Formulasi Fungsi Pencapaian Fuzzy Goal Programming

X 1 ≥ 176606 X 2 ≥ 272108

5.2.5.3. Formulasi Fungsi Pencapaian Fuzzy Goal Programming

Berdasarkan sasaran-sasaran yang ingin dicapai yang telah dirumuskan menggunakan metode fuzzy goal programming, maka formulasi untuk bulan Januari 2016 adalah: Max T Subject to 0.0000160103X1+0.0000131694X2+DN1-DP1 ≥6.41 T + 0.000018193X1 + 0.0000181793X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 Universitas Sumatera Utara T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 176606 X 2 ≥ 272108 ≤ T ≤ 1 Formulasi fungsi pencapaian untuk Februari – Desember 2016 metode Fuzzy Goal Programming dapat dilihat pada Tabel 5.40. Tabel 5.40. Formulasi Fuzzy Februari– Desember 2016 Periode Fungsi Februari Max T Subject to 0.0001777462X1+0.0001462058X2+DN1-DP1 ≥60.78 T + 0.0000200929X1 + 0.0000200929X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 181959 X 2 ≥ 194489 ≤ T ≤ 1 Universitas Sumatera Utara Tabel 5.40. Formulasi Fuzzy Februari– Desember 2016 Lanjutan Periode Fungsi Maret Max T Subject to 0.0000227734X1+0.0000187324X2+DN1-DP1 ≥ 8.63 T + 0.0000181793X1 + 0.0000181793X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 198316 X 2 ≥ 219771 ≤ T ≤ 1 April Max T Subject to 0.0000085727X1+0.0000070515X2+DN1-DP1 ≥ 3.89 T + 0.0000200929X1 + 0.0000200929X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 209318 X 2 ≥ 297389 ≤ T ≤ 1 Universitas Sumatera Utara Tabel 5.40. Formulasi Fuzzy Februari– Desember 2016 Lanjutan Periode Fungsi Mei Max T Subject to 0.0000109851X1+0.0000090358X2+DN1-DP1 ≥ 4.70 T + 0.0000190883X1 + 0.0000190883X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 203965 X 2 ≥ 272108 ≤ T ≤ 1 Juni Max T Subject to 0.0000770694X1+0.0000633938X2+DN1-DP1 ≥ 26.79 T + 0.0000181793X1 + 0.0000181793X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 187609 X 2 ≥ 194489 ≤ T ≤ 1 Universitas Sumatera Utara Tabel 5.40. Formulasi Fuzzy Februari– Desember 2016 Lanjutan Periode Fungsi Juli Max T Subject to 0.0000471359X1+0.0000387718X2+DN1-DP1 ≥ 16.85 T + 0.0000173530X1 + 0.0000173530X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 176606 X 2 ≥ 219771 ≤ T ≤ 1 Agustus Max T Subject to 0.0000113486X1+0.0000093348X2+DN1-DP1 ≥ 4.84 T + 0.0000181793X1 + 0.0000181793X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 181959 X 2 ≥ 297389 ≤ T ≤ 1 Universitas Sumatera Utara Tabel 5.40. Formulasi Fuzzy Februari– Desember 2016 Lanjutan Periode Fungsi September Max T Subject to 0.0000117447X1+0.0000096606X2+DN1-DP1 ≥ 4.96 T + 0.0000190883X1 + 0.0000190883X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 198316 X 2 ≥ 272108 ≤ T ≤ 1 Oktober Max T Subject to 0.0000280836X1+0.0000231002X2+DN1-DP1 ≥ 10.37 T + 0.0000181793X1 + 0.0000181793X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 209318 X 2 ≥ 194489 ≤ T ≤ 1 Universitas Sumatera Utara Tabel 5.40. Formulasi Fuzzy Februari– Desember 2016 Lanjutan Periode Fungsi November Max T Subject to 0.0000200806X1+0.0000165174X2+DN1-DP1 ≥ 7,73 T + 0.00002009293X1 + 0.0000200929X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 203965 X 2 ≥ 219771 ≤ T ≤ 1 Desember Max T Subject to 0.0000106359X1+0.0000087486X2+DN1-DP1 ≥ 4.60 T + 0.0000181793X1 + 0.0000181793X2 ≤ 9 -T+0.0000004355X1+0.0000003351X2 ≥ 0.008 T+0.0000021600X1+0.0000016620X2 ≤ 6 -T+0.0000005263X1+0.0000004053X2 ≥ 0.05 T+0.0000020000X1+0.0000015400X2 ≤ 5 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000004167X1+0.0000004167X2 ≥ 0.04 T+0.0000020000X1+0.0000020000X2 ≤ 6 -T+0.0000001695X1+0.0000001695X2 ≥ 0.01 T+0.0000010000X1+0.0000010000X2 ≤ 7 -T+0.0000000405X1+0.0000000324X2 ≥ 0.01 T+0.0000002000X1+0.0000001600X2 ≤ 6 -T+ 0.0000000661X1+0.0000005091X2 ≥ 0.06 T+0.0000004360X1+0.00000033600X2 ≤ 8 -T+0.0000003571X1+0.0000002857X2 ≥0.07 T+0.0000010000X1+0.0000080000X2 ≤4 T+0.00022917X1+0.00022197X2 ≤149.58 X 1 ≥ 187609 X 2 ≥ 297389 ≤ T ≤ 1 Sumber: Pengolahan Data Universitas Sumatera Utara Fungsi pencapaian yang telah dirumuskan diatas dapat dihitung dengan menggunakan software LINDO 6.1. Linier Interactive Discrete Optimizer agar diperoleh jumlah produksi optimum, cara penggunaan software sama seperti pada penggunaan Goal programming yang telah dilakukan sebelumnya. Diperoleh jumlah produksi optimum dari proses produksi Stanlee Star S-25 dan Stanlee Star G-20 dengan metode fuzzy goal programming ditunjukkan pada Tabel 5.41. Tabel 5.41. Rekapitulasi Hasil Perencanaan Produksi dengan Metode Fuzzy Goal Programming Periode Jumlah Produk Optimum A B Januari 176606 272108 Februari 181959 194489 Maret 198316 219771 April 209318 297389 Mei 204980 279403 Juni 187609 194515 Juli 176703 219771 Agustus 197260 297389 September 198316 272326 Oktober 209318 194489 November 203965 219771 Desember 187609 297717 Total 5.281.077 Sumber: Pengolahan Data Universitas Sumatera Utara

BAB VI ANALISIS PEMECAHAN MASALAH

6.1. Analisis Volume Produksi

Perhitungan optimasi perencanaan produksi menghasilkan jumlah produksi optimal yang dapat dihasilkan dengan memenuhi fungsi tujuan dan fungsi kendala yang dimiliki perusahaan, dapat dilihat pada Tabel 6.1. Tabel 6.1. Selisih Penjualan dengan Hasil Optimasi Perencanaan Produksi Periode Jumlah Produk Optimum Unit Peramalan Unit Selisih Unit A B A B A B Januari 176606 272108 176.606 272.108 1 Februari 181959 194489 181.959 194.489 Maret 198316 219771 198.316 219.771 1 April 209318 297389 209.318 297.389 Mei 204980 279403 203.965 272.108 1.015 7.296 Juni 187609 194515 187.609 194.489 26 July 176703 219771 176.606 219.771 97 Agustus 197260 297389 181.959 297.389 15.301 September 198316 272326 198.316 272.108 1 219 Oktober 209318 194489 209.318 194.489 November 203965 219771 203.965 219.771 Desember 187609 297717 187.609 297.389 328 Total 2331959 2959138 2.315.548 2.951.270 16.411 7.868 5291097 5.266.818 24.279 Sumber: Pengolahan Data Inventory = Selisih Produksi ×100 Inventory = 24.279 5.266.818 ×100=0,46 Universitas Sumatera Utara