Tabel 4.1 Nilai Penjualan Energi listrik PT PLN Persero Cabang Medan Tahun 2000 - 2009
Periode Tahun
Nilai Penjualan 1
2000 631.205
2 2001
801.558 3
2002 1.037.979
4 2003
1.086.555 5
2004 1.244.537
6 2005
1.304.708 7
2006 1.439.858
8 2007
1.519.339 9
2008 1.738.903
10 2009
1.829.358 Sumber : PT PLN Persero Cabang Medan
4.5.1 Penaksiran Model Peramalan
Dalam mengolah data pada table 4.1, penulis menulis menggunakan metode peramalan dengan metode pemulusan eksponensial satu-parameter dari Brown. Untuk
memenuhi perhitungan pemulusan eksponensial tunggal, ganda dan ramalan yang akan datang, maka kita harus menentukan parameter dari
nilai α terlebih dahulu yang
biasa digunakan dengan cara trial and error atau coba dan salah. Nilai
α yang dipilih d ari 0 α 1 , dih itung Mean Square Error MSE yang merupakan suatu ukuran
Universitas Sumatera Utara
ketepatan perhitungan dengan mengkuadratkan masing-masing elemen dalam sebuah susunan data dan kemudian dicoba nilai α yang lain.
Untuk menghitung nilai MSE pertama, dicari terlebih dahulu error yang merupakan hasil dari data asli dikurang hasil ramalan. Lalu tiap eror dikuadratkan dan
dibagi dengan benyaknya error. Secara matematis rumus MSE adalah sebagai berikut:
∑
=
=
N t
t
N e
MSE
1
2
Universitas Sumatera Utara
Tabel 4.2 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.1 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205 631.205,000
631.205,000 -
- -
- -
801.558 648.240,300
632.908,530 663.572,070
1.703,530 -
- -
1.037.979 687.214,170
638.339,094 736.089,246
5.430,564 665.275,600
372.703,400 138.907.824.371,560
1.086.555 727.148,253
647.220,010 807.076,496
8.880,916 741.519,810
345.035,190 119.049.282.338,336
1.244.537 778.887,128
660.386,722 897.387,534 13.166,712
815.957,412 428.579,588
183.680.463.250,250 1.304.708
831.469,215 677.494,971
985.443,459 17.108,249 910.554,246
394.153,755 155.357.182.186,446
1.439.858 892.308,093
698.976,283 1.085.639,904 21.481,312 1.002.551,708
437.306,292 191.236.792.865,359
1.519.339 955.011,184
724.579,773 1.185.442,595 25.603,490 1.107.121,216
412.217,784 169.923.501.553,872
1.738.903 1.033.400,366 755.461,833
1.311.338,899 30.882,059 1.211.046,085 527.856,915
278.632.922.778,349 1.829.358 1.112.996,129
791.215,262 1.434.776,996 35.753,430 1.342.220,958
487.137,042 237.302.497.654,186
3.404.989,965 1.474.090.466.998,360 Sumber: Perhitungan
Untuk α = 0,1 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 466.998,36
1.474.090.
= 184.261.308.374,80
Universitas Sumatera Utara
Tabel 4.3 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.2 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205 631.205,000
631.205,000 -
- -
- -
801.558 665.275,600
638.019,120 692.532,080
6.814,120 -
- -
1.037.979 739.816,280
658.378,552 821.254,008 20.359,432
699.346,200 338.632,800
114.672.173.235,840 1.086.555
809.164,024 688.535,646
929.792,402 30.157,094 841.613,440
244.941,560 59.996.367.815,234
1.244.537 896.238,619
730.076,241 1.062.400,997 41.540,595
959.949,496 284.587,504
80.990.047.432,950 1.304.708
977.932,495 779.647,492
1.176.217,499 49.571,251 1.103.941,592 200.766,408
40.307.150.581,222 1.439.858 1.070.317,596
837.781,513 1.302.853,680 58.134,021 1.225.788,750
214.069,250 45.825.643.898,316
1.519.339 1.160.121,877 902.249,586
1.417.994,168 64.468,073 1.360.987,701 158.351,299
25.075.133.978,597 1.738.903 1.275.878,102
976.975,289 1.574.780,914 74.725,703 1.482.462,241
256.440,759 65.761.862.706,629
1.829.358 1.386.574,081 1.058.895,047 1.714.253,115 81.919,759 1.649.506,618
179.851,382 32.346.519.730,012
1.877.640,963 464.974.899.378,799
Sumber: Perhitungan Untuk
α = 0,2 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 9.378,80
464.974.89
= 58.121.862.422,35 1
Universitas Sumatera Utara
Tabel 4.4 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.3 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205 631.205,000
631.205,000 -
- -
- -
801.558 682.310,900
646.536,770 718.085,030
15.331,770 -
- -
1.037.979 789.011,330
689.279,138 888.743,522
42.742,368 733.416,800
304.562,200 92.758.133.668,840
1.086.555 878.274,431
745.977,726 1.010.571,136
56.698,588 931.485,890
155.069,110 24.046.428.876,192
1.244.537 988.153,202
818.630,369 1.157.676,035
72.652,643 1.067.269,724 177.267,276
31.423.687.140,460 1.304.708 1.083.119,641
897.977,150 1.268.262,132
79.346,782 1.230.328,678 74.379,323
5.532.283.615,559 1.439.858 1.190.141,149
985.626,350 1.394.655,948
87.649,200 1.347.608,914 92.249,086
8.509.893.915,805 1.519.339 1.288.900,504 1.076.608,596
1.501.192,412 90.982,246 1.482.305,147
37.033,853 1.371.506.248,694
1.738.903 1.423.901,253 1.180.796,393 1.667.006,113
104.187,797 1.592.174,658 146.728,342
21.529.206.219,061 1.829.358 1.545.538,277 1.290.218,958
1.800.857,596 109.422,565 1.771.193,910
58.164,090 3.383.061.406,472
1.045.453,279 188.554.201.091,083
Sumber: Perhitungan Untuk
α = 0,3 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 1.091,083
188.554.20
= 23.569.275.136,39
Universitas Sumatera Utara
Tabel 4.5 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.4 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205 631.205,000
631.205,000 -
- -
- -
801.558 699.346,200
658.461,480 740.230,920
27.256,480 -
- -
1.037.979 834.799,320
728.996,616 940.602,024
70.535,136 767.487,400
270.491,600 73.165.705.670,560
1.086.555 935.501,592
811.598,606 1.059.404,578
82.601,990 1.011.137,160 75.417,840
5.687.850.590,266 1.244.537 1.059.115,755
910.605,466 1.207.626,044
99.006,860 1.142.006,568 102.530,432
10.512.489.486,107 1.304.708 1.157.352,653 1.009.304,341
1.305.400,965 98.698,875 1.306.632,904
-1.924,904 3.705.255,409
1.439.858 1.270.354,792 1.113.724,521 1.426.985,063
104.420,180 1.404.099,840 35.758,160
1.278.645.983,700 1.519.339 1.369.948,475 1.216.214,103
1.523.682,847 102.489,582 1.531.405,243
-12.066,243 145.594.218,784
1.738.903 1.517.530,285 1.336.740,576 1.698.319,994
120.526,473 1.626.172,429 112.730,571
12.708.181.634,018 1.829.358 1.642.261,371 1.458.948,894
1.825.573,848 122.208,318 1.818.846,467
10.511,533 110.492.318,415
593.448,988 103.612.665.157,258
Sumber: Perhitungan Untuk
α = 0,4 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 5.157,258
103.612.66
= 12.951.583.144,66
Universitas Sumatera Utara
Tabel 4.6 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.5 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205,000 631.205,000
631.205,000 -
- -
- -
801.558,000 716.381,500
673.793,250 758.969,750
42.588,250 -
- -
1.037.979,000 877.180,250
775.486,750 978.873,750
101.693,500 801.558,000 236.421,000 55.894.889.241,000
1.086.555,000 981.867,625
878.677,188 1.085.058,063
103.190,438 1.080.567,250 5.987,750
35.853.150,063 1.244.537,000 1.113.202,313
995.939,750 1.230.464,875
117.262,563 1.188.248,500 56.288,500
3.168.395.232,250 1.304.708,000 1.208.955,156 1.102.447,453
1.315.462,859 106.507,703 1.347.727,438 -43.019,438
1.850.672.002,816 1.439.858,000 1.324.406,578 1.213.427,016
1.435.386,141 110.979,563 1.421.970,563
17.887,438 319.960.420,316
1.519.339,000 1.421.872,789 1.317.649,902 1.526.095,676
104.222,887 1.546.365,703 -27.026,703 730.442.681,807
1.738.903,000 1.580.387,895 1.449.018,898 1.711.756,891
131.368,996 1.630.318,563 108.584,438 11.790.580.067,191 1.829.358,000 1.704.872,947 1.576.945,923
1.832.799,972 127.927,024 1.843.125,887 -13.767,887
189.554.704,700 341.355,098 73.980.347.500,144
Sumber: Perhitungan Untuk α = 0,5 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 .500,144
73.980.347
= 9.247.543.437,52
Universitas Sumatera Utara
Tabel 4.7 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.6 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205 631.205,000
631.205,000 -
- -
- -
801.558 733.416,800
692.532,080 774.301,520
61.327,080 -
- -
1.037.979 916.154,120
826.705,304 1.005.602,936 134.173,224
835.628,600 202.350,400 40.945.684.380,160 1.086.555 1.018.394,648
941.718,910 1.095.070,386 115.013,606 1.139.776,160 -53.221,160
2.832.491.871,746 1.244.537 1.154.080,059 1.069.135,600 1.239.024,519
127.416,689 1.210.083,992 34.453,008
1.187.009.760,248 1.304.708 1.244.456,824 1.174.328,334 1.314.585,313
105.192,734 1.366.441,208 -61.733,208 3.810.988.969,971
1.439.858 1.361.697,529 1.286.749,851 1.436.645,208 112.421,517 1.419.778,048
20.079,952 403.204.485,173
1.519.339 1.456.282,412 1.388.469,388 1.524.095,436 101.719,536 1.549.066,725 -29.727,725
883.737.625,590 1.738.903 1.625.854,765 1.530.900,614 1.720.808,916
142.431,226 1.625.814,972 113.088,028 12.788.902.017,580 1.829.358 1.747.956,706 1.661.134,269 1.834.779,143
130.233,655 1.863.240,142 -33.882,142 1.147.999.535,102
191.407,153 64.000.018.645,570 Sumber: Perhitungan
Untuk α = 0,6 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 .645,570
64.000.018
= 8.000.002.330,70
Universitas Sumatera Utara
Tabel 4.8 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.7 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205 631.205,000
631.205,000 -
- -
- -
801.558 750.452,100
714.677,970 786.226,230
83.472,970 -
- -
1.037.979 951.720,930
880.608,042 1.022.833,818 165.930,072 869.699,200
168.279,800 28.318.091.088,040 1.086.555
1.046.104,779 996.455,758 1.095.753,800 115.847,716 1.188.763,890 -102.208,890 10.446.657.195,032
1.244.537 1.185.007,334 1.128.441,861 1.241.572,806 131.986,103 1.211.601,516
32.935,484 1.084.746.106,314
1.304.708 1.268.797,800 1.226.691,018 1.310.904,582
98.249,157 1.373.558,910 -68.850,909
4.740.447.738,977 1.439.858
1.388.539,940 1.339.985,264 1.437.094,617 113.294,245 1.409.153,739 30.704,261
942.751.627,590 1.519.339
1.480.099,282 1.438.065,076 1.522.133,488 98.079,813 1.550.388,862
-31.049,862 964.093.911,651
1.738.903 1.661.261,885 1.594.302,842 1.728.220,927 156.237,766 1.620.213,300
118.689,700 14.087.244.770,439 1.829.358
1.778.929,165 1.723.541,268 1.834.317,062 129.238,426 1.884.458,693 -55.100,693
3.036.086.340,343 93.398,890 63.620.118.778,386
Sumber: Perhitungan Untuk α = 0,7 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 .778,386
63.620.118
= 7.952.514.847,30
Universitas Sumatera Utara
Tabel 4.9 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.8 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205 631.205,000
631.205,000 -
- -
- -
801.558 767.487,400
740.230,920 794.743,880
109.025,920 -
- -
1.037.979 983.880,680
935.150,728 1.032.610,632
194.919,808 903.769,800
134.209,200 18.012.109.364,640
1.086.555 1.066.020,136
1.039.846,254 1.092.194,018
104.695,526 1.227.530,440 -140.975,440
19.874.074.683,194 1.244.537
1.208.833,627 1.175.036,153
1.242.631,102 135.189,898
1.196.889,544 47.647,456
2.270.280.063,272 1.304.708
1.285.533,125 1.263.433,731
1.307.632,520 88.397,578
1.377.821,000 -73.113,000
5.345.510.769,000 1.439.858
1.408.993,025 1.379.881,166
1.438.104,884 116.447,435
1.396.030,098 43.827,902
1.920.884.972,684 1.519.339
1.497.269,805 1.473.792,077
1.520.747,533 93.910,911
1.554.552,319 -35.213,319
1.239.977.855,842 1.738.903
1.690.576,361 1.647.219,504
1.733.933,218 173.427,427
1.614.658,444 124.244,556
15.436.709.748,118 1.829.358
1.801.601,672 1.770.725,239
1.832.478,106 123.505,734
1.907.360,645 -78.002,645
6.084.412.587,009 22.624,710
70.183.960.043,759 Sumber: Perhitungan
Untuk α = 0,8 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 .043,759
70.183.960
= 8.772.995.005,47
Universitas Sumatera Utara
Tabel 4.10 Peramalan Nilai Penjualan Energy Listrik dengan Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown Dengan
α = 0.9 X
S
t t
S ΄
t
a ΄΄
b
t
F
t
e e
2
631.205 631.205,000
631.205,000 -
- -
- -
801.558 784.522,700
769.190,930 799.854,470
137.985,930 -
- -
1.037.979 1.012.633,370 988.289,126 1.036.977,614
219.098,196 937.840,400 100.138,600 10.027.739.209,960
1.086.555 1.079.162,837 1.070.075,466 1.088.250,208 81.786,340 1.256.075,810 169.520,810 28.737.305.023,056
1.244.537 1.227.999,584 1.212.207,172 1.243.791,995 142.131,706 1.170.036,548
74.500,452 5.550.317.348,204
1.304.708 1.297.037,158 1.288.554,160 1.305.520,157 76.346,988 1.385.923,702 -81.215,701
6.595.990.170,137 1.439.858 1.425.575,916 1.411.873,740 1.439.278,091
123.319,581 1.381.867,145 57.990,855
3.362.939.284,508 1.519.339 1.509.962,692 1.500.153,796 1.519.771,587
88.280,056 1.562.597,672 -43.258,672 1.871.312.698,791
1.738.903 1.716.008,969 1.694.423,452 1.737.594,486 194.269,655 1.608.051,643 130.851,357 17.122.077.644,025
1.829.358 1.818.023,097 1.805.663,132 1.830.383,061 111.239,681 1.931.864,142 102.506,142 10.507.509.120,833
-33.020,061 83.775.190.499,514 Sumber: Perhitungan
Untuk α = 0,9 ; N = 8, maka:
MSE =
∑
= N
t t
N e
1
2
=
8 .499,514
83.775.190
= 10.471.898.812,44
Universitas Sumatera Utara
Kemudian nilai- nilai MSE yang telah diperoleh kita dapat melihat nilai α yang
memberikan nilai MSE yang paling kecil. Perbandingan ukuran ketepatan metode peramalan nilai penjualan energy listrik di PT PLN Persero Cabang Medan
dengan melihat MSE adalah sebagai berikut: Table 4.11 Perbandingan Ukuran Ketepatan Metode Peramalan
α MSE
0.1 184.261.308.374,80
0.2 58.121.862.422,35
0.3 23.569.275.136,39
0.4 12.951.583.144,66
0.5 9.247.543.437,52
0.6 8.000.002.330,70
0.7 7.952.514.847,30
0.8 8.772.995.005,47
0.9 10.471.898812,44
Sumber: Perhitungan Dari table 4. Di atas dapat dilihat bahwa MSE yang paling kecil terd
apat pada α = 0,7, yaitu dengan MSE = 7.952.514.847,30
Universitas Sumatera Utara
Tabel 4.12 Pemulusan Eksponensial Ganda Linier Satu Parameter Dari Brown dengan menggunakan α = 0,7 pada Nilai Penjualan
Energi Listrik di PT PLN Persero Cabang Medan Tahun
Periode X
S
t t
S ΄
t
a ΄΄
b
t
F
t
2000 1
631.205 631.205,000
631.205,000 -
- -
2001 2
801.558 750.452,100
714.677,970 786.226,230
83.472,970 -
2002 3
1.037.979 951.720,930
880.608,042 1.022.833,818
165.930,072 869.699,200
2003 4
1.086.555 1.046.104,779
996.455,758 1.095.753,800
115.847,716 1.188.763,890
2004 5
1.244.537 1.185.007,334 1.128.441,861
1.241.572,806 131.986,103
1.211.601,516 2005
6 1.304.708
1.268.797,800 1.226.691,018 1.310.904,582
98.249,157 1.373.558,910
2006 7
1.439.858 1.388.539,940 1.339.985,264
1.437.094,617 113.294,245
1.409.153,739 2007
8 1.519.339
1.480.099,282 1.438.065,076 1.522.133,488
98.079,813 1.550.388,862
2008 9
1.738.903 1.661.261,885 1.594.302,842
1.728.220,927 156.237,766
1.620.213,300 2009
10 1.829.358
1.778.929,165 1.723.541,268 1.834.317,062
129.238,426 1.884.458,693
2010 11
1.963.555,489 2011
12 2.092.793,915
Sumber : Perhitungan
Universitas Sumatera Utara
4.5.2 Penentuan Bentuk Persamaan Peramalan
