Perbaikan Supply Chain di Sektor Logistik PT. Central Proteinaprima
LAMPIRAN
Universitas Sumatera Utara
LAMPIRAN LOSS OPPORTUNITY COST PT. CENTRAL PROTEINAPRIMA TAHUN 2015
Loss Opportunity Cost Produk Irawan 9001 Tahun 2015
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
2.530
Februari
Permintaan (Kg)
PT.
SWMS
5.817
PT.
BWP
3.941
CV.
WS
1.689
Total
Selisih
(Kg)
17.200
PT.
JWL
7.318
18.765
965
965
24.850
6.720
4.753
3.606
1.311
16.390
9.425
Maret
9.425
23.330
12.704
9.034
4.799
1.694
28.230
4.525
April
4.525
27.590
11.806
7.028
6.184
3.092
28.110
4.005
Mei
4.005
31.120
12.294
8.577
6.004
1.715
28.590
6.535
Juni
6.535
31.970
10.388
4.028
4.240
2.544
21.200
17.305
Juli
17.305
19.090
8.484
5.656
3.636
2.424
20.200
16.195
Agustus
16.195
7.080
9.280
7.888
3.712
2.320
23.200
75
September
75
25.020
14.204
7.520
3.899
2.228
27.850
-2.755
(Rp28.927.500)
Oktober
-
22.180
9.232
6.012
3.221
3.006
21.470
-2.045
(Rp21.472.500)
November
-
24.110
8.914
5.014
2.600
2.043
18.570
3.495
4.760
4.522
1.904
9.955
70.268
46.422
24.281
23.800
276.375
3.495
12.614
Desember
30.260
60.255
266.600
116.639
Total
Sumber: PT. Central Proteina Prima
Opportunity
Loss Cost
(Rp50.400.000)
I-I
Universitas Sumatera Utara
Loss Opportunity Cost Produk Irawan 682 Tahun 2015
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
970
Februari
Permintaan (Kg)
PT.
SWMS
10.846
PT.
BWP
10.846
CV.
WS
5.916
Total
Selisih
(Kg)
79.600
PT.
JWL
21.692
49.300
31.270
31.270
64.980
22.648
14.304
14.900
7.748
59.600
36.650
Maret
36.650
71.980
50.243
32.070
17.104
7.483
106.900
1.730
April
1.730
158.400
46.152
35.896
29.486
16.666
128.200
31.930
Mei
31.930
82.350
47.779
20.173
22.297
15.926
106.175
8.105
Juni
8.105
125.250
63.323
31.662
20.702
6.089
121.775
11.580
Juli
11.580
107.330
46.097
15.656
15.656
9.567
86.975
31.935
Agustus
31.935
101.700
53.632
31.181
24.945
14.967
124.725
8.910
September
8.910
124.430
49.193
26.939
28.110
12.884
117.125
16.215
Oktober
16.215
66.680
41.368
14.352
16.041
12.664
84.425
-1.530
November
-
95.900
30.879
26.590
20.586
7.720
85.775
10.125
Desember
10.125
119.830
60.612
30.306
25.255
10.102
126.275
3.680
189.420 1.198.430 533.617
Total
Sumber: PT. Central Proteina Prima
289.975
245.927
127.732
1.197.250
Opportunity
Loss Cost
Rp (14.535.000)
Rp (14.535.000)
Universitas Sumatera Utara
Loss Opportunity Cost Produk Irawan 683 Tahun 2015
Permintaan (Kg)
PT.
PT.
CV.
SWMS
BWP
WS
55.775
48.500
36.375
Total
Selisih
(Kg)
291.100
PT.
JWL
101.850
242.500
50.720
50.720
191.000
110.329
46.583
56.390
31.873
245.175
-3.455
Maret
-
256.580
119.021
51.009
43.722
29.148
242.900
13.680
April
13.680
338.030
143.705
108.655
66.595
31.545
350.500
1.210
Mei
1.210
275.430
115.259
74.095
57.629
27.443
274.425
2.215
Juni
2.215
288.080
124.025
73.288
53.556
31.006
281.875
8.420
Juli
8.420
351.430
115.372
85.789
65.082
29.583
295.825
64.025
Agustus
64.025
238.530
142.395
56.958
49.191
10.356
258.900
43.655
September
43.655
345.080
191.647
52.868
66.085
19.826
330.425
58.310
Oktober
58.310
210.280
122.280
77.089
26.583
39.874
265.825
2.765
November
2.765
240.700
105.624
55.013
30.807
28.607
220.050
23.415
Desember
23.415
243.780
145.989
46.827
49.581
33.054
275.450
-8.255
783.948
613.721
348.688
3.283.850
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
2.120
Februari
270.535 3.270.020 1.537.494
Total
Sumber: PT. Central Proteina Prima
Opportunity
Loss Cost
Rp (31.095.000)
Rp (74.295.000)
Rp (105.390.000)
Universitas Sumatera Utara
Loss Opportunity Cost Produk Irawan 683-SP Tahun 2015
Total
Selisih
(Kg)
273.450
PT.
JWL
114.774
Permintaan (Kg)
PT.
PT.
CV.
SWMS
BWP
WS
93.060
68.244
34.122
310.200
8.750
8.750
213.200
68.013
76.257
43.281
18.549
206.100
15.850
Maret
15.850
204.200
65.861
48.974
33.775
20.265
168.875
51.175
April
51.175
272.100
114.028
117.381
77.136
26.830
335.375
-12.100
Mei
-
310.400
114.582
88.140
67.574
23.504
293.800
16.600
Juni
16.600
398.600
126.242
110.940
95.638
49.732
382.550
32.650
Juli
32.650
259.080
92.117
109.946
68.345
26.744
297.150
-5.420
Agustus
-
265.400
78.888
66.432
39.444
22.836
207.600
57.800
September
57.800
253.580
101.747
101.747
77.081
27.749
308.325
3.055
Oktober
3.055
257.600
104.519
61.182
61.182
28.042
254.925
5.730
November
5.730
229.030
77.634
49.231
37.870
24.616
189.350
45.410
Desember
45.410
254.930
88.086
57.885
83.053
22.651
251.675
48.665
Total
282.520
3.191.570
1.146.490
981.175
752.622
325.638
3.205.925
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
45.500
Februari
Opportunity
Loss Cost
Rp (121.000.000)
Rp (54.200.000)
Rp
(175.200.000)
Sumber: PT. Central Proteina Prima
Universitas Sumatera Utara
Loss Opportunity Cost Produk Irawan 684-S Tahun 2015
Permintaan (Kg)
PT.
JWL
PT.
SWMS
PT.
BWP
CV.
WS
Total
Selisih
(Kg)
181.150
80.786
39.454
39.454
28.181
187.875
3.075
3.075
172.530
58.149
37.382
38.766
4.154
138.450
37.155
Maret
37.155
299.600
124.014
73.281
50.733
33.822
281.850
54.905
April
54.905
243.480
76.981
33.181
15.927
6.636
132.725
165.660
Mei
165.660
276.580
96.601
32.200
28.811
11.863
169.475
272.765
Juni
272.765
204.450
137.403
77.775
38.888
5.185
259.250
217.965
Juli
217.965
243.100
113.036
37.679
35.585
23.026
209.325
251.740
Agustus
251.740
236.550
142.224
68.149
56.297
29.630
296.300
191.990
September
191.990
331.430
111.110
66.666
63.888
36.111
277.775
245.645
Oktober
245.645
291.750
115.477
52.078
38.492
20.378
226.425
310.970
November
310.970
259.480
145.007
91.956
67.198
49.515
353.675
216.775
Desember
216.775
141.600
68.058
45.900
26.907
17.410
158.275
200.100
1.268.844
655.699
500.946
265.911
2.691.400
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
9.800
Februari
1.978.445 2.881.700
Total
Sumber: PT. Central Proteina Prima
Opportunity
Loss Cost
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 682 – PT. JWL
Irawan 682
Bulan
Demand
Januari
21.692
Februari
22.648
Maret
50.243
April
46.152
Mei
47.779
Juni
63.323
Juli
46.097
Agustus
53.632
September
49.193
Oktober
41.368
November
30.879
Desember
60.612
Total
533.617
Metode Peramalan Terpilih:
•
Metode Kuadratis
•
Metode Siklis
1.
t
1
2
3
4
5
6
7
8
9
10
11
12
78
Metode Kuadratis
y
21.692
22.648
50.243
46.152
47.779
63.323
46.097
53.632
49.193
41.368
30.879
60.612
533.617
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
t³
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
1
21.692
16
45.296
81
150.729
256
184.608
625
238.894
1.296
379.938
2.401
322.677
4.096
429.054
6.561
442.733
10.000
413.683
14.641
339.669
20.736
727.344
60.710
3.696.316
t²y
21.692
90.592
452.187
738.432
1.194.469
2.279.628
2.258.741
3.432.432
3.984.593
4.136.825
3.736.359
8.728.128
31.054.077
t'
13
14
15
16
17
18
19
20
21
22
23
24
222
y't
24.557
32.232
38.690
43.932
47.957
50.766
52.359
52.736
51.897
49.841
46.569
42.081
533.617
Universitas Sumatera Utara
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
� = � � � � − � � ��
� = (78 × 533.617) − (12 × 3.696.316) = −2.733.666
� = � �2 � � − � � �2�
� = (650 × 533.617) − (12 × 31.054.077) = −25.797.874
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�=
�� − ��
= 9.498,714
�� − � 2
� − ��
= −608,1283
�
∑ � − � ∑ � − � ∑ �2
= 15.666,727
�
� ′ = � + �� + �� 2
� ′ = 15.666,727 + 9.498,714� + (−608,1283)� 2
� ′ = 15.666,727 + 9.498,714(1) + (−608,1283)(1)2
= 24.557,31 ≈ 24.557
���� =
∑��=1|��� |
=
�
2,26
12
= 18,85%
2.
Metode Siklis
Jumlah periode adalah:
�=
12
=4
3
Universitas Sumatera Utara
SIKLIS
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
21692
1,000
0,000
Sin
(2πt/n)*Cos
(2πt/n)
0,000
2
22648
0,000
-1,000
3
50243
-1,000
4
46152
0,000
5
47778,75
1,000
0,000
0,000
6
63323
0,000
-1,000
0,000
7
46096,75
-1,000
0,000
0,000
8
53631,75
0,000
1,000
9
49192,5
1,000
10
41368,25
11
Sin^2
(2πt/n)
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
1,000
0,000
21692,00
0
0,000
0,000
1,000
0,00
-22648
0,000
0,000
1,000
0,000
-50243,00
0
1,000
0,000
0,000
1,000
0,00
46152
1,000
0,000
47778,75
0
0,000
1,000
0,00
-63323
1,000
0,000
-46096,75
0
0,000
0,000
1,000
0,00
53631,75
0,000
0,000
1,000
0,000
49192,50
0
0,000
-1,000
0,000
0,000
1,000
0,00
-41368,25
30879
-1,000
0,000
0,000
1,000
0,000
-30879,00
0
12
60612
0,000
1,000
0,000
0,000
1,000
0,00
60612
78
533617
0
0
0
6
6
-8555,5
33056,5
2πt
2πt
n
n
= n a + b ∑ sin� � + c ∑ cos� �
∑y
533.617
= 4 a + b (0) + c (0)
a
=
a
= 44.468,083
2πt
533.617
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-8555,5
= 44.468,083 (0) + b (0) + c (0)
b
=
b
= -1425,916
n
2πt
−8555 ,5
6
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
33.056,5
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= 5509,416
n
= 44.468,083 (0) + c (6) + -1425,916 (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
33.056 ,5
6
2πt
2πt
n
n
y’= 44.468,083 – 1425,916 sin � � +5509,416 cos � �
y’= 44.468,083 – 1425,916 sin (0,866) + 5509,416 cos (0,000) = 43042,167
Universitas Sumatera Utara
���� =
=
∑��=1 |��� |
3,28
�
12
= 27,29%
Metode Terpilih: Kuadratis
Verifikasi Peramalan
y
y't
e=y-y't
|MR|
UCL
LCL
21.692
24.557
-2.865
-
54.694,06
-54.694,06
22.648
32.232
-9.584
6.718,33
54.694,06
-54.694,06
50.243
38.690
11.553
21.136,93
54.694,06
-54.694,06
46.152
43.932
2.220
9.332,82
54.694,06
-54.694,06
47.779
47.957
-178
2.398,81
54.694,06
-54.694,06
63.323
50.766
12.557
12.734,95
54.694,06
-54.694,06
46.097
52.359
-6.263
18.819,30
54.694,06
-54.694,06
53.632
52.736
896
7.158,21
54.694,06
-54.694,06
49.193
51.897
-2.704
3.599,78
54.694,06
-54.694,06
41.368
49.841
-8.473
5.768,53
54.694,06
-54.694,06
30.879
46.569
-15.690
7.217,27
54.694,06
-54.694,06
60.612
42.081
18.531
34.221,24
54.694,06
-54.694,06
129.106,15
Peramalan Irawan 682 tahun
2016
40.000
PT. JWL
20.000
Irawan 682
0
UCL
LCL
-20.000
-40.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 683 – PT. JWL
Irawan 682
Bulan
Demand
Januari
101.850
Februari
110.329
Maret
119.021
April
143.705
Mei
115.259
Juni
124.025
Juli
115.372
Agustus
142.395
September
191.647
Oktober
122.280
November
105.624
Desember
145.989
Total
1.537.494
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
EKSPONENSIAL
t
y
lny
t.lny
t²
y'
1
101.850
11,53
11,53
1
2
110.329
11,61
23,22
4
3
119.021
11,69
35,06
9
4
143.705
11,88
47,50
16
5
115.259
11,65
58,27
25
6
124.025
11,73
70,37
36
7
115.372
11,66
81,59
49
8
142.395
11,87
94,93
64
9
191.647
12,16
109,47
81
10
122.280
11,71
117,14
100
11
105.624
11,57
127,24
121
12
145.989
11,89
142,70
144
78
1.537.494
140,95
919,03
650
112.965
115.263
117.607
119.999
122.439
124.930
127.471
130.063
132.709
135.408
138.162
140.972
1.517.987
Universitas Sumatera Utara
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 919,03) − (78 × 140,95)
�=
= −0,0200135
(12 × 650) − 782
∑ ��� − � ∑ �
ln � =
= 11,614
�
� = 110.713,2
� ′ = �� ��
� ′ = 110.713,2� −0,0200135 �
� ′ = 110.713,2� −0,0200135 (1) = 112.964,95 ≈ 112.965
�=
���� =
∑��=1|��� |
=
�
1,357
12
= 11,24%
2.
t
1
2
3
4
5
6
7
8
9
10
11
12
78
Metode Kuadratis
y
101.850
110.329
119.021
143.705
115.259
124.025
115.372
142.395
191.647
122.280
105.624
145.989
1.537.494
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
t³
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
1
101.850
16
220.658
81
357.063
256
574.820
625
576.293
1.296
744.150
2.401
807.602
4.096
1.139.160
6.561
1.724.819
10.000
1.222.795
14.641
1.161.864
20.736
1.751.862
60.710 10.382.935
t²y
101.850
441.315
1.071.189
2.299.280
2.881.463
4.464.900
5.653.216
9.113.280
15.523.367
12.227.950
12.780.504
21.022.344
87.580.657
t'
13
14
15
16
17
18
19
20
21
22
23
24
222
y't
102.712
111.130
118.408
124.547
129.548
133.409
136.130
137.713
138.157
137.461
135.626
132.653
1.537.494
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
� = � � � � − � � ��
� = (78 × 1.537.494) − (12 × 10.382.935) = −4.670.724
� = � �2 � � − � � �2�
� = (650 × 1.537.494) − (12 × 87.580.657) = −51.597.106
Universitas Sumatera Utara
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�� −��
�� −� 2
�−��
= 10126,336
= -569,574
�
∑ �−� ∑ �−� ∑ � 2
�=
= 93155,227
�
′
2
� = � + �� + ��
� ′ = 93155,227 + 9.498,714� + (−608,1283)� 2
� ′ = 93155,227 + 9.498,714(1) + (−608,1283)(1)2
= 102.711,99 ≈102.712
���� =
∑��=1|��� |
=
�
1,35
12
= 11,21%
Metode Terpilih: Kuadratis
Verifikasi Peramalan
y
101.850
110.329
119.021
143.705
115.259
124.025
115.372
142.395
191.647
y't
102.712
111.130
118.408
124.547
129.548
133.409
136.130
137.713
138.157
e=y-y't
-862
-801
613
19.158
-14.289
-9.384
-20.759
4.682
53.490
|MR|
61,14
1.413,79
18.544,69
33.446,67
4.905,48
11.375,12
25.440,53
48.807,93
UCL
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
LCL
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
Universitas Sumatera Utara
y
y't
e=y-y't
122.280 137.461 -15.182
105.624 135.626 -30.002
145.989 132.653 13.336
|MR|
UCL
LCL
68.671,42 65.490,63 -65.490,63
14.820,77 65.490,63 -65.490,63
43.338,38 65.490,63 -65.490,63
270.825,91
Peramalan Irawan 683 tahun 2016
80.000
60.000
PT. JWL
40.000
20.000
Irawan 683
0
UCL
-20.000
LCL
-40.000
-60.000
-80.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 683-SP – PT. JWL
Irawan 682
Bulan
Demand
Januari
114.774
Februari
68.013
Maret
65.861
April
114.028
Mei
114.582
Juni
126.242
Juli
92.117
Agustus
78.888
September
101.747
Oktober
104.519
November
77.634
Desember
88.086
Total
1.146.490
Metode Peramalan Terpilih:
•
Metode Kuadratis
•
Metode Siklis
1.
Metode Kuadratis
t
y
t²
t³
1
2
3
4
5
6
7
8
9
10
11
12
78
114.774
68.013
65.861
114.028
114.582
126.242
92.117
78.888
101.747
104.519
77.634
88.086
1.146.490
1
4
9
16
25
36
49
64
81
100
121
144
650
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
1
16
81
256
625
1.296
2.401
4.096
6.561
10.000
14.641
20.736
60.710
114.774
136.026
197.584
456.110
572.910
757.449
644.816
631.104
915.725
1.045.193
853.969
1.057.035
7.382.694
t²y
t'
y't
114.774
272.052
592.751
1.824.440
2.864.550
4.544.694
4.513.709
5.048.832
8.241.527
10.451.925
9.393.654
12.684.420
60.547.328
13
14
15
16
17
18
19
20
21
22
23
24
222
89.274
93.664
97.079
99.519
100.984
101.473
100.987
99.526
97.089
93.677
89.290
83.928
42.286
Universitas Sumatera Utara
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
� = � � � � − � � ��
� = (78 × 1.146.490) − (12 × 7.382.694) = 833.898
� = � �2 � � − � � �2�
� = (650 × 1.146.490) − (12 × 60.547.328) = 18.650.570
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�=
�� − ��
= 5.853,246
�� − � 2
� − ��
= −487,630
�
∑ � − � ∑ � − � ∑ �2
= 83.908,066
�
� ′ = � + �� + �� 2
� ′ = 83.908,066 + 5.853,246 + (−487,630)� 2
� ′ = 83.908,066 + 5.853,246(1) + (−487,630)(1)2
= 89.273,68 ≈ 89.274
���� =
∑��=1|��� |
=
�
2,22
12
= 18,50%
2.
Metode Siklis
Jumlah periode adalah:
�=
12
=6
2
Universitas Sumatera Utara
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
0,433
0,750
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,250
99394,28
57387
0,750
0,250
58899,26
-34006,5
0,000
0,000
1,000
0,00
-65861,25
-0,500
0,433
0,750
0,250
-98747,82
-57013,75
-0,866
0,500
-0,433
0,750
0,250
-99228,01
57291
0,000
1,000
0,000
0,000
1,000
0,00
126241,5
92116,5
0,866
0,500
0,433
0,750
0,250
79772,89
46058,25
8
78888
0,866
-0,500
-0,433
0,750
0,250
68317,01
-39444
9
101747,25
0,000
-1,000
0,000
0,000
1,000
0,00
-101747,25
10
104519,25
-0,866
-0,500
0,433
0,750
0,250
-90513,67
-52259,625
11
77633,5
-0,866
0,500
-0,433
0,750
0,250
-67230,61
38816,75
12
88086,25
0,000
1,000
0,000
0,000
1,000
0,00
88086,25
78
1.146.490
0
0
0
6
6
-49.336,665
63.548,375
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
114774
0,866
0,500
2
68013
0,866
-0,500
-0,433
3
65861,25
0,000
-1,000
4
114027,5
-0,866
5
114582
6
126241,5
7
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
∑y
1.146.490
= 12 a + b (0) + c (0)
a
=
a
= 95.540,833
2πt
1.146 .490
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-49.336,665
= 95.540,833 (0) + b (6) + c (0)
b
=
b
= -8.222,778
n
2πt
−49.336 ,665
6
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
63.548,375
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= 10.591,395
n
= 95.540,833 (0) + c (6) + -8.222,778 (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
63.548 ,375
6
2πt
2πt
n
n
y’= 95.540,833 – 8.222,778 sin � � +5509,416 cos � �
y’= 95.540,833 – 8.222,778 sin (0,866) + 5509,416 cos (0,500) = 93.715,605
Universitas Sumatera Utara
���� =
=
∑��=1 |��� |
1,96
�
12
= 16,32%
Metode Terpilih: Siklis
Verifikasi Peramalan
y
y't
e=y-y't
|MR|
UCL
LCL
114.774
68.013
65.861
114.028
114.582
126.242
92.117
78.888
101.747
104.519
77.634
88.086
93.716
83.124
84.949
97.366
107.957
106.132
93.716
83.124
84.949
97.366
107.957
106.132
21.058
-15.111
-19.088
16.661
6.625
20.109
-1.599
-4.236
16.798
7.153
-30.324
-18.046
36.169,60
3.976,98
35.749,63
10.036,90
13.484,73
21.708,38
2.637,10
21.034,02
9.644,62
37.477,15
12.277,98
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
204.197,08
Peramalan Irawan 683-SP tahun
2016
100.000
PT. JWL
50.000
0
-50.000
Irawan 683-SP
UCL
LCL
-100.000
PERAMALAN PRODUK IRAWAN 684-S – PT. JWL
Universitas Sumatera Utara
Irawan 682
Bulan
Demand
Januari
80.786
Februari
58.149
Maret
124.014
April
76.981
Mei
96.601
Juni
137.403
Juli
113.036
Agustus
142.224
September
111.110
Oktober
115.477
November
145.007
Desember
68.058
Total
1.268.844
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Siklis
1.
Metode Eksponensial
EKSPONENSIAL
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
lny
80.786
11,2996
58.149
10,9708
124.014
11,7281
76.981
11,2513
96.601
11,4783
137.403
11,8307
113.036
11,6355
142.224
11,8652
111.110
11,6183
115.477
11,6568
145.007
11,8845
68.058
11,1281
1.268.844
138,3472
� ∑ �. ��� − ∑ � ∑ ���
�=
� ∑ � 2 − (∑ �)2
t.lny
t²
y'
11,2996
21,9415
35,1844
45,0052
57,3917
70,9840
81,4482
94,9213
104,5645
116,5682
130,7299
133,5374
903,5760
1
86.060
88.699
91.419
94.223
97.112
100.090
103.160
106.323
109.584
112.944
116.408
119.978
1.226.000
4
9
16
25
36
49
64
81
100
121
144
650
Universitas Sumatera Utara
(12 × 903,57) − (78 × 138,34)
= −0,030206
(12 × 650) − 782
�=
ln � =
∑ ��� − � ∑ �
= 11,33259
�
� = 83.499,2
� ′ = �� ��
� ′ = 83.499,2� −0,0302065 �
� ′ = 83.499,2� −0,0302065 (1) = 86.059,85 ≈ 86.060
���� =
∑��=1|��� |
=
�
2,69
12
= 22,42%
2.
Metode Siklis
Jumlah periode adalah:
�=
12
=4
3
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
0,000
1,000
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,000
80786,25
0
0,000
1,000
0,00
-58149
0,000
1,000
0,000
-124014,00
0
1,000
0,000
0,000
1,000
0,00
76980,5
0,000
0,000
1,000
0,000
96600,75
0
0,000
-1,000
0,000
0,000
1,000
0,00
-137402,5
113036
-1,000
0,000
0,000
1,000
0,000
-113035,50
0
8
142224
0,000
1,000
0,000
0,000
1,000
0,00
142224
9
111110
1,000
0,000
0,000
1,000
0,000
111110,00
0
10
115477
0,000
-1,000
0,000
0,000
1,000
0,00
-115476,75
11
145007
-1,000
0,000
0,000
1,000
0,000
-145006,75
0
12
68058
0,000
1,000
0,000
0,000
1,000
0,00
68058,25
78
1.268.844
0
0
0
6
6
-93559,25
-23765,5
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
80786
1,000
0,000
2
58149
0,000
-1,000
0,000
3
124014
-1,000
0,000
4
76981
0,000
5
96601
1,000
6
137403
7
Universitas Sumatera Utara
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
∑y
1.268.844
= 12 a + b (0) + c (0)
a
=
a
= 105.737,02
2πt
1.268 .844
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-48.237,499
= 95.540,833 (0) + b (4) + c (0)
b
=
b
= -23.389,81
n
2πt
−93.559,25
4
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
26.455
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= -5.941,375
n
= 95.540,833 (0) + c (4) + -8.222,778 (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
−23.765,5
4
2πt
2πt
n
n
y’= 105.737,02 – 23.389,81 sin � � - 5.941,375 cos � �
y’= 105.737,02 – 23.389,81 sin (0,866) - 5.941,375 co�(−0,500) = 82.347,208
���� =
=
∑��=1 |��� |
2,92
�
12
= 24,34%
Metode Terpilih: Eksponensial
Universitas Sumatera Utara
Verifikasi Peramalan
y
80.786
58.149
124.014
76.981
96.601
137.403
113.036
142.224
111.110
115.477
145.007
68.058
y't
86.060
88.699
91.419
94.223
97.112
100.090
103.160
106.323
109.584
112.944
116.408
119.978
e=y-y't
-5.274
-30.550
32.595
-17.242
-511
37.312
9.876
35.901
1.526
2.532
28.599
-51.920
|MR|
25.276,42
63.144,89
49.837,02
16.730,75
37.823,64
27.436,44
26.024,93
34.374,58
1.006,18
26.066,37
80.518,35
388.239,58
UCL
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
LCL
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
Peramalan Irawan 684-S tahun 2016
150.000
100.000
Irawan 684-S
LCL
Desember
November
Oktober
Agustus
Juli
Juni
Mei
April
September
-100.000
Maret
-50.000
Februari
0
Januari
PT. JWL
50.000
UCL
-150.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 9001 – PT. SWMS
Irawan 9001
Bulan
Demand
5.817
Januari
4.753
Februari
9.034
Maret
7.028
April
8.577
Mei
4.028
Juni
5.656
Juli
7.888
Agustus
7.520
September
Oktober
November
Desember
6.012
5.014
4.760
Total
76085
Metode Peramalan Terpilih:
•
Metode Kuadratis
•
Metode Siklis
1.
Metode Kuadratis
KUADRATIS
ty
t
y
t²
t³
t⁴
1
2
3
4
5
6
7
8
9
10
11
12
78
5.817
4.753
9.034
7.028
8.577
4.028
5.656
7.888
7.520
6.012
5.014
4.760
76.085
1
4
9
16
25
36
49
64
81
100
121
144
650
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
1
16
81
256
625
1.296
2.401
4.096
6.561
10.000
14.641
20.736
60.710
5.817
9.506
27.101
28.110
42.885
24.168
39.592
63.104
67.676
60.116
55.153
57.120
480.348
t²y
t'
y't
5.817
19.012
81.302
112.440
214.425
145.008
277.144
504.832
609.080
601.160
606.682
685.440
3.862.342
13
14
15
16
17
18
19
20
21
22
23
24
222
5.867
6.324
6.670
6.904
7.027
7.039
6.940
6.729
6.407
5.974
5.430
4.774
76.085
Universitas Sumatera Utara
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
� = � � � � − � � ��
� = (78 × 76.085) − (12 × 480.348) = 170.487
� = � �2 � � − � � �2�
� = (650 × 76.085) − (12 × 3.862.342) = 3.107.369
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�=
�� − ��
= 623,8973
�� − � 2
� − ��
= −55,6345
�
∑ � − � ∑ � − � ∑ �2
= 8.298,648
�
� ′ = � + �� + �� 2
� ′ = 8.298,648 + 623,8973� + (−55,6345)� 2
� ′ = 8.298,648 + 623,8973(1) + (−55,6345)(1)2
= 5.866,91 ≈ 5.867
���� =
∑��=1|��� |
=
�
2,16
12
= 18,00%
2.
Metode Siklis
Jumlah periode adalah:
�=
12
=6
2
Universitas Sumatera Utara
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
12
5.817
4.753
9.034
7.028
8.577
4.028
5.656
7.888
7.520
6.012
5.014
4.760
0,866
0,866
0,000
-0,866
-0,866
0,000
0,866
0,866
0,000
-0,866
-0,866
0,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
78
76085
0
0
0
2
3
4
5
6
7
8
9
10
11
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
5037,65
4116,18
0,00
-6085,82
-7427,68
0,00
4898,10
6831,01
0,00
-5206,05
-4342,04
0,00
2908,575
-2376,55
-9033,6
-3513,75
4288,5
4028
2828
-3944
-7519,5
-3005,8
2506,95
4760
6
6
-2178,6395
-8073,175
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
∑y
76.085
= 12 a + b (0) + c (0)
a
=
a
= 6.340,445
2πt
76.085
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-2.178,6395
= 6.340,445 (0) + b (6) + c (0)
b
=
b
= -363,106
n
2πt
−2.178,639
6
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
-8.073,175
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= -1.345,529
n
= 6.340,445 (0) + c (6) + -363,106 (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
−8.073,175
6
2πt
2πt
n
n
y’= 6.340,445 – 363,106 sin � � – 1.345,529 cos � �
y’= 6.340,445 – 363,106 sin (0,866) – 1.345,529 cos (0,500) = 5.353
Universitas Sumatera Utara
���� =
=
∑��=1 |��� |
1,91
�
12
= 15,93%
Metode Terpilih: Siklis
Verifikasi Peramalan
y
y't
e=y-y't
|MR|
UCL
LCL
5.817
4.753
9.034
7.028
8.577
4.028
5.656
7.888
7.520
6.012
5.014
4.760
5.353
6.699
7.686
7.328
5.982
4.995
5.353
6.699
7.686
7.328
5.982
4.995
464
-1.946
1.348
-300
2.595
-967
303
1.189
-166
-1.316
-968
-235
2.409,58
3.293,29
1.647,79
2.895,03
3.561,79
1.269,69
886,47
1.355,71
1.149,59
347,83
733,31
19.550,07
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
Permintaan Irawan 9001 tahun 2016
6.000
2.000
Irawan 9001
LCL
Desember
November
Oktober
September
Juli
Juni
Mei
April
Agustus
-4.000
Maret
-2.000
Februari
0
Januari
PT. SWMS
4.000
UCL
-6.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 682 – PT. SWMS
Irawan 682
Bulan
Demand
Januari
10.846
Februari
14.304
Maret
32.070
April
35.896
Mei
20.173
Juni
31.662
Juli
15.656
Agustus
31.181
September 26.939
Oktober
14.352
November 26.590
Desember
30.306
Total
289.975
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Siklis
1.
Metode Eksponensial
EKSPONENSIAL
t.lny
t
y
lny
1
2
3
4
5
6
7
8
9
10
11
12
78
10.846
14.304
32.070
35.896
20.173
31.662
15.656
31.181
26.939
14.352
26.590
30.306
289.975
9,2916
9,5683
10,3757
10,4884
9,9121
10,3629
9,6586
10,3476
10,2013
9,5717
10,1883
10,3191
120,2854
9,2916
19,1366
31,1270
41,9535
49,5606
62,1771
67,6100
82,7806
91,8119
95,7166
112,0713
123,8292
787,0660
t²
1
y'
144
18.460
19.145
19.856
20.593
21.357
22.149
22.971
23.824
24.708
25.625
26.576
27.562
222
272.826
4
9
16
25
36
49
64
81
100
121
Universitas Sumatera Utara
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 787,066) − (78 × 120,285)
�=
= 0,03643
(12 × 650) − 782
∑ ��� − � ∑ �
ln � =
= 9,7869
�
� = 17.799,488
�=
� ′ = �� ��
� ′ = 17.799,488� 0,03643 �
� ′ = 17.799,488� 0,03643 (1) = 18.460,06 ≈ 18.460
���� =
=
3.
∑��=1 |��� |
3,87
12
�
= 32,24
Metode Siklis
Jumlah periode adalah:
�=
12
=4
3
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
2
10.846
14.304
32.070
35.896
20.173
31.662
15.656
31.181
26.939
14.352
26.590
30.306
289.975
0,866
0,866
0,000
-0,866
-0,866
0,000
0,866
0,866
0,000
-0,866
-0,866
0,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0
0
0
3
4
5
6
7
8
9
10
11
12
78
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
9392,64
12387,26
0,00
-31085,94
-17470,03
0,00
13557,66
27002,96
0,00
-12429,05
-23027,16
0,00
5423
-7152
-32070
-17948
10086,625
31661,5
7827,75
-15590,625
-26938,75
-7176,125
13295,125
30306
6
6
-21671,65
-8275,5
Universitas Sumatera Utara
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
∑y
289.975
= 12 a + b (0) + c (0)
a
=
a
= 24.164,562
2πt
289.975
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-21.671,65
= 24.164,562 (0) + b (4) + c (0)
b
=
b
= -5417,912
n
2πt
−21.671,65
4
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
-8.275,5
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= -2.068,875
n
= 24.164,562 (0) + c (4) + (-5417,912) (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
−8.275,5
4
2πt
2πt
n
n
y’= 24.164,562 – 5417,912 sin � � - 2.068,875 cos � �
y’= 24.164,562 – 5417,912 sin (0,866) - 2.068,875 co�(−0,500) = 18.438
���� =
=
∑��=1 |��� |
4,11
�
12
= 34,25%
Metode Terpilih: Eksponensial
Universitas Sumatera Utara
Verifikasi Peramalan
y
10.846
14.304
32.070
35.896
20.173
31.662
15.656
31.181
26.939
14.352
26.590
30.306
y't
18.460
19.145
19.856
20.593
21.357
22.149
22.971
23.824
24.708
25.625
26.576
27.562
e=y-y't
-7.614
-4.841
12.214
15.303
-1.184
9.512
-7.316
7.357
2.231
-11.273
14
2.744
|MR|
2.772,91
17.055,49
3.089,12
16.486,98
10.695,66
16.828,00
14.673,24
5.126,65
13.503,46
11.287,01
2.729,46
114.247,98
UCL
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
LCL
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
Permintaan 682 tahun 2016
40.000
30.000
PT. SWMS
20.000
10.000
Irawan 682
0
LCL
-10.000
UCL
-20.000
-30.000
-40.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 683 – PT. SWMS
Irawan 683
Bulan Demand
Januari
55.775
Februari
46.583
Maret
51.009
April
108.655
Mei
74.095
Juni
73.288
Juli
85.789
Agustus
56.958
September
52.868
Oktober
77.089
November
55.013
Desember
46.827
Total
783.948
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
EKSPONENSIAL
lny
t.lny
55.775 10,929
46.583 10,749
51.009 10,840
108.655 11,596
74.095 11,213
73.288 11,202
85.789 11,360
56.958 10,950
52.868 10,876
77.089 11,253
55.013 10,915
46.827 10,754
783.948 132,637
10,929
21,498
32,519
46,384
56,065
67,213
79,518
87,601
97,880
112,527
120,068
129,050
861,253
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
y'
65.321
64.918
64.518
64.120
63.725
63.331
62.941
62.553
62.167
61.783
61.402
61.024
757.803
Universitas Sumatera Utara
�=
�=
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 861,253) − (78 × 132,637)
= −0,006187
(12 × 650) − 782
ln � =
∑ ��� − � ∑ �
= 11,0932
�
� = 65.726,669
� ′ = �� ��
� ′ = 65.726,669� −0,006187 �
� ′ = 65.726,669� −0,006187 (1) = 65.321,27 ≈ 65.321
���� =
∑��=1|��� |
=
�
2,67
12
= 22,28%
2.
Metode Kuadratis
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
t²
t³
55.775
46.583
51.009
108.655
74.095
73.288
85.789
56.958
52.868
77.089
55.013
46.827
783.948
1
4
9
16
25
36
49
64
81
100
121
144
650
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
t²y
t'
y't
1
55.775
55.775
13 50.951
16
93.167
186.333
14 59.898
81
153.027
459.081
15 66.944
256
434.620
1.738.480 16 72.091
625
370.474
1.852.369 17 75.338
1.296
439.725
2.638.350 18 76.686
2.401
600.525
4.203.673 19 76.134
4.096
455.664
3.645.312 20 73.683
6.561
475.812
4.282.308 21 69.331
10.000 770.893
7.708.925 22 63.081
14.641 605.138
6.656.513 23 54.930
20.736 561.918
6.743.016 24 44.880
60.710 5.016.736 40.170.135 222 783.948
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
Universitas Sumatera Utara
� = � � � � − � � ��
� = (78 × 783.948) − (12 × 5.016.736) = 947.112
� = � �2 � � − � � �2�
� = (650 × 783.948) − (12 × 40.170.135) = 27.524.586
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�� −��
�� −� 2
�−��
= 11.795,578
= -949,808
�
∑ �−� ∑ �−� ∑ � 2
�=
= 40.105,693
�
� ′ = � + �� + �� 2
� ′ = 40.105,693 + 11.795,578� + (−949,808)� 2
� ′ = 40.105,693 + 11.795,578(1) + (−949,808)(1)2
= 50.951,46 ≈ 50.951
���� =
∑��=1|��� |
=
�
2,03
12
= 16,89%
Metode Terpilih: Kuadratis
Universitas Sumatera Utara
Verifikasi Peramalan
y
55.775
46.583
51.009
108.655
74.095
73.288
85.789
56.958
52.868
77.089
55.013
46.827
y't
50.951
59.898
66.944
72.091
75.338
76.686
76.134
73.683
69.331
63.081
54.930
44.880
e=y-y't
4.824
-13.314
-15.935
36.564
-1.244
-3.399
9.655
-16.725
-16.463
14.009
82
1.946
|MR|
18.137,90
2.620,79
52.499,08
37.807,55
2.154,94
13.053,68
26.379,70
261,16
30.472,03
13.926,35
1.864,01
199.177,20
UCL
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
LCL
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
Permintaan 683 tahun 2016
60.000
40.000
PT. SWMS
20.000
Irawan 683
0
LCL
UCL
-20.000
-40.000
-60.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 683-SP – PT. SWMS
Irawan 683-SP
Bulan
Demand
Januari
93.060
Februari
76.257
Maret
48.974
April
117.381
Mei
88.140
Juni
110.940
Juli
109.946
Agustus
66.432
September
101.747
Oktober
61.182
November
49.231
Desember
57.885
Total
981.175
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
EKSPONENSIAL
lny
t.lny
93.060 11,441
76.257 11,242
48.974 10,799
117.381 11,673
88.140 11,387
110.940 11,617
109.946 11,608
66.432 11,104
101.747 11,530
61.182 11,022
49.231 10,804
57.885 10,966
981.175 135,193
11,441
22,484
32,397
46,693
56,933
69,700
81,254
88,831
103,772
110,216
118,847
131,595
874,164
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
y'
93.198
90.256
87.406
84.647
81.975
79.387
76.880
74.453
72.103
69.826
67.622
65.487
943.239
Universitas Sumatera Utara
�=
�=
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 874,164) − (78 × 135,193)
= −0,032079
(12 × 650) − 782
ln � =
∑ ��� − � ∑ �
= 11,474
�
� = 96.236,405
� ′ = �� ��
� ′ = 96.236,405� −0,032079 �
� ′ = 96.236,405� −0,032079 (1) = 93.198,16 ≈ 93.198
���� =
∑��=1|��� |
=
�
2,96
12
= 24,68%
2.
Metode Kuadratis
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
t²
t³
93.060
76.257
48.974
117.381
88.140
110.940
109.946
66.432
101.747
61.182
49.231
57.885
981.175
1
4
9
16
25
36
49
64
81
100
121
144
650
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
t²y
1
93.060
93.060
16
152.514
305.028
81
146.921
440.764
256
469.525
1.878.100
625
440.700
2.203.500
1.296
665.637
3.993.822
2.401
769.619
5.387.330
4.096
531.456
4.251.648
6.561
915.725
8.241.527
10.000 611.820
6.118.200
14.641 541.541
5.956.951
20.736 694.623
8.335.476
60.710 6.033.141 47.205.406
t'
y't
13 74.916
14 83.470
15 89.831
16 93.999
17 95.975
18 95.759
19 93.350
20 88.748
21 81.954
22 72.967
23 61.788
24 48.417
25 981.175
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
Universitas Sumatera Utara
� = � � � � − � � ��
� = (78 × 981.175) − (12 × 6.033.141) = 4.133.919
� = � �2 � � − � � �2�
� = (650 × 981.175) − (12 × 47.205.406) = 71.298.559
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�� −��
�� −� 2
�−��
= 11.795,578
= -1.096,254
�
∑ �−� ∑ �−� ∑ � 2
�=
= 64.170,272
�
� ′ = � + �� + �� 2
� ′ = 64.170,272 + 11.795,578� + (−1.096,254)� 2
� ′ = 64.170,272 + 11.795,578(1) + (−1.096,254)(1)2
= 74.916,28 ≈ 74.916
���� =
∑��=1|��� |
=
�
2,84
12
= 23,68%
Metode Terpilih: Kuadratis
Universitas Sumatera Utara
Verifikasi Peramalan
y
93.060
76.257
48.974
117.381
88.140
110.940
109.946
66.432
101.747
61.182
49.231
57.885
y't
74.916
83.470
89.831
93.999
95.975
95.759
93.350
88.748
81.954
72.967
61.788
48.417
e=y-y't
18.144
-7.213
-40.857
23.382
-7.835
15.181
16.596
-22.316
19.793
-11.785
-12.557
9.468
|MR|
25.356,50
33.644,24
64.239,02
31.217,22
23.016,03
1.415,04
38.911,95
42.109,31
31.578,68
771,92
22.025,84
314.285,76
UCL
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
LCL
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
Permintaan 683-SP tahun 2016
100.000
80.000
60.000
PT. SWMS
40.000
20.000
Irawan 683-SP
0
LCL
-20.000
UCL
-40.000
-60.000
-80.000
-100.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 684-S – PT. SWMS
Irawan 684-S
Bulan
Demand
Januari
39.454
Februari
37.382
Maret
73.281
April
33.181
Mei
32.200
Juni
77.775
Juli
37.679
Agustus
68.149
September
66.666
Oktober
52.078
November
91.956
Desember
45.900
Total
655.699
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
EKSPONENSIAL
lny
t.lny
39.454 10,583
37.382 10,529
73.281 11,202
33.181 10,410
32.200 10,380
77.775 11,262
37.679 10,537
68.149 11,129
66.666 11,107
52.078 10,860
91.956 11,429
45.900 10,734
655.699 130,162
10,583
21,058
33,606
41,639
51,899
67,569
73,758
89,036
99,967
108,605
125,720
128,811
852,250
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
y'
40.483
42.275
44.147
46.101
48.141
50.272
52.498
54.822
57.248
59.783
62.429
65.192
623.391
Universitas Sumatera Utara
�=
�=
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 874,164) − (78 × 135,193)
= 0,04331
(12 × 650) − 782
ln � =
∑ ��� − � ∑ �
= 10,5653
�
� = 38.767,114
� ′ = �� ��
� ′ = 38.767,114� 0,04331 �
� ′ = 38.767,114� 0,04331 (1) = 40.483,17 ≈ 40.483
���� =
∑��=1|��� |
=
�
3,41
12
= 28,43%
2.
Metode Kuadratis
t
y
1 39.454
2 37.382
3 73.281
4 33.181
5 32.200
6 77.775
7 37.679
8 68.149
9 66.666
10 52.078
11 91.956
12 45.900
78 655.699
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
t³
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
t²y
t'
y't
1
39.454
39.454
13 39.439
16
74.763
149.526
14 43.194
81
219.843
659.529
15 46.652
256
132.725
530.900
16 49.812
625
161.001
805.006
17 52.676
1.296
466.650
2.799.900 18 55.241
2.401
263.750
1.846.247 19 57.510
4.096
545.192
4.361.536 20 59.481
6.561
599.994
5.399.946 21 61.155
10.000 520.778
5.207.775 22 62.532
14.641 1.011.511 11.126.616 23 63.612
20.736 550.797
6.609.564 24 64.394
60.710 4.586.457 39.535.998 25 655.699
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
Universitas Sumatera Utara
� = � � � � − � � ��
� = (78 × 655.699) − (12 × 4.586.457) = −3.892.937
� = � �2 � � − � � �2�
� = (650 × 655.699) − (12 × 39.535.998) = −48.227.464
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�� −��
�� −� 2
�−��
= 4.201,006
= -148,645
�
∑ �−� ∑ �−� ∑ � 2
�=
= 35.386,710
�
� ′ = � + �� + �� 2
� ′ = 35.386,710 + 4.201,006� + (−148,645)� 2
� ′ = 35.386,710 + 4.201,006(1) + (−148,645)(1)2
= 39.439,07 ≈ 39.439
���� =
∑��=1|��� |
=
�
3,59
12
= 29,95%
Metode Terpilih: Eksponensial
Universitas Sumatera Utara
Verifikasi Peramalan
y
39.454
37.382
73.281
33.181
32.200
77.775
37.679
68.149
66.666
52.078
91.956
45.900
y't
e=y-y't
-1.029
-4.894
29.134
-12.919
-15.941
27.503
-14.819
13.327
9.418
-7.705
29.527
-19.293
40.483
42.275
44.147
46.101
48.141
50.272
52.498
54.822
57.248
59.783
62.429
65.192
|MR|
3.864,27
34.028,15
42.053,94
3.021,69
43.443,73
42.321,85
28.146,64
3.909,73
17.122,40
37.231,42
48.819,22
303.963,04
UCL
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
LCL
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
Permintaan 684-S tahun 2016
100.000
80.000
60.000
20.000
Irawan 684-S
0
Desember
November
Oktober
Agustus
Juli
Juni
Mei
April
September
-60.000
Maret
-40.000
Februari
-20.000
LCL
Januari
PT. SWMS
40.000
UCL
-80.000
-100.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 9001 – PT. BWP
Irawan 9001
Bulan
Januari
Februari
Maret
April
Mei
Juni
Juli
Agustus
Demand
3.941
3.606
4.799
6.184
6.004
4.240
3.636
3.712
September
3.899
Oktober
November
3.221
2.600
Desember
4.522
Total
50.363
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Siklis
2.
Metode Eksponensial
t
y
EKSPONENSIAL
lny
t.lny
t²
y'
1
8,279
4.772
1 3.941 8,279
4
4.638
2 3.606 8,190 16,381
9
4.509
3 4.799 8,476 25,429
4.382
4 6.184 8,730 34,919 16
4.259
5 6.004 8,700 43,501 25
4.140
6 4.240 8,352 50,114 36
4.024
7 3.636 8,199 57,390 49
3.911
8 3.712 8,219 65,755 64
3.802
9 3.899 8,268 74,416 81
3.695
10 3.221 8,077 80,773 100
3.592
11 2.600 7,863 86,495 121
3.491
12 4.522 8,417 101,001 144
78 50.363 99,771 644,452 650 1.761.609
Universitas Sumatera Utara
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 644,452) − (78 × 99,771)
�=
= −0,0284
(12 × 650) − 782
∑ ��� − � ∑ �
ln � =
= 8,4989
�
� = 4.909,609
� ′ = �� ��
� ′ = 4.909,609� −0,0284�
� ′ = 4.909,609� −0,0284(1) = 4.772,09 ≈ 4.772
�=
���� =
∑��=1|��� |
=
�
2,11
12
= 17,55%
4.
Metode Siklis
Jumlah periode adalah:
�=
12
=6
2
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
12
3941
3606
4799
6184
6004
4240
3636
3712
3899
3221
2600
4522
0,866
0,866
0,000
-0,866
-0,866
0,000
0,866
0,866
0,000
-0,866
-0,866
0,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
78
50362,95
0
0
0
2
3
4
5
6
7
8
9
10
11
∑y
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
3412,60
3122,62
0,00
-5355,52
-5199,38
0,00
3148,78
3214,59
0,00
-2788,95
-2251,43
0,00
1970,325
-1802,9
-4799,1
-3092,1
3001,95
4240
1818
-1856
-3899
-1610,25
1299,9
4522
6
6
-2696,6807
-207,175
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
Universitas Sumatera Utara
50.363
= 12 a + b (0) + c (0)
a
=
a
= 4.196,912
2πt
50.363
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-2.696,68
= = 4.196,912 (0) + b (6) + c (0)
b
=
b
= -449,446
n
2πt
−2.696,68
6
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
-207,175
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= -34,529
n
y’
y’
y’
= 4.196,912 (0) + c (6) + (-449,446) (0)
−207 ,175
6
2πt
2πt
n
n
= a + b sin � �+ c� �
2πt
2πt
n
n
= 4.196,912 – 449,446 sin � � - -34,529 cos � �
= 4.196,912 – 449,446 sin (0,866) - -34,529 co�(−0,500) = 3.790,43
���� =
=
∑��=1 |��� |
2,15
�
12
= 17,96%
Metode Terpilih: Eksponensial
Universitas Sumatera Utara
Verifikasi Peramalan
y
3.941
3.606
4.799
6.184
6.004
4.240
3.636
3.712
3.899
3.221
2.600
4.522
y't
e=y-y't
|MR|
UCL
LCL
4.772
-831
2.133,62 -2.133,62
4.638 -1.033
201,19 2.133,62 -2.133,62
4.509
291
1.323,22 2.133,62 -2.133,62
4.382 1.802 1.511,38 2.133,62 -2.133,62
4.259 1.744
57,56
2.133,62 -2.133,62
4.140
100
1.644,59 2.133,62 -2.133,62
4.024
-388
488,03 2.133,62 -2.133,62
3.911
-199
188,72 2.133,62 -2.133,62
3.802
97
296,56 2.133,62 -2.133,62
3.695
-475
572,01 2.133,62 -2.133,62
3.592
-992
517,19 2.133,62 -2.133,62
3.491 1.031 2.022,81 2.133,62 -2.133,62
8.823,26
Permintaan Irawan 9001 tahun 2016
3.000
1.000
Irawan 9001
UCL
Desember
November
Oktober
September
Juli
Juni
Mei
April
Agustus
-2.000
Maret
-1.000
Februari
0
Januari
PT. BWP
2.000
LCL
-3.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 682 – PT. BWP
Irawan 682
Bulan
Demand
10.846
Januari
Februari
14.900
Maret
17.104
April
29.486
Mei
22.297
Juni
20.702
Juli
15.656
Agustus
24.945
September
28.110
Oktober
16.041
November
20.586
Desember
25.255
Total
245.927
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
EKSPONENSIAL
lny
t.lny
t²
1
y'
10.846
9,292
9,292
15.779
4
14.900
9,609
19,218
16.431
9
17.109
17.104
9,747
29,241
29.486 10,292 41,167 16 17.816
22.297 10,012 50,061 25 18.552
20.702
9,938
59,628 36 19.318
15.656
9,659
67,610 49 20.116
24.945 10,124 80,995 64 20.947
28.110 10,244 92,195 81 21.812
16.041
9,683
96,829 100 22.713
20.586
9,932 109,256 121 23.651
25.255 10,137 121,641 144 24.628
245.927 118,668 777,133 650 238.874
Universitas Sumatera Utara
�=
�=
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 777,133) − (78 × 118,668)
= 0,04047
(12 × 650) − 782
ln � =
∑ ��� − � ∑ �
= 9,625
�
� = 15.153,002
� ′ = �� ��
� ′ = 15.153,002� 0,04047 �
� ′ = 15.153,002� 0,04047 (1) = 15.778,90 ≈ 15.779
���� =
∑��=1|��� |
=
�
2,45
12
= 20,39%
2.
Metode Kuadratis
t
y
1 10.846
2 14.900
3 17.104
4 29.486
5 22.297
6 20.702
7 15.656
8 24.945
9 28.110
10 16.041
11 20.586
12 25.255
78 245.927
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
t³
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
t²y
t'
y't
1
10.846
10.846
13 13.404
16
29.800
59.600
14 15.885
81
51.312
153.936
15 18.008
256
117.944
471.776
16 19.774
625
111.484
557.419
17 21.182
1.296
124.211
745.263
18 22.233
2.401
109.589
767.120
19 22.926
4.096
199.560
1.596.480 20 23.262
6.561
252.990
2.276.910 21 23.240
10.000 160.408
1.604.075 22 22.860
14.641 226.446
2.490.906 23 22.123
20.736 303.060
3.636.720 24 21.029
60.710 1.697.648 14.371.050 222 245.927
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
Universitas Sumatera Utara
� = � � � � − � � ��
� = (78 × 245.927) − (12 × 1.697.648) = −1.189.493
� = � �2 � � − � � �2�
� = (650 × 245.927) − (12 × 14.371.050) = −12.600.216
� = � � � �
Universitas Sumatera Utara
LAMPIRAN LOSS OPPORTUNITY COST PT. CENTRAL PROTEINAPRIMA TAHUN 2015
Loss Opportunity Cost Produk Irawan 9001 Tahun 2015
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
2.530
Februari
Permintaan (Kg)
PT.
SWMS
5.817
PT.
BWP
3.941
CV.
WS
1.689
Total
Selisih
(Kg)
17.200
PT.
JWL
7.318
18.765
965
965
24.850
6.720
4.753
3.606
1.311
16.390
9.425
Maret
9.425
23.330
12.704
9.034
4.799
1.694
28.230
4.525
April
4.525
27.590
11.806
7.028
6.184
3.092
28.110
4.005
Mei
4.005
31.120
12.294
8.577
6.004
1.715
28.590
6.535
Juni
6.535
31.970
10.388
4.028
4.240
2.544
21.200
17.305
Juli
17.305
19.090
8.484
5.656
3.636
2.424
20.200
16.195
Agustus
16.195
7.080
9.280
7.888
3.712
2.320
23.200
75
September
75
25.020
14.204
7.520
3.899
2.228
27.850
-2.755
(Rp28.927.500)
Oktober
-
22.180
9.232
6.012
3.221
3.006
21.470
-2.045
(Rp21.472.500)
November
-
24.110
8.914
5.014
2.600
2.043
18.570
3.495
4.760
4.522
1.904
9.955
70.268
46.422
24.281
23.800
276.375
3.495
12.614
Desember
30.260
60.255
266.600
116.639
Total
Sumber: PT. Central Proteina Prima
Opportunity
Loss Cost
(Rp50.400.000)
I-I
Universitas Sumatera Utara
Loss Opportunity Cost Produk Irawan 682 Tahun 2015
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
970
Februari
Permintaan (Kg)
PT.
SWMS
10.846
PT.
BWP
10.846
CV.
WS
5.916
Total
Selisih
(Kg)
79.600
PT.
JWL
21.692
49.300
31.270
31.270
64.980
22.648
14.304
14.900
7.748
59.600
36.650
Maret
36.650
71.980
50.243
32.070
17.104
7.483
106.900
1.730
April
1.730
158.400
46.152
35.896
29.486
16.666
128.200
31.930
Mei
31.930
82.350
47.779
20.173
22.297
15.926
106.175
8.105
Juni
8.105
125.250
63.323
31.662
20.702
6.089
121.775
11.580
Juli
11.580
107.330
46.097
15.656
15.656
9.567
86.975
31.935
Agustus
31.935
101.700
53.632
31.181
24.945
14.967
124.725
8.910
September
8.910
124.430
49.193
26.939
28.110
12.884
117.125
16.215
Oktober
16.215
66.680
41.368
14.352
16.041
12.664
84.425
-1.530
November
-
95.900
30.879
26.590
20.586
7.720
85.775
10.125
Desember
10.125
119.830
60.612
30.306
25.255
10.102
126.275
3.680
189.420 1.198.430 533.617
Total
Sumber: PT. Central Proteina Prima
289.975
245.927
127.732
1.197.250
Opportunity
Loss Cost
Rp (14.535.000)
Rp (14.535.000)
Universitas Sumatera Utara
Loss Opportunity Cost Produk Irawan 683 Tahun 2015
Permintaan (Kg)
PT.
PT.
CV.
SWMS
BWP
WS
55.775
48.500
36.375
Total
Selisih
(Kg)
291.100
PT.
JWL
101.850
242.500
50.720
50.720
191.000
110.329
46.583
56.390
31.873
245.175
-3.455
Maret
-
256.580
119.021
51.009
43.722
29.148
242.900
13.680
April
13.680
338.030
143.705
108.655
66.595
31.545
350.500
1.210
Mei
1.210
275.430
115.259
74.095
57.629
27.443
274.425
2.215
Juni
2.215
288.080
124.025
73.288
53.556
31.006
281.875
8.420
Juli
8.420
351.430
115.372
85.789
65.082
29.583
295.825
64.025
Agustus
64.025
238.530
142.395
56.958
49.191
10.356
258.900
43.655
September
43.655
345.080
191.647
52.868
66.085
19.826
330.425
58.310
Oktober
58.310
210.280
122.280
77.089
26.583
39.874
265.825
2.765
November
2.765
240.700
105.624
55.013
30.807
28.607
220.050
23.415
Desember
23.415
243.780
145.989
46.827
49.581
33.054
275.450
-8.255
783.948
613.721
348.688
3.283.850
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
2.120
Februari
270.535 3.270.020 1.537.494
Total
Sumber: PT. Central Proteina Prima
Opportunity
Loss Cost
Rp (31.095.000)
Rp (74.295.000)
Rp (105.390.000)
Universitas Sumatera Utara
Loss Opportunity Cost Produk Irawan 683-SP Tahun 2015
Total
Selisih
(Kg)
273.450
PT.
JWL
114.774
Permintaan (Kg)
PT.
PT.
CV.
SWMS
BWP
WS
93.060
68.244
34.122
310.200
8.750
8.750
213.200
68.013
76.257
43.281
18.549
206.100
15.850
Maret
15.850
204.200
65.861
48.974
33.775
20.265
168.875
51.175
April
51.175
272.100
114.028
117.381
77.136
26.830
335.375
-12.100
Mei
-
310.400
114.582
88.140
67.574
23.504
293.800
16.600
Juni
16.600
398.600
126.242
110.940
95.638
49.732
382.550
32.650
Juli
32.650
259.080
92.117
109.946
68.345
26.744
297.150
-5.420
Agustus
-
265.400
78.888
66.432
39.444
22.836
207.600
57.800
September
57.800
253.580
101.747
101.747
77.081
27.749
308.325
3.055
Oktober
3.055
257.600
104.519
61.182
61.182
28.042
254.925
5.730
November
5.730
229.030
77.634
49.231
37.870
24.616
189.350
45.410
Desember
45.410
254.930
88.086
57.885
83.053
22.651
251.675
48.665
Total
282.520
3.191.570
1.146.490
981.175
752.622
325.638
3.205.925
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
45.500
Februari
Opportunity
Loss Cost
Rp (121.000.000)
Rp (54.200.000)
Rp
(175.200.000)
Sumber: PT. Central Proteina Prima
Universitas Sumatera Utara
Loss Opportunity Cost Produk Irawan 684-S Tahun 2015
Permintaan (Kg)
PT.
JWL
PT.
SWMS
PT.
BWP
CV.
WS
Total
Selisih
(Kg)
181.150
80.786
39.454
39.454
28.181
187.875
3.075
3.075
172.530
58.149
37.382
38.766
4.154
138.450
37.155
Maret
37.155
299.600
124.014
73.281
50.733
33.822
281.850
54.905
April
54.905
243.480
76.981
33.181
15.927
6.636
132.725
165.660
Mei
165.660
276.580
96.601
32.200
28.811
11.863
169.475
272.765
Juni
272.765
204.450
137.403
77.775
38.888
5.185
259.250
217.965
Juli
217.965
243.100
113.036
37.679
35.585
23.026
209.325
251.740
Agustus
251.740
236.550
142.224
68.149
56.297
29.630
296.300
191.990
September
191.990
331.430
111.110
66.666
63.888
36.111
277.775
245.645
Oktober
245.645
291.750
115.477
52.078
38.492
20.378
226.425
310.970
November
310.970
259.480
145.007
91.956
67.198
49.515
353.675
216.775
Desember
216.775
141.600
68.058
45.900
26.907
17.410
158.275
200.100
1.268.844
655.699
500.946
265.911
2.691.400
Bulan
Stok
(Kg)
Produksi
(Kg)
Januari
9.800
Februari
1.978.445 2.881.700
Total
Sumber: PT. Central Proteina Prima
Opportunity
Loss Cost
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 682 – PT. JWL
Irawan 682
Bulan
Demand
Januari
21.692
Februari
22.648
Maret
50.243
April
46.152
Mei
47.779
Juni
63.323
Juli
46.097
Agustus
53.632
September
49.193
Oktober
41.368
November
30.879
Desember
60.612
Total
533.617
Metode Peramalan Terpilih:
•
Metode Kuadratis
•
Metode Siklis
1.
t
1
2
3
4
5
6
7
8
9
10
11
12
78
Metode Kuadratis
y
21.692
22.648
50.243
46.152
47.779
63.323
46.097
53.632
49.193
41.368
30.879
60.612
533.617
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
t³
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
1
21.692
16
45.296
81
150.729
256
184.608
625
238.894
1.296
379.938
2.401
322.677
4.096
429.054
6.561
442.733
10.000
413.683
14.641
339.669
20.736
727.344
60.710
3.696.316
t²y
21.692
90.592
452.187
738.432
1.194.469
2.279.628
2.258.741
3.432.432
3.984.593
4.136.825
3.736.359
8.728.128
31.054.077
t'
13
14
15
16
17
18
19
20
21
22
23
24
222
y't
24.557
32.232
38.690
43.932
47.957
50.766
52.359
52.736
51.897
49.841
46.569
42.081
533.617
Universitas Sumatera Utara
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
� = � � � � − � � ��
� = (78 × 533.617) − (12 × 3.696.316) = −2.733.666
� = � �2 � � − � � �2�
� = (650 × 533.617) − (12 × 31.054.077) = −25.797.874
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�=
�� − ��
= 9.498,714
�� − � 2
� − ��
= −608,1283
�
∑ � − � ∑ � − � ∑ �2
= 15.666,727
�
� ′ = � + �� + �� 2
� ′ = 15.666,727 + 9.498,714� + (−608,1283)� 2
� ′ = 15.666,727 + 9.498,714(1) + (−608,1283)(1)2
= 24.557,31 ≈ 24.557
���� =
∑��=1|��� |
=
�
2,26
12
= 18,85%
2.
Metode Siklis
Jumlah periode adalah:
�=
12
=4
3
Universitas Sumatera Utara
SIKLIS
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
21692
1,000
0,000
Sin
(2πt/n)*Cos
(2πt/n)
0,000
2
22648
0,000
-1,000
3
50243
-1,000
4
46152
0,000
5
47778,75
1,000
0,000
0,000
6
63323
0,000
-1,000
0,000
7
46096,75
-1,000
0,000
0,000
8
53631,75
0,000
1,000
9
49192,5
1,000
10
41368,25
11
Sin^2
(2πt/n)
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
1,000
0,000
21692,00
0
0,000
0,000
1,000
0,00
-22648
0,000
0,000
1,000
0,000
-50243,00
0
1,000
0,000
0,000
1,000
0,00
46152
1,000
0,000
47778,75
0
0,000
1,000
0,00
-63323
1,000
0,000
-46096,75
0
0,000
0,000
1,000
0,00
53631,75
0,000
0,000
1,000
0,000
49192,50
0
0,000
-1,000
0,000
0,000
1,000
0,00
-41368,25
30879
-1,000
0,000
0,000
1,000
0,000
-30879,00
0
12
60612
0,000
1,000
0,000
0,000
1,000
0,00
60612
78
533617
0
0
0
6
6
-8555,5
33056,5
2πt
2πt
n
n
= n a + b ∑ sin� � + c ∑ cos� �
∑y
533.617
= 4 a + b (0) + c (0)
a
=
a
= 44.468,083
2πt
533.617
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-8555,5
= 44.468,083 (0) + b (0) + c (0)
b
=
b
= -1425,916
n
2πt
−8555 ,5
6
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
33.056,5
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= 5509,416
n
= 44.468,083 (0) + c (6) + -1425,916 (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
33.056 ,5
6
2πt
2πt
n
n
y’= 44.468,083 – 1425,916 sin � � +5509,416 cos � �
y’= 44.468,083 – 1425,916 sin (0,866) + 5509,416 cos (0,000) = 43042,167
Universitas Sumatera Utara
���� =
=
∑��=1 |��� |
3,28
�
12
= 27,29%
Metode Terpilih: Kuadratis
Verifikasi Peramalan
y
y't
e=y-y't
|MR|
UCL
LCL
21.692
24.557
-2.865
-
54.694,06
-54.694,06
22.648
32.232
-9.584
6.718,33
54.694,06
-54.694,06
50.243
38.690
11.553
21.136,93
54.694,06
-54.694,06
46.152
43.932
2.220
9.332,82
54.694,06
-54.694,06
47.779
47.957
-178
2.398,81
54.694,06
-54.694,06
63.323
50.766
12.557
12.734,95
54.694,06
-54.694,06
46.097
52.359
-6.263
18.819,30
54.694,06
-54.694,06
53.632
52.736
896
7.158,21
54.694,06
-54.694,06
49.193
51.897
-2.704
3.599,78
54.694,06
-54.694,06
41.368
49.841
-8.473
5.768,53
54.694,06
-54.694,06
30.879
46.569
-15.690
7.217,27
54.694,06
-54.694,06
60.612
42.081
18.531
34.221,24
54.694,06
-54.694,06
129.106,15
Peramalan Irawan 682 tahun
2016
40.000
PT. JWL
20.000
Irawan 682
0
UCL
LCL
-20.000
-40.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 683 – PT. JWL
Irawan 682
Bulan
Demand
Januari
101.850
Februari
110.329
Maret
119.021
April
143.705
Mei
115.259
Juni
124.025
Juli
115.372
Agustus
142.395
September
191.647
Oktober
122.280
November
105.624
Desember
145.989
Total
1.537.494
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
EKSPONENSIAL
t
y
lny
t.lny
t²
y'
1
101.850
11,53
11,53
1
2
110.329
11,61
23,22
4
3
119.021
11,69
35,06
9
4
143.705
11,88
47,50
16
5
115.259
11,65
58,27
25
6
124.025
11,73
70,37
36
7
115.372
11,66
81,59
49
8
142.395
11,87
94,93
64
9
191.647
12,16
109,47
81
10
122.280
11,71
117,14
100
11
105.624
11,57
127,24
121
12
145.989
11,89
142,70
144
78
1.537.494
140,95
919,03
650
112.965
115.263
117.607
119.999
122.439
124.930
127.471
130.063
132.709
135.408
138.162
140.972
1.517.987
Universitas Sumatera Utara
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 919,03) − (78 × 140,95)
�=
= −0,0200135
(12 × 650) − 782
∑ ��� − � ∑ �
ln � =
= 11,614
�
� = 110.713,2
� ′ = �� ��
� ′ = 110.713,2� −0,0200135 �
� ′ = 110.713,2� −0,0200135 (1) = 112.964,95 ≈ 112.965
�=
���� =
∑��=1|��� |
=
�
1,357
12
= 11,24%
2.
t
1
2
3
4
5
6
7
8
9
10
11
12
78
Metode Kuadratis
y
101.850
110.329
119.021
143.705
115.259
124.025
115.372
142.395
191.647
122.280
105.624
145.989
1.537.494
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
t³
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
1
101.850
16
220.658
81
357.063
256
574.820
625
576.293
1.296
744.150
2.401
807.602
4.096
1.139.160
6.561
1.724.819
10.000
1.222.795
14.641
1.161.864
20.736
1.751.862
60.710 10.382.935
t²y
101.850
441.315
1.071.189
2.299.280
2.881.463
4.464.900
5.653.216
9.113.280
15.523.367
12.227.950
12.780.504
21.022.344
87.580.657
t'
13
14
15
16
17
18
19
20
21
22
23
24
222
y't
102.712
111.130
118.408
124.547
129.548
133.409
136.130
137.713
138.157
137.461
135.626
132.653
1.537.494
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
� = � � � � − � � ��
� = (78 × 1.537.494) − (12 × 10.382.935) = −4.670.724
� = � �2 � � − � � �2�
� = (650 × 1.537.494) − (12 × 87.580.657) = −51.597.106
Universitas Sumatera Utara
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�� −��
�� −� 2
�−��
= 10126,336
= -569,574
�
∑ �−� ∑ �−� ∑ � 2
�=
= 93155,227
�
′
2
� = � + �� + ��
� ′ = 93155,227 + 9.498,714� + (−608,1283)� 2
� ′ = 93155,227 + 9.498,714(1) + (−608,1283)(1)2
= 102.711,99 ≈102.712
���� =
∑��=1|��� |
=
�
1,35
12
= 11,21%
Metode Terpilih: Kuadratis
Verifikasi Peramalan
y
101.850
110.329
119.021
143.705
115.259
124.025
115.372
142.395
191.647
y't
102.712
111.130
118.408
124.547
129.548
133.409
136.130
137.713
138.157
e=y-y't
-862
-801
613
19.158
-14.289
-9.384
-20.759
4.682
53.490
|MR|
61,14
1.413,79
18.544,69
33.446,67
4.905,48
11.375,12
25.440,53
48.807,93
UCL
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
65.490,63
LCL
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
-65.490,63
Universitas Sumatera Utara
y
y't
e=y-y't
122.280 137.461 -15.182
105.624 135.626 -30.002
145.989 132.653 13.336
|MR|
UCL
LCL
68.671,42 65.490,63 -65.490,63
14.820,77 65.490,63 -65.490,63
43.338,38 65.490,63 -65.490,63
270.825,91
Peramalan Irawan 683 tahun 2016
80.000
60.000
PT. JWL
40.000
20.000
Irawan 683
0
UCL
-20.000
LCL
-40.000
-60.000
-80.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 683-SP – PT. JWL
Irawan 682
Bulan
Demand
Januari
114.774
Februari
68.013
Maret
65.861
April
114.028
Mei
114.582
Juni
126.242
Juli
92.117
Agustus
78.888
September
101.747
Oktober
104.519
November
77.634
Desember
88.086
Total
1.146.490
Metode Peramalan Terpilih:
•
Metode Kuadratis
•
Metode Siklis
1.
Metode Kuadratis
t
y
t²
t³
1
2
3
4
5
6
7
8
9
10
11
12
78
114.774
68.013
65.861
114.028
114.582
126.242
92.117
78.888
101.747
104.519
77.634
88.086
1.146.490
1
4
9
16
25
36
49
64
81
100
121
144
650
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
1
16
81
256
625
1.296
2.401
4.096
6.561
10.000
14.641
20.736
60.710
114.774
136.026
197.584
456.110
572.910
757.449
644.816
631.104
915.725
1.045.193
853.969
1.057.035
7.382.694
t²y
t'
y't
114.774
272.052
592.751
1.824.440
2.864.550
4.544.694
4.513.709
5.048.832
8.241.527
10.451.925
9.393.654
12.684.420
60.547.328
13
14
15
16
17
18
19
20
21
22
23
24
222
89.274
93.664
97.079
99.519
100.984
101.473
100.987
99.526
97.089
93.677
89.290
83.928
42.286
Universitas Sumatera Utara
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
� = � � � � − � � ��
� = (78 × 1.146.490) − (12 × 7.382.694) = 833.898
� = � �2 � � − � � �2�
� = (650 × 1.146.490) − (12 × 60.547.328) = 18.650.570
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�=
�� − ��
= 5.853,246
�� − � 2
� − ��
= −487,630
�
∑ � − � ∑ � − � ∑ �2
= 83.908,066
�
� ′ = � + �� + �� 2
� ′ = 83.908,066 + 5.853,246 + (−487,630)� 2
� ′ = 83.908,066 + 5.853,246(1) + (−487,630)(1)2
= 89.273,68 ≈ 89.274
���� =
∑��=1|��� |
=
�
2,22
12
= 18,50%
2.
Metode Siklis
Jumlah periode adalah:
�=
12
=6
2
Universitas Sumatera Utara
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
0,433
0,750
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,250
99394,28
57387
0,750
0,250
58899,26
-34006,5
0,000
0,000
1,000
0,00
-65861,25
-0,500
0,433
0,750
0,250
-98747,82
-57013,75
-0,866
0,500
-0,433
0,750
0,250
-99228,01
57291
0,000
1,000
0,000
0,000
1,000
0,00
126241,5
92116,5
0,866
0,500
0,433
0,750
0,250
79772,89
46058,25
8
78888
0,866
-0,500
-0,433
0,750
0,250
68317,01
-39444
9
101747,25
0,000
-1,000
0,000
0,000
1,000
0,00
-101747,25
10
104519,25
-0,866
-0,500
0,433
0,750
0,250
-90513,67
-52259,625
11
77633,5
-0,866
0,500
-0,433
0,750
0,250
-67230,61
38816,75
12
88086,25
0,000
1,000
0,000
0,000
1,000
0,00
88086,25
78
1.146.490
0
0
0
6
6
-49.336,665
63.548,375
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
114774
0,866
0,500
2
68013
0,866
-0,500
-0,433
3
65861,25
0,000
-1,000
4
114027,5
-0,866
5
114582
6
126241,5
7
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
∑y
1.146.490
= 12 a + b (0) + c (0)
a
=
a
= 95.540,833
2πt
1.146 .490
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-49.336,665
= 95.540,833 (0) + b (6) + c (0)
b
=
b
= -8.222,778
n
2πt
−49.336 ,665
6
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
63.548,375
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= 10.591,395
n
= 95.540,833 (0) + c (6) + -8.222,778 (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
63.548 ,375
6
2πt
2πt
n
n
y’= 95.540,833 – 8.222,778 sin � � +5509,416 cos � �
y’= 95.540,833 – 8.222,778 sin (0,866) + 5509,416 cos (0,500) = 93.715,605
Universitas Sumatera Utara
���� =
=
∑��=1 |��� |
1,96
�
12
= 16,32%
Metode Terpilih: Siklis
Verifikasi Peramalan
y
y't
e=y-y't
|MR|
UCL
LCL
114.774
68.013
65.861
114.028
114.582
126.242
92.117
78.888
101.747
104.519
77.634
88.086
93.716
83.124
84.949
97.366
107.957
106.132
93.716
83.124
84.949
97.366
107.957
106.132
21.058
-15.111
-19.088
16.661
6.625
20.109
-1.599
-4.236
16.798
7.153
-30.324
-18.046
36.169,60
3.976,98
35.749,63
10.036,90
13.484,73
21.708,38
2.637,10
21.034,02
9.644,62
37.477,15
12.277,98
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
-49.378,57
204.197,08
Peramalan Irawan 683-SP tahun
2016
100.000
PT. JWL
50.000
0
-50.000
Irawan 683-SP
UCL
LCL
-100.000
PERAMALAN PRODUK IRAWAN 684-S – PT. JWL
Universitas Sumatera Utara
Irawan 682
Bulan
Demand
Januari
80.786
Februari
58.149
Maret
124.014
April
76.981
Mei
96.601
Juni
137.403
Juli
113.036
Agustus
142.224
September
111.110
Oktober
115.477
November
145.007
Desember
68.058
Total
1.268.844
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Siklis
1.
Metode Eksponensial
EKSPONENSIAL
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
lny
80.786
11,2996
58.149
10,9708
124.014
11,7281
76.981
11,2513
96.601
11,4783
137.403
11,8307
113.036
11,6355
142.224
11,8652
111.110
11,6183
115.477
11,6568
145.007
11,8845
68.058
11,1281
1.268.844
138,3472
� ∑ �. ��� − ∑ � ∑ ���
�=
� ∑ � 2 − (∑ �)2
t.lny
t²
y'
11,2996
21,9415
35,1844
45,0052
57,3917
70,9840
81,4482
94,9213
104,5645
116,5682
130,7299
133,5374
903,5760
1
86.060
88.699
91.419
94.223
97.112
100.090
103.160
106.323
109.584
112.944
116.408
119.978
1.226.000
4
9
16
25
36
49
64
81
100
121
144
650
Universitas Sumatera Utara
(12 × 903,57) − (78 × 138,34)
= −0,030206
(12 × 650) − 782
�=
ln � =
∑ ��� − � ∑ �
= 11,33259
�
� = 83.499,2
� ′ = �� ��
� ′ = 83.499,2� −0,0302065 �
� ′ = 83.499,2� −0,0302065 (1) = 86.059,85 ≈ 86.060
���� =
∑��=1|��� |
=
�
2,69
12
= 22,42%
2.
Metode Siklis
Jumlah periode adalah:
�=
12
=4
3
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
0,000
1,000
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,000
80786,25
0
0,000
1,000
0,00
-58149
0,000
1,000
0,000
-124014,00
0
1,000
0,000
0,000
1,000
0,00
76980,5
0,000
0,000
1,000
0,000
96600,75
0
0,000
-1,000
0,000
0,000
1,000
0,00
-137402,5
113036
-1,000
0,000
0,000
1,000
0,000
-113035,50
0
8
142224
0,000
1,000
0,000
0,000
1,000
0,00
142224
9
111110
1,000
0,000
0,000
1,000
0,000
111110,00
0
10
115477
0,000
-1,000
0,000
0,000
1,000
0,00
-115476,75
11
145007
-1,000
0,000
0,000
1,000
0,000
-145006,75
0
12
68058
0,000
1,000
0,000
0,000
1,000
0,00
68058,25
78
1.268.844
0
0
0
6
6
-93559,25
-23765,5
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
80786
1,000
0,000
2
58149
0,000
-1,000
0,000
3
124014
-1,000
0,000
4
76981
0,000
5
96601
1,000
6
137403
7
Universitas Sumatera Utara
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
∑y
1.268.844
= 12 a + b (0) + c (0)
a
=
a
= 105.737,02
2πt
1.268 .844
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-48.237,499
= 95.540,833 (0) + b (4) + c (0)
b
=
b
= -23.389,81
n
2πt
−93.559,25
4
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
26.455
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= -5.941,375
n
= 95.540,833 (0) + c (4) + -8.222,778 (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
−23.765,5
4
2πt
2πt
n
n
y’= 105.737,02 – 23.389,81 sin � � - 5.941,375 cos � �
y’= 105.737,02 – 23.389,81 sin (0,866) - 5.941,375 co�(−0,500) = 82.347,208
���� =
=
∑��=1 |��� |
2,92
�
12
= 24,34%
Metode Terpilih: Eksponensial
Universitas Sumatera Utara
Verifikasi Peramalan
y
80.786
58.149
124.014
76.981
96.601
137.403
113.036
142.224
111.110
115.477
145.007
68.058
y't
86.060
88.699
91.419
94.223
97.112
100.090
103.160
106.323
109.584
112.944
116.408
119.978
e=y-y't
-5.274
-30.550
32.595
-17.242
-511
37.312
9.876
35.901
1.526
2.532
28.599
-51.920
|MR|
25.276,42
63.144,89
49.837,02
16.730,75
37.823,64
27.436,44
26.024,93
34.374,58
1.006,18
26.066,37
80.518,35
388.239,58
UCL
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
93.883,39
LCL
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
-93.883,39
Peramalan Irawan 684-S tahun 2016
150.000
100.000
Irawan 684-S
LCL
Desember
November
Oktober
Agustus
Juli
Juni
Mei
April
September
-100.000
Maret
-50.000
Februari
0
Januari
PT. JWL
50.000
UCL
-150.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 9001 – PT. SWMS
Irawan 9001
Bulan
Demand
5.817
Januari
4.753
Februari
9.034
Maret
7.028
April
8.577
Mei
4.028
Juni
5.656
Juli
7.888
Agustus
7.520
September
Oktober
November
Desember
6.012
5.014
4.760
Total
76085
Metode Peramalan Terpilih:
•
Metode Kuadratis
•
Metode Siklis
1.
Metode Kuadratis
KUADRATIS
ty
t
y
t²
t³
t⁴
1
2
3
4
5
6
7
8
9
10
11
12
78
5.817
4.753
9.034
7.028
8.577
4.028
5.656
7.888
7.520
6.012
5.014
4.760
76.085
1
4
9
16
25
36
49
64
81
100
121
144
650
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
1
16
81
256
625
1.296
2.401
4.096
6.561
10.000
14.641
20.736
60.710
5.817
9.506
27.101
28.110
42.885
24.168
39.592
63.104
67.676
60.116
55.153
57.120
480.348
t²y
t'
y't
5.817
19.012
81.302
112.440
214.425
145.008
277.144
504.832
609.080
601.160
606.682
685.440
3.862.342
13
14
15
16
17
18
19
20
21
22
23
24
222
5.867
6.324
6.670
6.904
7.027
7.039
6.940
6.729
6.407
5.974
5.430
4.774
76.085
Universitas Sumatera Utara
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
� = � � � � − � � ��
� = (78 × 76.085) − (12 × 480.348) = 170.487
� = � �2 � � − � � �2�
� = (650 × 76.085) − (12 × 3.862.342) = 3.107.369
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�=
�� − ��
= 623,8973
�� − � 2
� − ��
= −55,6345
�
∑ � − � ∑ � − � ∑ �2
= 8.298,648
�
� ′ = � + �� + �� 2
� ′ = 8.298,648 + 623,8973� + (−55,6345)� 2
� ′ = 8.298,648 + 623,8973(1) + (−55,6345)(1)2
= 5.866,91 ≈ 5.867
���� =
∑��=1|��� |
=
�
2,16
12
= 18,00%
2.
Metode Siklis
Jumlah periode adalah:
�=
12
=6
2
Universitas Sumatera Utara
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
12
5.817
4.753
9.034
7.028
8.577
4.028
5.656
7.888
7.520
6.012
5.014
4.760
0,866
0,866
0,000
-0,866
-0,866
0,000
0,866
0,866
0,000
-0,866
-0,866
0,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
78
76085
0
0
0
2
3
4
5
6
7
8
9
10
11
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
5037,65
4116,18
0,00
-6085,82
-7427,68
0,00
4898,10
6831,01
0,00
-5206,05
-4342,04
0,00
2908,575
-2376,55
-9033,6
-3513,75
4288,5
4028
2828
-3944
-7519,5
-3005,8
2506,95
4760
6
6
-2178,6395
-8073,175
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
∑y
76.085
= 12 a + b (0) + c (0)
a
=
a
= 6.340,445
2πt
76.085
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-2.178,6395
= 6.340,445 (0) + b (6) + c (0)
b
=
b
= -363,106
n
2πt
−2.178,639
6
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
-8.073,175
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= -1.345,529
n
= 6.340,445 (0) + c (6) + -363,106 (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
−8.073,175
6
2πt
2πt
n
n
y’= 6.340,445 – 363,106 sin � � – 1.345,529 cos � �
y’= 6.340,445 – 363,106 sin (0,866) – 1.345,529 cos (0,500) = 5.353
Universitas Sumatera Utara
���� =
=
∑��=1 |��� |
1,91
�
12
= 15,93%
Metode Terpilih: Siklis
Verifikasi Peramalan
y
y't
e=y-y't
|MR|
UCL
LCL
5.817
4.753
9.034
7.028
8.577
4.028
5.656
7.888
7.520
6.012
5.014
4.760
5.353
6.699
7.686
7.328
5.982
4.995
5.353
6.699
7.686
7.328
5.982
4.995
464
-1.946
1.348
-300
2.595
-967
303
1.189
-166
-1.316
-968
-235
2.409,58
3.293,29
1.647,79
2.895,03
3.561,79
1.269,69
886,47
1.355,71
1.149,59
347,83
733,31
19.550,07
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
-4.727,56
Permintaan Irawan 9001 tahun 2016
6.000
2.000
Irawan 9001
LCL
Desember
November
Oktober
September
Juli
Juni
Mei
April
Agustus
-4.000
Maret
-2.000
Februari
0
Januari
PT. SWMS
4.000
UCL
-6.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 682 – PT. SWMS
Irawan 682
Bulan
Demand
Januari
10.846
Februari
14.304
Maret
32.070
April
35.896
Mei
20.173
Juni
31.662
Juli
15.656
Agustus
31.181
September 26.939
Oktober
14.352
November 26.590
Desember
30.306
Total
289.975
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Siklis
1.
Metode Eksponensial
EKSPONENSIAL
t.lny
t
y
lny
1
2
3
4
5
6
7
8
9
10
11
12
78
10.846
14.304
32.070
35.896
20.173
31.662
15.656
31.181
26.939
14.352
26.590
30.306
289.975
9,2916
9,5683
10,3757
10,4884
9,9121
10,3629
9,6586
10,3476
10,2013
9,5717
10,1883
10,3191
120,2854
9,2916
19,1366
31,1270
41,9535
49,5606
62,1771
67,6100
82,7806
91,8119
95,7166
112,0713
123,8292
787,0660
t²
1
y'
144
18.460
19.145
19.856
20.593
21.357
22.149
22.971
23.824
24.708
25.625
26.576
27.562
222
272.826
4
9
16
25
36
49
64
81
100
121
Universitas Sumatera Utara
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 787,066) − (78 × 120,285)
�=
= 0,03643
(12 × 650) − 782
∑ ��� − � ∑ �
ln � =
= 9,7869
�
� = 17.799,488
�=
� ′ = �� ��
� ′ = 17.799,488� 0,03643 �
� ′ = 17.799,488� 0,03643 (1) = 18.460,06 ≈ 18.460
���� =
=
3.
∑��=1 |��� |
3,87
12
�
= 32,24
Metode Siklis
Jumlah periode adalah:
�=
12
=4
3
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
2
10.846
14.304
32.070
35.896
20.173
31.662
15.656
31.181
26.939
14.352
26.590
30.306
289.975
0,866
0,866
0,000
-0,866
-0,866
0,000
0,866
0,866
0,000
-0,866
-0,866
0,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0
0
0
3
4
5
6
7
8
9
10
11
12
78
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
9392,64
12387,26
0,00
-31085,94
-17470,03
0,00
13557,66
27002,96
0,00
-12429,05
-23027,16
0,00
5423
-7152
-32070
-17948
10086,625
31661,5
7827,75
-15590,625
-26938,75
-7176,125
13295,125
30306
6
6
-21671,65
-8275,5
Universitas Sumatera Utara
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
∑y
289.975
= 12 a + b (0) + c (0)
a
=
a
= 24.164,562
2πt
289.975
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-21.671,65
= 24.164,562 (0) + b (4) + c (0)
b
=
b
= -5417,912
n
2πt
−21.671,65
4
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
-8.275,5
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= -2.068,875
n
= 24.164,562 (0) + c (4) + (-5417,912) (0)
2πt
2πt
n
n
y’= a + b sin � �+ c� �
−8.275,5
4
2πt
2πt
n
n
y’= 24.164,562 – 5417,912 sin � � - 2.068,875 cos � �
y’= 24.164,562 – 5417,912 sin (0,866) - 2.068,875 co�(−0,500) = 18.438
���� =
=
∑��=1 |��� |
4,11
�
12
= 34,25%
Metode Terpilih: Eksponensial
Universitas Sumatera Utara
Verifikasi Peramalan
y
10.846
14.304
32.070
35.896
20.173
31.662
15.656
31.181
26.939
14.352
26.590
30.306
y't
18.460
19.145
19.856
20.593
21.357
22.149
22.971
23.824
24.708
25.625
26.576
27.562
e=y-y't
-7.614
-4.841
12.214
15.303
-1.184
9.512
-7.316
7.357
2.231
-11.273
14
2.744
|MR|
2.772,91
17.055,49
3.089,12
16.486,98
10.695,66
16.828,00
14.673,24
5.126,65
13.503,46
11.287,01
2.729,46
114.247,98
UCL
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
27.627,24
LCL
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
-27.627,24
Permintaan 682 tahun 2016
40.000
30.000
PT. SWMS
20.000
10.000
Irawan 682
0
LCL
-10.000
UCL
-20.000
-30.000
-40.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 683 – PT. SWMS
Irawan 683
Bulan Demand
Januari
55.775
Februari
46.583
Maret
51.009
April
108.655
Mei
74.095
Juni
73.288
Juli
85.789
Agustus
56.958
September
52.868
Oktober
77.089
November
55.013
Desember
46.827
Total
783.948
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
EKSPONENSIAL
lny
t.lny
55.775 10,929
46.583 10,749
51.009 10,840
108.655 11,596
74.095 11,213
73.288 11,202
85.789 11,360
56.958 10,950
52.868 10,876
77.089 11,253
55.013 10,915
46.827 10,754
783.948 132,637
10,929
21,498
32,519
46,384
56,065
67,213
79,518
87,601
97,880
112,527
120,068
129,050
861,253
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
y'
65.321
64.918
64.518
64.120
63.725
63.331
62.941
62.553
62.167
61.783
61.402
61.024
757.803
Universitas Sumatera Utara
�=
�=
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 861,253) − (78 × 132,637)
= −0,006187
(12 × 650) − 782
ln � =
∑ ��� − � ∑ �
= 11,0932
�
� = 65.726,669
� ′ = �� ��
� ′ = 65.726,669� −0,006187 �
� ′ = 65.726,669� −0,006187 (1) = 65.321,27 ≈ 65.321
���� =
∑��=1|��� |
=
�
2,67
12
= 22,28%
2.
Metode Kuadratis
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
t²
t³
55.775
46.583
51.009
108.655
74.095
73.288
85.789
56.958
52.868
77.089
55.013
46.827
783.948
1
4
9
16
25
36
49
64
81
100
121
144
650
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
t²y
t'
y't
1
55.775
55.775
13 50.951
16
93.167
186.333
14 59.898
81
153.027
459.081
15 66.944
256
434.620
1.738.480 16 72.091
625
370.474
1.852.369 17 75.338
1.296
439.725
2.638.350 18 76.686
2.401
600.525
4.203.673 19 76.134
4.096
455.664
3.645.312 20 73.683
6.561
475.812
4.282.308 21 69.331
10.000 770.893
7.708.925 22 63.081
14.641 605.138
6.656.513 23 54.930
20.736 561.918
6.743.016 24 44.880
60.710 5.016.736 40.170.135 222 783.948
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
Universitas Sumatera Utara
� = � � � � − � � ��
� = (78 × 783.948) − (12 × 5.016.736) = 947.112
� = � �2 � � − � � �2�
� = (650 × 783.948) − (12 × 40.170.135) = 27.524.586
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�� −��
�� −� 2
�−��
= 11.795,578
= -949,808
�
∑ �−� ∑ �−� ∑ � 2
�=
= 40.105,693
�
� ′ = � + �� + �� 2
� ′ = 40.105,693 + 11.795,578� + (−949,808)� 2
� ′ = 40.105,693 + 11.795,578(1) + (−949,808)(1)2
= 50.951,46 ≈ 50.951
���� =
∑��=1|��� |
=
�
2,03
12
= 16,89%
Metode Terpilih: Kuadratis
Universitas Sumatera Utara
Verifikasi Peramalan
y
55.775
46.583
51.009
108.655
74.095
73.288
85.789
56.958
52.868
77.089
55.013
46.827
y't
50.951
59.898
66.944
72.091
75.338
76.686
76.134
73.683
69.331
63.081
54.930
44.880
e=y-y't
4.824
-13.314
-15.935
36.564
-1.244
-3.399
9.655
-16.725
-16.463
14.009
82
1.946
|MR|
18.137,90
2.620,79
52.499,08
37.807,55
2.154,94
13.053,68
26.379,70
261,16
30.472,03
13.926,35
1.864,01
199.177,20
UCL
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
48.164,67
LCL
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
-48.164,67
Permintaan 683 tahun 2016
60.000
40.000
PT. SWMS
20.000
Irawan 683
0
LCL
UCL
-20.000
-40.000
-60.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 683-SP – PT. SWMS
Irawan 683-SP
Bulan
Demand
Januari
93.060
Februari
76.257
Maret
48.974
April
117.381
Mei
88.140
Juni
110.940
Juli
109.946
Agustus
66.432
September
101.747
Oktober
61.182
November
49.231
Desember
57.885
Total
981.175
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
EKSPONENSIAL
lny
t.lny
93.060 11,441
76.257 11,242
48.974 10,799
117.381 11,673
88.140 11,387
110.940 11,617
109.946 11,608
66.432 11,104
101.747 11,530
61.182 11,022
49.231 10,804
57.885 10,966
981.175 135,193
11,441
22,484
32,397
46,693
56,933
69,700
81,254
88,831
103,772
110,216
118,847
131,595
874,164
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
y'
93.198
90.256
87.406
84.647
81.975
79.387
76.880
74.453
72.103
69.826
67.622
65.487
943.239
Universitas Sumatera Utara
�=
�=
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 874,164) − (78 × 135,193)
= −0,032079
(12 × 650) − 782
ln � =
∑ ��� − � ∑ �
= 11,474
�
� = 96.236,405
� ′ = �� ��
� ′ = 96.236,405� −0,032079 �
� ′ = 96.236,405� −0,032079 (1) = 93.198,16 ≈ 93.198
���� =
∑��=1|��� |
=
�
2,96
12
= 24,68%
2.
Metode Kuadratis
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
t²
t³
93.060
76.257
48.974
117.381
88.140
110.940
109.946
66.432
101.747
61.182
49.231
57.885
981.175
1
4
9
16
25
36
49
64
81
100
121
144
650
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
t²y
1
93.060
93.060
16
152.514
305.028
81
146.921
440.764
256
469.525
1.878.100
625
440.700
2.203.500
1.296
665.637
3.993.822
2.401
769.619
5.387.330
4.096
531.456
4.251.648
6.561
915.725
8.241.527
10.000 611.820
6.118.200
14.641 541.541
5.956.951
20.736 694.623
8.335.476
60.710 6.033.141 47.205.406
t'
y't
13 74.916
14 83.470
15 89.831
16 93.999
17 95.975
18 95.759
19 93.350
20 88.748
21 81.954
22 72.967
23 61.788
24 48.417
25 981.175
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
Universitas Sumatera Utara
� = � � � � − � � ��
� = (78 × 981.175) − (12 × 6.033.141) = 4.133.919
� = � �2 � � − � � �2�
� = (650 × 981.175) − (12 × 47.205.406) = 71.298.559
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�� −��
�� −� 2
�−��
= 11.795,578
= -1.096,254
�
∑ �−� ∑ �−� ∑ � 2
�=
= 64.170,272
�
� ′ = � + �� + �� 2
� ′ = 64.170,272 + 11.795,578� + (−1.096,254)� 2
� ′ = 64.170,272 + 11.795,578(1) + (−1.096,254)(1)2
= 74.916,28 ≈ 74.916
���� =
∑��=1|��� |
=
�
2,84
12
= 23,68%
Metode Terpilih: Kuadratis
Universitas Sumatera Utara
Verifikasi Peramalan
y
93.060
76.257
48.974
117.381
88.140
110.940
109.946
66.432
101.747
61.182
49.231
57.885
y't
74.916
83.470
89.831
93.999
95.975
95.759
93.350
88.748
81.954
72.967
61.788
48.417
e=y-y't
18.144
-7.213
-40.857
23.382
-7.835
15.181
16.596
-22.316
19.793
-11.785
-12.557
9.468
|MR|
25.356,50
33.644,24
64.239,02
31.217,22
23.016,03
1.415,04
38.911,95
42.109,31
31.578,68
771,92
22.025,84
314.285,76
UCL
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
76.000,01
LCL
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
-76.000,01
Permintaan 683-SP tahun 2016
100.000
80.000
60.000
PT. SWMS
40.000
20.000
Irawan 683-SP
0
LCL
-20.000
UCL
-40.000
-60.000
-80.000
-100.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 684-S – PT. SWMS
Irawan 684-S
Bulan
Demand
Januari
39.454
Februari
37.382
Maret
73.281
April
33.181
Mei
32.200
Juni
77.775
Juli
37.679
Agustus
68.149
September
66.666
Oktober
52.078
November
91.956
Desember
45.900
Total
655.699
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
EKSPONENSIAL
lny
t.lny
39.454 10,583
37.382 10,529
73.281 11,202
33.181 10,410
32.200 10,380
77.775 11,262
37.679 10,537
68.149 11,129
66.666 11,107
52.078 10,860
91.956 11,429
45.900 10,734
655.699 130,162
10,583
21,058
33,606
41,639
51,899
67,569
73,758
89,036
99,967
108,605
125,720
128,811
852,250
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
y'
40.483
42.275
44.147
46.101
48.141
50.272
52.498
54.822
57.248
59.783
62.429
65.192
623.391
Universitas Sumatera Utara
�=
�=
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 874,164) − (78 × 135,193)
= 0,04331
(12 × 650) − 782
ln � =
∑ ��� − � ∑ �
= 10,5653
�
� = 38.767,114
� ′ = �� ��
� ′ = 38.767,114� 0,04331 �
� ′ = 38.767,114� 0,04331 (1) = 40.483,17 ≈ 40.483
���� =
∑��=1|��� |
=
�
3,41
12
= 28,43%
2.
Metode Kuadratis
t
y
1 39.454
2 37.382
3 73.281
4 33.181
5 32.200
6 77.775
7 37.679
8 68.149
9 66.666
10 52.078
11 91.956
12 45.900
78 655.699
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
t³
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
t²y
t'
y't
1
39.454
39.454
13 39.439
16
74.763
149.526
14 43.194
81
219.843
659.529
15 46.652
256
132.725
530.900
16 49.812
625
161.001
805.006
17 52.676
1.296
466.650
2.799.900 18 55.241
2.401
263.750
1.846.247 19 57.510
4.096
545.192
4.361.536 20 59.481
6.561
599.994
5.399.946 21 61.155
10.000 520.778
5.207.775 22 62.532
14.641 1.011.511 11.126.616 23 63.612
20.736 550.797
6.609.564 24 64.394
60.710 4.586.457 39.535.998 25 655.699
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
Universitas Sumatera Utara
� = � � � � − � � ��
� = (78 × 655.699) − (12 × 4.586.457) = −3.892.937
� = � �2 � � − � � �2�
� = (650 × 655.699) − (12 × 39.535.998) = −48.227.464
� = � � � �2 − � � �3
� = (78 × 650) − (12 × 6.084) = −22.308
2
� = �� �� − � � � 2
� = 782 − (12 × 650) = −1.716
�=
�=
�� −��
�� −� 2
�−��
= 4.201,006
= -148,645
�
∑ �−� ∑ �−� ∑ � 2
�=
= 35.386,710
�
� ′ = � + �� + �� 2
� ′ = 35.386,710 + 4.201,006� + (−148,645)� 2
� ′ = 35.386,710 + 4.201,006(1) + (−148,645)(1)2
= 39.439,07 ≈ 39.439
���� =
∑��=1|��� |
=
�
3,59
12
= 29,95%
Metode Terpilih: Eksponensial
Universitas Sumatera Utara
Verifikasi Peramalan
y
39.454
37.382
73.281
33.181
32.200
77.775
37.679
68.149
66.666
52.078
91.956
45.900
y't
e=y-y't
-1.029
-4.894
29.134
-12.919
-15.941
27.503
-14.819
13.327
9.418
-7.705
29.527
-19.293
40.483
42.275
44.147
46.101
48.141
50.272
52.498
54.822
57.248
59.783
62.429
65.192
|MR|
3.864,27
34.028,15
42.053,94
3.021,69
43.443,73
42.321,85
28.146,64
3.909,73
17.122,40
37.231,42
48.819,22
303.963,04
UCL
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
73.503,79
LCL
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
-73.503,79
Permintaan 684-S tahun 2016
100.000
80.000
60.000
20.000
Irawan 684-S
0
Desember
November
Oktober
Agustus
Juli
Juni
Mei
April
September
-60.000
Maret
-40.000
Februari
-20.000
LCL
Januari
PT. SWMS
40.000
UCL
-80.000
-100.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 9001 – PT. BWP
Irawan 9001
Bulan
Januari
Februari
Maret
April
Mei
Juni
Juli
Agustus
Demand
3.941
3.606
4.799
6.184
6.004
4.240
3.636
3.712
September
3.899
Oktober
November
3.221
2.600
Desember
4.522
Total
50.363
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Siklis
2.
Metode Eksponensial
t
y
EKSPONENSIAL
lny
t.lny
t²
y'
1
8,279
4.772
1 3.941 8,279
4
4.638
2 3.606 8,190 16,381
9
4.509
3 4.799 8,476 25,429
4.382
4 6.184 8,730 34,919 16
4.259
5 6.004 8,700 43,501 25
4.140
6 4.240 8,352 50,114 36
4.024
7 3.636 8,199 57,390 49
3.911
8 3.712 8,219 65,755 64
3.802
9 3.899 8,268 74,416 81
3.695
10 3.221 8,077 80,773 100
3.592
11 2.600 7,863 86,495 121
3.491
12 4.522 8,417 101,001 144
78 50.363 99,771 644,452 650 1.761.609
Universitas Sumatera Utara
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 644,452) − (78 × 99,771)
�=
= −0,0284
(12 × 650) − 782
∑ ��� − � ∑ �
ln � =
= 8,4989
�
� = 4.909,609
� ′ = �� ��
� ′ = 4.909,609� −0,0284�
� ′ = 4.909,609� −0,0284(1) = 4.772,09 ≈ 4.772
�=
���� =
∑��=1|��� |
=
�
2,11
12
= 17,55%
4.
Metode Siklis
Jumlah periode adalah:
�=
12
=6
2
SIKLIS
Sin
Sin^2
(2πt/n)*Cos
(2πt/n)
(2πt/n)
t
Y
Sin(2πt/n)
Cos(2πt/n)
1
12
3941
3606
4799
6184
6004
4240
3636
3712
3899
3221
2600
4522
0,866
0,866
0,000
-0,866
-0,866
0,000
0,866
0,866
0,000
-0,866
-0,866
0,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,500
-0,500
-1,000
-0,500
0,500
1,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
0,433
-0,433
0,000
78
50362,95
0
0
0
2
3
4
5
6
7
8
9
10
11
∑y
Cos^2
(2πt/n)
Y*Sin(2πt/n)
Y*Cos(2πt/n)
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,750
0,750
0,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
0,250
0,250
1,000
3412,60
3122,62
0,00
-5355,52
-5199,38
0,00
3148,78
3214,59
0,00
-2788,95
-2251,43
0,00
1970,325
-1802,9
-4799,1
-3092,1
3001,95
4240
1818
-1856
-3899
-1610,25
1299,9
4522
6
6
-2696,6807
-207,175
2πt
2πt
n
n
= t a + b ∑ sin� � + c ∑ cos� �
Universitas Sumatera Utara
50.363
= 12 a + b (0) + c (0)
a
=
a
= 4.196,912
2πt
50.363
12
2πt
2πt
2πt
2πt
n
n
n
n
∑ y sin� �
=a ∑ sin� � + b ∑ sin2� �+ c ∑ sin� �cos� �
-2.696,68
= = 4.196,912 (0) + b (6) + c (0)
b
=
b
= -449,446
n
2πt
−2.696,68
6
2πt
2πt
2πt
2πt
n
n
n
n
∑ y cos � �
-207,175
= a ∑ cos � �+ c ∑ cos2� �+ b ∑ sin� �cos� �
c
=
c
= -34,529
n
y’
y’
y’
= 4.196,912 (0) + c (6) + (-449,446) (0)
−207 ,175
6
2πt
2πt
n
n
= a + b sin � �+ c� �
2πt
2πt
n
n
= 4.196,912 – 449,446 sin � � - -34,529 cos � �
= 4.196,912 – 449,446 sin (0,866) - -34,529 co�(−0,500) = 3.790,43
���� =
=
∑��=1 |��� |
2,15
�
12
= 17,96%
Metode Terpilih: Eksponensial
Universitas Sumatera Utara
Verifikasi Peramalan
y
3.941
3.606
4.799
6.184
6.004
4.240
3.636
3.712
3.899
3.221
2.600
4.522
y't
e=y-y't
|MR|
UCL
LCL
4.772
-831
2.133,62 -2.133,62
4.638 -1.033
201,19 2.133,62 -2.133,62
4.509
291
1.323,22 2.133,62 -2.133,62
4.382 1.802 1.511,38 2.133,62 -2.133,62
4.259 1.744
57,56
2.133,62 -2.133,62
4.140
100
1.644,59 2.133,62 -2.133,62
4.024
-388
488,03 2.133,62 -2.133,62
3.911
-199
188,72 2.133,62 -2.133,62
3.802
97
296,56 2.133,62 -2.133,62
3.695
-475
572,01 2.133,62 -2.133,62
3.592
-992
517,19 2.133,62 -2.133,62
3.491 1.031 2.022,81 2.133,62 -2.133,62
8.823,26
Permintaan Irawan 9001 tahun 2016
3.000
1.000
Irawan 9001
UCL
Desember
November
Oktober
September
Juli
Juni
Mei
April
Agustus
-2.000
Maret
-1.000
Februari
0
Januari
PT. BWP
2.000
LCL
-3.000
Universitas Sumatera Utara
PERAMALAN PRODUK IRAWAN 682 – PT. BWP
Irawan 682
Bulan
Demand
10.846
Januari
Februari
14.900
Maret
17.104
April
29.486
Mei
22.297
Juni
20.702
Juli
15.656
Agustus
24.945
September
28.110
Oktober
16.041
November
20.586
Desember
25.255
Total
245.927
Metode Peramalan Terpilih:
•
Metode Eksponensial
•
Metode Kuadratis
1.
Metode Eksponensial
t
1
2
3
4
5
6
7
8
9
10
11
12
78
y
EKSPONENSIAL
lny
t.lny
t²
1
y'
10.846
9,292
9,292
15.779
4
14.900
9,609
19,218
16.431
9
17.109
17.104
9,747
29,241
29.486 10,292 41,167 16 17.816
22.297 10,012 50,061 25 18.552
20.702
9,938
59,628 36 19.318
15.656
9,659
67,610 49 20.116
24.945 10,124 80,995 64 20.947
28.110 10,244 92,195 81 21.812
16.041
9,683
96,829 100 22.713
20.586
9,932 109,256 121 23.651
25.255 10,137 121,641 144 24.628
245.927 118,668 777,133 650 238.874
Universitas Sumatera Utara
�=
�=
� ∑ �. ��� − ∑ � ∑ ���
� ∑ � 2 − (∑ �)2
(12 × 777,133) − (78 × 118,668)
= 0,04047
(12 × 650) − 782
ln � =
∑ ��� − � ∑ �
= 9,625
�
� = 15.153,002
� ′ = �� ��
� ′ = 15.153,002� 0,04047 �
� ′ = 15.153,002� 0,04047 (1) = 15.778,90 ≈ 15.779
���� =
∑��=1|��� |
=
�
2,45
12
= 20,39%
2.
Metode Kuadratis
t
y
1 10.846
2 14.900
3 17.104
4 29.486
5 22.297
6 20.702
7 15.656
8 24.945
9 28.110
10 16.041
11 20.586
12 25.255
78 245.927
t²
1
4
9
16
25
36
49
64
81
100
121
144
650
t³
1
8
27
64
125
216
343
512
729
1.000
1.331
1.728
6.084
KUADRATIS
t⁴
ty
t²y
t'
y't
1
10.846
10.846
13 13.404
16
29.800
59.600
14 15.885
81
51.312
153.936
15 18.008
256
117.944
471.776
16 19.774
625
111.484
557.419
17 21.182
1.296
124.211
745.263
18 22.233
2.401
109.589
767.120
19 22.926
4.096
199.560
1.596.480 20 23.262
6.561
252.990
2.276.910 21 23.240
10.000 160.408
1.604.075 22 22.860
14.641 226.446
2.490.906 23 22.123
20.736 303.060
3.636.720 24 21.029
60.710 1.697.648 14.371.050 222 245.927
2
� = �� � 2 � − � � � 4
� = (650)2 − (12 × 60.710) = −306.020
Universitas Sumatera Utara
� = � � � � − � � ��
� = (78 × 245.927) − (12 × 1.697.648) = −1.189.493
� = � �2 � � − � � �2�
� = (650 × 245.927) − (12 × 14.371.050) = −12.600.216
� = � � � �