X
10
+ d
106 +
− d
106 -
= 3.530.358,33 X
11
+ d
107 +
− d
107 -
= 2.376.675,92 X
12
+ d
108 +
− d
108 -
= 3.492.827,66
5.2.2.3. Formulasi Fungsi Tujuan
Formulasi fungsi tujuan dilakukan untuk mendapatkan hasil optimasi yang mendekati nilai sasaran yang diinginkan. Fungsi tujuan yang digunakan bertujuan
untuk meminimalkan variabel deviasional dari setiap sasaran yang ingin dicapai. Perusahaan memiliki 8 tujuan yang ingin dicapai, yaitu:
1. Memenuhi permintaan CPO
Bentuk goal programming-nya adalah: Min Z =
∑ �
� −
60 �=49
2. Meminimumkan biaya produksi CPO
Bentuk goal programming-nya adalah: Min Z =
∑ �
� +
12 �=1
3. Meminimumkan biaya produksi TBS
Bentuk goal programming-nya adalah: Min Z =
∑ �
� +
24 �=13
4. Meminimumkan biaya pembelian TBS
Bentuk goal programming-nya adalah: Min Z =
∑ �
� +
36 �=25
5. Pemenuhan kapasitas produksi
Bentuk goal programming-nya adalah: Min Z =
∑ �
� −
+ �
� +
48 �=37
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6. Memaksimalkan pengolahan TBS
Bentuk goal programming-nya adalah: Min Z =
∑ �
� −
96 �=85
7. Menghindari over produksi TBS
Bentuk goal programming-nya adalah: Min Z =
∑ �
� −
+ �
� +
72 �=61
+ ∑
�
� −
+ �
� +
84 �=73
8. Mencapai keuntungan
Bentuk goal programming-nya adalah: Min Z =
∑ �
� −
97 �=108
Maka, model fungsi tujuannya dapat dituliskan sebagai berikut:
Min Z =
∑ �
� +
�� �=�
+ ∑
�
� +
�� �=��
+ ∑
�
� +
�� �=��
+ ∑
�
� +
�� �=��
+ ∑
�
� −
+ �
� +
�� �=��
+ ∑
�
� −
�� �=��
+ ∑
�
� −
+ �
� +
�� �=��
+ ∑
�
� −
+ �
� +
�� �=��
+ ∑
�
� −
�� �=��
+ ∑
�
� −
�� �=���
Dengan kendala:
1 6.105,36. X
1
+ d
1 +
− d
1 -
= 27.346.757.899,53 2
6.160,92. X
2
+ d
2 +
− d
2 -
= 26.877.426.087,57 3
6.531,70. X
3
+ d
3 +
− d
3 -
= 28.546.946.689,50 4
6.224,24. X
4
+ d
4 +
− d
4 -
= 29.908.216.418,34 5
6.278,15. X
5
+ d
5 +
− d
5 -
= 31.911.245.165,06 6
6.308,02. X
6
+ d
6 +
− d
6 -
= 34.981.304.637,82 7
6.442,66. X
7
+ d
7 +
− d
7 -
= 37.890.730.287,29 8
5.973,51. X
8
+ d
8 +
− d
8 -
= 38.712.347.643,90 9
5.866,83. X
9
+ d
9 +
− d
9 -
= 38.272.784.502,40 10
6.075,67. X
10
+ d
10 +
− d
10 -
= 36.333.037.145,74 11
5.988,31. X
11
+ d
11 +
− d
11 -
= 33.825.569.063,66
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12 5.858,96. X
12
+ d
12 +
− d
12 -
= 29.823.516.060,50 13
826. X
13
+ d
13 +
− d
13 -
= 11.185.604.444 14
853. X
14
+ d
14 +
− d
14 -
= 11.435.211.375 15
877. X
15
+ d
15 +
− d
15 -
= 11.582.383.771 16
866. X
16
+ d
16 +
− d
16 -
= 11.832.034.162 17
806. X
17
+ d
17 +
− d
17 -
= 10.786.463.454 18
891. X
18
+ d
18 +
− d
18 -
= 11.919.520.899 19
833. X
19
+ d
19 +
− d
19 -
= 11.318.544.104 20
794,18. X
20
+ d
20 +
− d
20 -
= 10.853.796.128 21
813,81. X
21
+ d
21 +
− d
21 -
= 11.168.109.056 22
810. X
22
+ d
22 +
− d
22 -
= 11.059.172.190 23
886. X
23
+ d
23 +
− d
23 -
= 11.996.851.990 24
809. X
24
+ d
24 +
− d
24 -
= 11.059.081.776 25
1.821,35 .X
25
+ d
25 +
− d
25 -
= 13.206.014.905,49 26
1.892,95 .X
26
+ d
26 +
− d
26 -
= 12.834.075.061,90 27
1.947,43 .X
27
+ d
27 +
− d
27 -
= 13.598.885.264,50 28
1.818,86 .X
28
+ d
28 +
− d
28 -
= 15.649.598.680,76 29
1.778,87 .X
29
+ d
29 +
− d
29 -
= 18.055.017.496,50 30
1.719,18 .X
30
+ d
30 +
− d
30 -
= 20.642.069.907,82 31
1.684,25 .X
31
+ d
31 +
− d
31 -
= 22.651.431.573,51 32
1.484,79 .X
32
+ d
32 +
− d
32 -
= 23.783.718.406,18 33
1.427,23 .X
33
+ d
33 +
− d
33 -
= 23.215.262.045,40 34
1.475,45 .X
34
+ d
34 +
− d
34 -
= 20.734.304.420,69
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35 1.513,28 .X
35
+ d
35 +
− d
35 -
= 19.129.466.548,17 36
1.506,70 .X
36
+ d
36 +
− d
36 -
= 15.147.065.479,23 37
X
1
+ d
37 +
− d
37 -
= 8.556.000 38
X
2
+ d
38 +
− d
38 -
= 8.004.000 39
X
3
+ d
39 +
− d
39 -
= 8.556.000 40
X
4
+ d
40 +
− d
40 -
= 8.280.000 41
X
5
+ d
41 +
− d
41 -
= 8.556.000 42
X
6
+ d
42 +
− d
42 -
= 8.280.000 43
X
7
+ d
43 +
− d
43 -
= 8.556.000 44
X
8
+ d
44 +
− d
44 -
= 8.556.000 45
X
9
+ d
45 +
− d
45 -
= 8.280.000 46
X
10
+ d
46 +
− d
46 -
= 8.556.000 47
X
11
+ d
47 +
− d
47 -
= 8.280.000 48
X
12
+ d
48 +
− d
48 -
= 8.556.000 49
X
1
+ d
49 +
− d
49 -
= 4.702.065,62 50
X
2
+ d
50 +
− d
50 -
= 4.399.124,97 51
X
3
+ d
51 +
− d
51 -
= 4.357.466,27 52
X
4
+ d
52 +
− d
52 -
= 4.588.251,94 53
X
5
+ d
53 +
− d
53 -
= 5.029.643,15 54
X
6
+ d
54 +
− d
54 -
= 5.563.369,47 55
X
7
+ d
55 +
− d
55 -
= 6.046.419,38 56
X
8
+ d
56 +
− d
56 -
= 6.349.360,03 57
X
9
+ d
57 +
− d
57 -
= 6.391.018,73
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58 X
10
+ d
58 +
− d
58 -
= 6.160.233,06 59
X
11
+ d
59 +
− d
59 -
= 5.718.841,85 60
X
12
+ d
60 +
− d
60 -
= 5.185.115,53 61
X
13
+ d
61 +
− d
61 -
= 13.541.894 62
X
14
+ d
62 +
− d
62 -
= 13.405.875 63
X
15
+ d
63 +
− d
63 -
= 13.206.823 64
X
16
+ d
64 +
− d
64 -
= 13.662.857 65
X
17
+ d
65 +
− d
65 -
= 13.382.709 66
X
18
+ d
66 +
− d
66 -
= 13.377.689 67
X
19
+ d
67 +
− d
67 -
= 13.587.688 68
X
20
+ d
68 +
− d
68 -
= 13.666.744 69
X
21
+ d
69 +
− d
69 -
= 13.723.208 70
X
22
+ d
70 +
− d
70 -
= 13.653.299 71
X
23
+ d
71 +
− d
71 -
= 13.540.465 72
X
24
+ d
72 +
− d
72 -
= 13.670.064 73
X
25
+ d
73 +
− d
73 -
= 5.823.161,34 74
X
26
+ d
74 +
− d
74 -
= 5.406.415,94 75
X
27
+ d
75 +
− d
75 -
= 5.647.897,62 76
X
28
+ d
76 +
− d
76 -
= 7.174.603,15 77
X
29
+ d
77 +
− d
77 -
= 8.688.109,58 78
X
30
+ d
78 +
− d
78 -
= 10.494.578,76 79
X
31
+ d
79 +
− d
79 -
= 11.905.258,47
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80 X
32
+ d
80 +
− d
80 -
= 14.267.165,96 81
X
33
+ d
81 +
− d
81 -
= 14.444.249,38 82
X
34
+ d
82 +
− d
82 -
= 12.290.693,97 83
X
35
+ d
83 +
− d
83 -
= 10.922.939,94 84
X
36
+ d
84 +
− d
84 -
= 8.327.514,09 85
0,2313 X
13
+ 0,2313 X
25
– X
1
+ d
85 +
− d
85 -
= 0 86
0,2319 X
14
+ 0,2319 X
26
– X
2
+ d
86 +
− d
86 -
= 0 87
0,2318 X
15
+ 0,2318 X
27
– X
3
+ d
87 +
− d
87 -
= 0 88
0,2306 X
16
+ 0,2306 X
28
– X
4
+ d
88 +
− d
88 -
= 0 89
0,2303 X
17
+ 0,2303 X
29
– X
5
+ d
89 +
− d
89 -
= 0 90
0,2323 X
18
+ 0,2323 X
30
– X
6
+ d
90 +
− d
90 -
= 0 91
0,2307 X
19
+ 0,2307 X
31
– X
7
+ d
91 +
− d
91 -
= 0 92
0,2320 X
20
+ 0,2320 X
32
– X
8
+ d
92 +
− d
92 -
= 0 93
0,2316 X
21
+ 0,2316 X
33
– X
9
+ d
93 +
− d
93 -
= 0 94
0,2305 X
22
+ 0,2305 X
34
– X
10
+ d
94 +
− d
94 -
= 0 95
0,2309 X
23
+ 0,2309 X
35
– X
11
+ d
95 +
− d
95 -
= 0 96
0,2314 X
24
+ 0,2314 X
36
– X
12
+ d
96 +
− d
96 -
= 0 97
X
1
+ d
97 +
− d
97 -
= 2.935.131,11 98
X
2
+ d
98 +
− d
98 -
= 3.158.200,28 99
X
3
+ d
99 +
− d
99 -
= 3.473.867,41 100
X
4
+ d
100 +
− d
100 -
= 2.681.189,80 101
X
5
+ d
101 +
− d
101 -
= 3.679.623,19
Universitas Sumatera Utara
102 X
6
+ d
102 +
− d
102 -
= 3.219.872,20 103
X
7
+ d
103 +
− d
103 -
= 3.965.580,42 104
X
8
+ d
104 +
− d
104 -
= 3.804.435,24 105
X
9
+ d
105 +
− d
105 -
= 3.680.547,57 106
X
10
+ d
106 +
− d
106 -
= 3.530.358,33 107
X
11
+ d
107 +
− d
107 -
= 2.376.675,92 108
X
12
+ d
108 +
− d
108 -
= 3.492.827,66 109
di
+
, di
-
, X
i
, X
j
, X
k
≥ 0
5.2.3. Penyelesaian Model Goal Programming dengan Software LINDO 6.1.
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