A = Kecepatan produksi
n = Jenis produk 1, 2, 3, 4 Picnic Shrimp, Cocktail Shrimp, Small Shrimp,
dan Medium Shrimp i
= Bulan ke 1,2,…12 Mei 2010 – April 2011 d
-
= deviasi negatif d
+
= deviasi positif P
k
= Prioritas ke k k=1,2,3 dan 4 Z
k
= Fungsi sasaran ke k k=1,2,3 dan 4 Fungsi persamaannya adalah:
∑
= 4
1 n
Xn An
≤ bi
Formula fungsi untuk pemakaian jam kerja adalah: AX
1
+ AX
2
+ AX
3
+ AX
4
≤ bi Dalam hal ini diharapkan deviasi positif kelebihan jam kerja diusahakan
nol. Oleh karena itu model goal programming untuk perencanaan untuk bulan Mei 2010 adalah:
0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 240 Maka fungsi sasarannya adalah Minimumkan Z
4
= P
4
d
7 +
5.4. Penyusunan Formulasi
Adapun fungsi sasaran untuk tiap bulannya adalah Z = Z
1
+ Z
2
+ Z
3
+ Z
4.
Secara keseluruhan formulasi Goal Programing selama periode perencanaan yaitu:
1. Mei 2010
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
Universitas Sumatera Utara
ST: X
1
+ d
1 -
– d
1 +
=132465 X
2
+ d
2 -
– d
2 +
=30558 X
3
+ d
3 -
– d
3 +
=15073 X
4
+ d
4 -
– d
4 +
=6338 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 310565250 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 240 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
2. Juni 2010
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 133684 X
2
+ d
2 -
– d
2 +
= 30823 X
3
+ d
3 -
– d
3 +
= 15128 X
4
+ d
4 -
– d
4 +
= 6442 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
=313328900 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 260 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
3. Juli 2010
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST:
Universitas Sumatera Utara
X
1
+ d
1 -
– d
1 +
= 134903 X
2
+ d
2 -
– d
2 +
= 31088 X
3
+ d
3 -
– d
3 +
= 15163 X
4
+ d
4 -
– d
4 +
= 6546 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 316055550 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 250 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0 4. Agustus 2010
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 136122 X
2
+ d
2 -
– d
2 +
= 31353 X
3
+ d
3 -
– d
3 +
= 15177 X
4
+ d
4 -
– d
4 +
= 6650 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 318743350 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 250 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
5. September 2010
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 137341
Universitas Sumatera Utara
X
2
+ d
2 -
– d
2 +
= 31619 X
3
+ d
3 -
– d
3 +
= 15170 X
4
+ d
4 -
– d
4 +
= 6753 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 321392200 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 240 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
6. Oktober 2010
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 138560 X
2
+ d
2 -
– d
2 +
= 31884 X
3
+ d
3 -
– d
3 +
= 15143 X
4
+ d
4 -
– d
4 +
= 6857 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 324004150 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 250 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
7. November 2010
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 139779 X
2
+ d
2 -
– d
2 +
= 32149
Universitas Sumatera Utara
X
3
+ d
3 -
– d
3 +
= 15095 X
4
+ d
4 -
– d
4 +
= 6961 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 326577250 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 250 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
8. Desember 2010
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 140998 X
2
+ d
2 -
– d
2 +
= 32414 X
3
+ d
3 -
– d
3 +
= 15026 X
4
+ d
4 -
– d
4 +
= 7065 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 329111500 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 250 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
9. Januari 2011
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 142217 X
2
+ d
2 -
– d
2 +
= 32679 X
3
+ d
3 -
– d
3 +
= 14936
Universitas Sumatera Utara
X
4
+ d
4 -
– d
4 +
= 7169 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 331606900 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 250 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
10. Februari 2011
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 143436 X
2
+ d
2 -
– d
2 +
= 32945 X
3
+ d
3 -
– d
3 +
= 14826 X
4
+ d
4 -
– d
4 +
= 7272 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 334065200 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 240 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
11. Maret 2011
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 144655 X
2
+ d
2 -
– d
2 +
= 33210 X
3
+ d
3 -
– d
3 +
= 14695 X
4
+ d
4 -
– d
4 +
= 7376
Universitas Sumatera Utara
1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 336484750 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 260 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
12. April 2011
Minimumkan Z = P
1
d
1 -
+d
2 -
+d
3 -
+d
4 -
+ P
2
d
5 -
+ P
3
d
6 +
+ P
4
d
7 +
ST: X
1
+ d
1 -
– d
1 +
= 145874 X
2
+ d
2 -
– d
2 +
= 33475 X
3
+ d
3 -
– d
3 +
= 14543 X
4
+ d
4 -
– d
4 +
= 7480 1600X
1
+ 1900X
2
+ 1850X
3
+ 2000X
4
+ d
5 -
– d
5 +
= 338865450 0,13670X
1
+ 0,13672X
2
+ 0,13674X
3
+ 0,13561X
4
+ d
6 -
– d
6 +
= 30000 0,001178 X
1
+ 0,001178 X
2
+ 0,001178 X
3
+ 0,001178 X
4
+ d
7 -
– d
7 +
= 250 X
1
, X
2
, X
3
, X
4
,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 +
≥ 0
5.5. Penyelesaian Formulasi Goal Programming