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RISET OPERASI Lecture I
17/04/2010
1
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Pada pe Pada peri rins nsip ipny nya a pe peny nyel eles esai aian an pe pers rsoa oala lan n mi mini nimi misa sasi si hamp ha mpir ir sa sama ma de deng ngan an ma maks ksim imas asi, i, pe perb rbed edaa aann nnya ya bi bila la di persoalan solu so lusi si op opti timu mumn mnya ya te terc rcap apai ai pa pada da saat sa at fu fungs ngsi i gar garis is tu tuju juan an me menyi nyingg nggung ung da daera erah h fe feasi asibl ble e yang dari titi k o rgi n. Seda ngk an pad a solu so lusi si op opti timu mum m te terc rcap apai ai pa pada da sa saat at fu fung ngsi si gar is t uju an m enyi ngg ung daer ah feas ible ya ng
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Contoh : Perusa Per usahaa haan n maka makanan nan ROY ROYAL AL mer merenc encana anakan kan untu untuk k mem membua buatt dua jen jenis is mak makana anan n yai yaitu tu Roya Ro yall Be Bee e da dan n Ro Roya yall Je Jell lly. y. Ke Kedu dua a je jeni nis s ma maka kanan nan ter terse sebut but me meng ngan andu dung ng vi vita tami min n da dan n prot pr otei ein. n. Ro Roya yall Be Bee e pa pali ling ng se sedi diki kitt di dipr prod oduk uksi si 2 un unit it da dan n Ro Roya yall Je Jell lly y pa pali ling ng se sedi diki kitt diprod dip roduks uksii 1 uni unit. t. Tab Tabel el ber beriku ikutt men menunj unjukk ukkan an jum jumlah lah vit vitami amin n dan pro protei tein n dal dalam am set setiap iap jenis makanan :
Jeni Jeniss mak makan anan an Vit Vitami amin n (un (unit) it)
Prot Pr otein ein (un (unit) it) Biaya Biaya per uni unitt (ri (ribu bu rup a
Royal Bee
2
2
100
Royal Jelly
1
3
80
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Langkah –langkah dalam perumusan 1.
Tent Te ntuk ukan an vari variab abel el X1 = Ro Roya yal l Be Bee e X2 = Ro Roya yal l Jell Jelly y
2.
Rumu Ru musk skan an Fun Fungs gsi i Tuju Tujuan an : Zmin = 100 X1 + 8 0 X2 Rumu Ru musk skan an Fun Fun si Kend Kendal ala a Sumbe Sumberd rda a a 1. 2X1 + X2 ≥ 8 (vi (vitam tamin) in) 2. 2X1 + 3X2 ≥ 12 (prote (protein) in) 3. X1 ≥ 2
3.
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Solusi Sol usi opt optima imal l ter tercap capai ai pad pada a tit titik ik
(terde (te rdekat kat den dengan gan tit titik ik
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Masukkan Masukk an X2 ke ke kend ndal ala a (1 (1) ) 2X1 + X2 = 8 2X1 + 2 = 8 2X1 = 6 X1 = 3 Masu Ma sukk kkan an ni nila lai i X1dan X2 ke Z Z min = 2X1 + 80X2 = 100.3 + 80.2 = 300 + 160 = Untuk mem Untuk memini inimum mumkan kan bia biaya ya pro produk duksi, si, mak maka a X 1 = 3 dan X2 = 2 dengan biaya bia ya pro produk duksi si 460 rib ribu u rup rupiah iah. .
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Contoh soa Contoh soal: l: 1. Ca Car ril ila ah op opt tim ima asi dar ari i pe per rsam ama aan ya yan ng di dib baw awah ah ini den eng gan metode met ode gra grafik fik dan sim simple pleks ks M a k Z = 3 X1 + 5X2 Kendal Ken dala a : 2X1 ≤ 8 3X ≤ 15
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3. Sele Selesa saik ikan an li line near ar pr prog ogra ram m be beri riku kut t in ini i de deng ngan an me meto tode de gr graf afik ik dan sim simple pleks ks Maksimumkan Z = 2 X1 +3X2 +X3 Dengan Denga n fungs fungsi i kendal kendala: a:
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Penggunaan sofware spreadsheet untuk pemecahan LP dan simpleks dengan solver Microsoft Excel mempunyai modul yang disebut Excel SOLVER yang
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Mengaktifkan sofware solver a. Dari Menu Menu Tools, Tools, pilih pilih Add-In Add-Ins s b. Akan muncul jendela jendela seperti seperti dibawah dibawah ini, ini, lalu clik box SOLVER SOLVER add-in add-in dan tekan tombol OK sistem Excel di komputer anda akan terinstal fitur ini
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Memahami Solver Parameters Dari Dari Menu Menu Toll Tolls, s, pili pilihh SOLV SOLVER ER sehi sehing ngga ga munc muncul ul jend jendel elaa sepe sepert rti i dibawah ini :
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