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Goal Programming

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Submitted By ammufarrih
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Goal Programming (Programasi Tujuan Ganda)
Riset Operasi 2 Jur. Manajemen FE UNEJ

11/5/2010

hadi paramu metode kuantitatif

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Ruang Lingkup
► PL

yang dibahas sejauh ini berkaitan dengan optimasi(memaksimumkan profit / meminimumkan biaya). ► Persoalan PL merupakan permasalahan yang dipecahkan atau diukur dengan satu dimensi, yaitu maksimisasi atau minimisasi. ► Seorang manajer bisa dihadapkan pada situasi dimana ia harus mencapai beberapa tujuan sekaligus (tujuan ganda atau multiple goals): Efisensi dan efektivitas
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Ruang Lingkup
► Charnes

dan Coopers (1961) dan Lee dan Ignazio (1970an) mengembangkan Goal Programming ► Teknik GP merupakan salah satu teknik dalam pemrograman matematik yang tidak bekerja atas dasar “optimasi” tetapi “pemuasan” atau “pemenuhan” tujuan.

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Karakteristik Formulasi Dalam GP
► Fungsi

tujuan selalu diekspresikan dalam bentuk minimisasi: meminimumkan penyimpangan dari target (tujuan). ► Ada dua variabel deviasional:
 d1- = underachievement (penyimpangan dibawah) target profit  d1+ =overachievement (penyimpangan diatas) target profit
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Karakteristik Formulasi Dalam GP
► Fungsi kendala

dapat diklasifikasikan menjadi:

 Fungsi kendala teknik (technical constraint function): kendala yang berkaitan dengan kapasitas teknis  Fungsi kendala tujuan (goal constraint function): kendala yang berkaitan dengan pencapaian target  Suatu persoalan GP bisa tidak mempunyai technical constraint function atau semua kendala adalah goal constraint function.
► Semua

goal constraint function mempunyai tanda “=“

 Tidak perlu ada Slack Variable, Surplus Variabel, dan Artificial Variable
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Contoh Soal
Sebuah Mutual Fund diminta oleh kliennya untuk menginvestasikan $250.000 pada beberapa alternatif, sebagai berikut:
Obyek Investasi Obligasi Pemerintah Gold Star Electronic, Tbk Garuda Indonesia Kimia Farma Agro Lestari
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Tingkat Return yang diproyeksikan (%) 5,3 6,8 4,9 8,4 11,8
6

Contoh Soal


Klien ini menginginkan beberapa hal dengan prioritas berikut ini:
    portfolio investasi memberikan tingkat pengembalian sebesar-besarnya; sebanyak-banyaknya 40% dana ditanamkan pada kombinasi perusahaan elektronik, penerbangan, dan apotik; paling tidak 20% dana diinvestasikan pada obligasi pemerintah; tidak lebih dari 30% dana diinvestasikan pada perusahaan agribisnis. hadi paramu metode kuantitatif 7

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Jenis GP
► Goal

Programming yang mempunyai tujuan tanpa Prioritas
 Semua goals dianggap setara (sama penting)

► Goal

Programming yang mempunyai tujuan dengan Prioritas
 Setiap goal memiliki tingkat urgensi yang berbeda  Prioritas 1 >>> Prioritas 2 >>> … Prioritas n

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GP: Tujuan Dengan Prioritas
Minimumkan: P1 d1-+ P2 d2++ P3 d3- + P4 d4+ Dengan kendala 0,053X1 + 0,068X2 + 0,049X3 + 0,084X4 + 0,118X5+d1- d1+= 999.999 X2 +X3 + X4 +d2- - d2+= 100.000 X1 + d3- - d3+= 50.000 X5 + d4- - d4+= 75.000 X1 + X2 + X3 + X4 + X5  250.000

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Output GP
Decision variable analysis X1 X2 X3 X4 X5 Priority analysis Priority 1 Priority 2 Priority 3 Priority 4 Constraint Analysis Goal/Cnstrnt 1 Goal/Cnstrnt 2 Goal/Cnstrnt 3 Goal/Cnstrnt 4 Goal/Cnstrnt 5 Value 0 0 0 0 250000 Nonachievement 99999968452 0 50000 175000 RHS 1.00E+11 100000 50000 75000 250000

d+ (row i) 0 0 0 175000 0

d- (row i) 1.00E+11 100000 50000 0 0

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Membaca Output
► Decision

Variable Value

 Menginformasikan nilai variabel keputusan yang bisa memenuhi target.  Contoh: semua dana dialokasikan pada X5
► Priority

Analysis

 Menunjukkan apakah prioritas-prioritas tercapai  Jika kolom nonachievement tidak bernilai nol, target pada prioritas tidak tercapai, dan sebaliknya
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Membaca Output
► Constraint

Analysis

 Menginformasikan dampak dari goals achievement dan nonachievement pada goal constraints  Kolom RHS menunjukkan target pada suatu goal constraint  Kolom d+(row i) mengindikasikan terjadinya overachievement pada goal constraint, dan d-(row i) mengindikasikan terjadinya underachievement

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Implikasi Praktikal Dari Goal

Programming
► memberikan

gambaran pada pengambil keputusan bahwa dalam penetapan tujuan terdapat tujuan yang saling berlawanan (kontradiktif) satu sama lain. ► konsep GP dapat diaplikasikan untuk simulasi dalam rangka untuk menguji paket prioritas tujuan tertentu.

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