Juni Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 187609 X 2 + d 12 - - d 12 + = 194489 X 1 + d 13 - - d 13 + = 169969 X 2 + d 14 - - d 14 + =200160 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 523987385 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 17640 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Universitas Sumatera Utara Tabel 5.36. Formulasi Fungsi Pencapaian Februari– Desember 2016 Lanjutan Periode Fungsi Juli Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 176606 X 2 + d 12 - - d 12 + = 219771 X 1 + d 13 - - d 13 + = 155432 X 2 + d 14 - - d 14 + =219721 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 538749834 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 18480 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Agustus Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 181959 X 2 + d 12 - - d 12 + = 297389 X 1 + d 13 - - d 13 + = 133930 X 2 + d 14 - - d 14 + =248654 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 643066467 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 17640 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Universitas Sumatera Utara Tabel 5.36. Formulasi Fungsi Pencapaian Februari– Desember 2016 Lanjutan Periode Fungsi September Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 198316 X 2 + d 12 - - d 12 + = 272108 X 1 + d 13 - - d 13 + = 147670 X 2 + d 14 - - d 14 + =230166 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 636373916 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 16800 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Oktober Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 209318 X 2 + d 12 - - d 12 + = 194489 X 1 + d 13 - - d 13 + = 178615 X 2 + d 14 - - d 14 + =188527 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 556714001 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 17640 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Universitas Sumatera Utara Tabel 5.36. Formulasi Fungsi Pencapaian Februari– Desember 2016 Lanjutan Periode Fungsi November Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 203965 X 2 + d 12 - - d 12 + = 219771 X 1 + d 13 - - d 13 + = 166902 X 2 + d 14 - - d 14 + =204287 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 579993368 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 15960 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Desember Min Z = d 11 - +d 12 - + d 13 - +d 14 - + d 15 - + d 1 + + d 2 + + d 3 + + d 4 + + d 5 + + d 6 + + d 7 + + d 8 + + d 9 + + d 10 + Subject To X 1 + d 11 - - d 11 + = 187609 X 2 + d 12 - - d 12 + = 297389 X 1 + d 13 - - d 13 + = 136310 X 2 + d 14 - - d 14 + =245451 1.508X 1 + 1.240X 2 + d 15 - - d 15 + = 651583385 0,04581X 1 + 0,04581X 2 + d 1 - - d 1 + = 17640 8,31X 1 + 10,80X 2 + d 2 - - d 2 + = 25000000 0,77X 1 + 1,00X 2 + d 3 - - d 3 + = 2000000 1,00X 1 + 1,00X 2 + d 4 - - d 4 + = 2500000 1,00X 1 + 1,00X 2 + d 5 - - d 5 + = 2500000 1,00X 1 + 1,00X 2 + d 6 - - d 6 + = 6000000 0,08X 1 + 0,10X 2 + d 7 - - d 7 + = 2500000 0,84X 1 + 0,11X 2 + d 8 - - d 8 + = 1750000 0,04X 1 + 0,05X 2 + d 9 - - d 9 + = 150000 X 1 + X 2 + d 10 - - d 10 + = 648.357 X 1, X 2, d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - , d 4 + , d 5 - , d 5 + , d 6 - , d 6 + , d 7 - , d 7 + , d 8 - , d 8 + , d 9 - , d 9 + d 10 - , d 10 + , d 11 - , d 11 + , d 12 - , d 12 + , d 13 - , d 13 + , d 14 - , d 14 + , d 15 - , d 15 + , ≥ 0 Sumber: Pengolahan Data Universitas Sumatera Utara

5.2.4.5. Penyelesaian Fungsi Pencapaian dengan Software LINDO 6.1.