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Gudang 1 2 3 kapasitas
1 100 100 120 150
2 120 100 100 450
3 100 110 120 300
4 100 110 120 300
Demand 400 400 400 1200
formulasi
1. identikasi variabel
X1,1ban!akn!a barang dikirim dari gudang 1 ke pasar 1
"1,2ban!akn!a barang dikirim dari gudang 1 ke pasar 2
"1,3ban!akn!a barang dikirim dari gudang 1 ke pasar 3
"2,1ban!akn!a barang dikirim dari gudang 2 ke pasar 1
"2,2ban!akn!a barang dikirim dari gudang 2 ke pasar 2
"2,3ban!akn!a barang dikirim dari gudang 2 ke pasar 3
"3,1ban!akn!a barang dikirim dari gudang 3 ke pasar 1
"3,2ban!akn!a barang dikirim dari gudang 3 ke pasar 2
"3,3ban!akn!a barang dikirim dari gudang 3 ke pasar 3
"4,1ban!akn!a barang dikirim dari gudang 4 ke pasar 1
"4,2ban!akn!a barang dikirim dari gudang 4 ke pasar 2
"4,3ban!akn!a barang dikirim dari gudang 4 ke pasar 3
2.#dentikasi kendala $tandarisasi %anonikal
"1,1&"1,2&"1,3'150 "1,1&"1,2&"1,3&"a150
"2,1&"2,2&"2,3'450 "2,1&"2,2&"2,3&"b450
"3,1&"3,2&"3,3'300 "3,1&"3,2&"3,3&"(300
"4,1&"4,2&"4,3'300 "4,1&"4,2&"4,3&"d300
"1,1&"2,1&"3,1&"4,1)400 "1,1&"2,1&"3,1&"4,1*"e400
"1,2&"2,2&"3,2&"4,2)400 "1,2&"2,2&"3,2&"4,2*"f400
"1,3&"2,3&"3,3&"4,3)400 "1,3&"2,3&"3,3&"4,3*"g400
3.#dentikasi +ungsi b-ektif
in100"1,1&100"1,2&120"1,3&120"2,1&100"2,2&100"2,3&100"3,1&110"3,2&120"
rimal
asis
100 100 120 120 100 100
"1,1 "1,2 "1,3 "2,1 "2,2 "2,3
0 "a 1 1 1 0 0 0
0 "b 1 1 1 0 0 0
0 "( 1 1 1 0 0 0
0 "d 1 1 1 0 0 0
1000 "/ 1 0 0 1 0 0
1000 "i 0 1 0 0 1 0
1000 "- 0 0 1 0 0 1
( ro *00 *00 *0 *0 *00 *00
"1,1&"1,2
"2,1&"2,2
"3,1&"3,2
"4,1&"4,2
"1,1&"2,1
"1,2&"2,2
"1,3&"2,3
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100 "1,1 1 1 1 0 0 0
0 "b 0 0 0 0 0 0
0 "( 0 0 0 0 0 0
0 "d 0 0 0 0 0 0
1000 "/ 0 *1 *1 1 0 0
1000 "i 0 1 0 0 1 0
1000 "- 0 0 1 0 0 1
( ro 0 0 20 *0 *00 *00
100 "1,1 1 1 1 0 0 0
0 "b 0 0 0 0 0 0
0 "( 0 0 0 0 0 0
0 "d 0 0 0 0 0 0
1000 "/ 0 *1 *1 1 0 0
100 "2,2 0 1 0 0 1 0
1000 "- 0 0 1 0 0 1
( ro 0 00 20 *0 0 *00
100 "1,1 1 1 1 0 0 0
0 "b 0 0 0 0 0 0
0 "( 0 0 0 0 0 0
0 "d 0 0 0 0 0 0
1000 "/ 0 *1 *1 1 0 0
100 "2,2 0 1 0 0 1 0
100 "2,3 0 0 1 0 0 1
( ro 0 00 20 *0 0 0
100 "1,1 1 1 1 0 0 0
0 "b 0 0 0 0 0 0
0 "( 0 0 0 0 0 0
0 "d 0 0 0 0 0 0
100 "3,1 0 *1 *1 1 0 0
100 "2,2 0 1 0 0 1 0
100 "2,3 0 0 1 0 0 1
( ro 0 0 20 20 0 0
Dual "1,1 "b "( "d "3,1 "2,2 "2,3
1 0 0 0 0 0 0
1 1 0 0 0 0 0
1 0 1 0 0 0 0
1 0 0 1 0 0 0
1 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1
(b 100 0 0 0 100 100 100
1 0 0 0 0 0 0
*1 1 0 0 0 0 0
*1 0 1 0 0 0 0
*1 0 0 1 0 0 0
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*1 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1
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,3&100"4,1&110"4,2&120"4,3&m"/&m"i&m"-
100 110 120 100 110 120 0 0
"3,1 "3,2 "3,3 "4,1 "4,2 "4,3 "a "b
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0
0 1 0 0 1 0 0 0
0 0 1 0 0 1 0 0
*00 *0 *0 *00 *0 *0 0 0
"1,3&xa150
"2,3&xb450
"3,3&xc300
"4,3&xd300
"3,1&"4,1*"e&xh400
"3,2&"4,2*"f&xi400
"3,3&"4,3*"g&xj400
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0 0 0 0 0 0 1 0
0 0 0 0 0 0 *1 1
0 0 0 0 0 0 *1 0
0 0 0 0 0 0 *1 0
1 0 0 1 0 0 *1 0
0 1 0 0 1 0 0 0
0 0 1 0 0 1 0 0
*00 *0 *0 *00 *0 *0 00 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 *1 1
0 0 0 0 0 0 *1 0
0 0 0 0 0 0 *1 0
1 0 0 1 0 0 *1 0
0 1 0 0 1 0 0 0
0 0 1 0 0 1 0 0
*00 10 *0 *00 10 *0 00 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 *1 1
0 0 0 0 0 0 *1 0
0 0 0 0 0 0 *1 0
1 0 0 1 0 0 *1 0
0 1 0 0 1 0 0 0
0 0 1 0 0 1 0 0
*00 10 20 *00 10 20 00 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 *1 1
0 0 0 0 0 0 *1 0
0 0 0 0 0 0 *1 0
1 0 0 1 0 0 *1 0
0 1 0 0 1 0 0 0
0 0 1 0 0 1 0 0
0 10 20 0 10 20 0 0
6arga beli gudang7ton 6arga -ual dipasar
0 0 0 0 100 100 100
150 450 300 300 400 400 400
0 0 0 0 40000 40000 40000
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0 0 0 0 0 1000 1000 1000
"( "d "e "f "g "/ "i "-
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 *1 0 0 1 0 0
0 0 0 *1 0 0 1 0
0 0 0 0 *1 0 0 1
0 0 1000 1000 1000 0 0 0
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0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 *1 0 0 1 0 0
0 0 0 *1 0 0 1 0
0 0 0 0 *1 0 0 1
0 0 1000 1000 1000 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 *1 0 0 1 0 0
0 0 0 *1 0 0 1 0
0 0 0 0 *1 0 0 1
0 0 1000 100 1000 0 00 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 *1 0 0 1 0 0
0 0 0 *1 0 0 1 0
0 0 0 0 *1 0 0 1
0 0 1000 100 100 0 00 00
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 *1 0 0 1 0 0
0 0 0 *1 0 0 1 0
0 0 0 0 *1 0 0 1
0 0 100 100 100 00 00 00
120000
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konstanta ratio
150 150
450 450
300 300
300 300
400 400
4008
4008
1200000 *00
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1508
3008
1508
1508
2508
400 400
4008
1095000 *00
1508
3008
1508
1508
2508
4008
400 400
:05000 *00
1508
3008
1508
1508
250 250
4008
4008
345000 *33.3333 *00
1508
3008
1508
1508
250 250
4008
4008
120000 8 0
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produk
$umber Da!a
laba7unitteknis tenaga ker-a administrasi
1 3 1 2 9
2 1 2 2 9
3 2 2 1 :
tersedia 400 400 40
1.#dentikasi ;ariabel
"1ban!akn!a -am teknis digunakan
"2ban!akn!a -am tenaga ker-a digunakan
"3 ban!akn!a -am administrasi digunakan
2.#dentikasi %endala $tandarisasi & %anonikal
3"1&"2&2"3'400 3"1&"2&2"3&"4400
"1&2"2&2"3'400 "1&2"2&2"3&"54002"1&2"2&"3'40 2"1&2"2&"3&"940
3.#dentikasi +ungsi b-ektif
ma"9"1&9"2&:"3
ma"1440
sumber da!a penggunaan tersedia eban %er-a
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?.@eknis 450 400 112.5
@.%er-a 400 400 100
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ma" >9"1&9"2&:"3
kendala baru standarisasi non*%anonikal
3"1&"2&2"3&"4400 3"1&"2&2"3&"4400 3"1&"2&2"3&
"1&2"2&2"3&"5400 "1&2"2&2"3&"5400 "1&2"2&2"3&
2"1&2"2&"3&"940 2"1&2"2&"3&"940 2"1&2"2&"3&
"1)100 "1*":100 *X1&X:*100
asis9 9 :
"1 "2 "3
: "4 3 1 2
9 "5 1 2 2
9 "9 2 2 1
0 ": *1 0 0
( ro *33 *25 *25
ratio 33: "4 0 1 2
9 "5 0 2 2
9 "9 0 2 1
9 "1 1 0 0
( ro 0 *25 *25
solusi optimal
="2 0= "30 =A4:0
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0 0 0%onstanta Basio
"4 "5 "9
1 0 0 450 225
0 1 0 400 200
0 0 1 40 40
0 0 0
0.5 0 0 225 450
*1 1 0 *50 *50
*0.5 0 1 255 1:0
*3.5 0 0
1 *0.5 0 250 100
*1 1 0 *50 8
1 *1.5 1 330 4.25:1425:
*1 *2.5 0
27 : 47 : * 57 : 14.25:1425:
* 37 : 17 : 47 : 13.5:1425:1
27 : * 37 : 27 : 4.25:1425:
*1 17 : *2 27 : * 17 : 14: 17 :
ketC
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bottlene(k
bottlene(k
bottlene(k
optimal hasil point (a)
i optimal hasil point (a)
! c!"(#$"*'$4'c1$%)!
uk 4, +ang butuh % jam la+anan teknis, 1 jam tenaga kerja, dan 3 jam a
0 0 0 %onstanta
"4 "5 "9 ":
1 0 0 2 400
0 1 0 1 400
0 0 1 3 40
0 0 0
1 *1 17 3 2 190
0 1 * 17 3 0 240
0 0 17 3 1 190
0 0 *3 0
1 *1 17 5 27 5 2 112
0 37 5 * 17 5 0 144
0 * 17 5 27 5 1 112
0 *2 27 5 *2 17 5 0 2019
! unit atau lebih tentukan solusi
! c!"(c3$"*'$4'$%)!
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4400
5400 ))))gunakan dual simple"
940
0 0 0 0%onstanta
"4 "5 "9 ":
1 0 0 0 400
0 1 0 0 400
0 0 1 0 40
0 0 0 1 *100
*: *9 *9 0
01 0 0 3 100
0 1 0 1 300
0 0 1 2 20
0 0 0 *1 100
*: *9 *9 *33 4:0
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minsitrasi, dan produk dapat memberikan keuntungan perunit sebesar &unit
Basio
200
400
190
40
144
40
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diambil dari 2a optimal
asis9 9 : 0 0
"1 "2 "3 "4 "5
: "3 0 0 1 27 : 47 :
9 "2 0 1 0 * 37 : 17 :
9 "1 1 0 0 27 : * 37 : ro 0 0 0 *1 17 : *2 27 :
persamaan Gomor! 1
0E"1&1E"2&0"3&*37:E"4&17:E"5&47:E"913 47:
0&0E"1&1&0E"2&0&0E"3&*1&47:E"4&0&17:E"5&0&47:E"913&47:E
ma"9"1&9"2&:"3
asis9 9 : 0 0
"1 "2 "3 "4 "5
: "3 0 0 1 27 : 47 :
9 "2 0 1 0 * 37 : 17 :
9 "1 1 0 0 27 : * 37 :
0 ": 0 0 0 * 47 : * 17 :
ro 0 0 0 *1 17 : *2 27 :
ratio 2 19
: "3 0 0 1 1 37 4
9 "2 0 1 0 *1 0
9 "1 1 0 0 0 * 17 2
0 ": *0 *0 *0 1 17 4
ro 0 0 0 *1 *2 17 4
ratio
X11=X2113= X315 =A14:
0"1&0"2&0"3&47:"4&17:"5&47:"9F47:
0"1&0"2&0"3&47:"4&17:"5&47:"9*":47:
0"1&0"2&0"3*47:"4*17:"5*47:"9&x#*47:
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0%onstanta Basio
"9 pe(a/an
* 57 : 14 27 : 27:
47 : 13 47 : 47:
27 : 4 27 : 27:* 17 : 14: 17 : 17:
0 0%onstanta ratio
"9 ": pe(a/an
* 57 : 0 14 27 : 27:
47 : 0 13 47 : 47:
27 : 0 4 27 : 27:
* 47 : 1 * 47 : *47:
* 17 : 0 14: 17 : 17:
17 4
0 *1 17 4 15
0 1 13
0 17 2 4
1 *1 37 4 1
0 * 17 4 14:
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simple" biasa berfokus pada ratio minus dan ( ro
dual simple" berfokus pada ratio !ang berkebalikan--lihat ko
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nstanta terminus dan kendala minus
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+ormulasi standarisasi
"1F50 "1F50
"2F100 "2F100
"3F100 "3F100
"1&"2&"3F1900 "1&"2&"3F1900
"1&2"2&2"30 "1&2"2&2"30