BAB 4 PENGOLAHAN DATA
4.1 Data yang akan Diolah
Pengambilan data dilakukan di Kantor Badan Pusat Statistik Sumatera Utara, data yang diambil adalah data perolehan nilai air minum yang disalurkan PDAM
Tirtanadi Medan pada tahun 2009 sampai dengan 2011.
Tabel 4.1 Data Nilai Air Minum yang Disalurkan PDAM Medan Tahun 2009 - 2011
Bulan Tahun Nilai Air Minum yang Disalurkan
Januari 09 21.473.831.050
Februari 09 21.548.149.420
Maret 09 21.789.329.725
April 09 22.005.291.800
Mei 09 22.264.141.990
Juni 09 22.481.546.105
Juli 09 22.851.209.020
Agustu 09 22.845.663.820
Septembe 09 22.927.399.070
Oktober 09 22.854.910.720
November 09 22.764.705.655
Desember 09 22.819.191.990
Januari 010 22.977.014.134
Februari 010 22.942.268.240
Maret 010 23.444.261.325
April 010 23.821.534.330
Mei 010 24.200.283.345
Juni 010 24.451.483.354
Juli 010 24.403.585.445
Agustus 010 24.272.090.440
September 010 24.082.631.404
Oktober 010 24.551.663.651
November 010 24.612.143.420
Desember 010 20.195.839.321
Universitas Sumatera Utara Universitas Sumatera Utara
Lanjutan Tabel 4.1 Januari 011
18.547.485.425 Februari 011
22.317.670.660 Maret 011
23.490.850.795 April 011
23.401.919.900 Mei 011
24.440.969.550 Juni 011
25.113.931.440 Juli 011
25.401.258.645 Agustus 011
25.321.323.110 September 011
25.080.556.135 Oktober 011
25.109.569.925 November 011
25.282.275.715 Desember 011
25.569.779.015 Sumber : BPS Sumatera Utara
Dari data pada Tabel 4.1 di atas, untuk perolehan nilai air minum yang disalurkan maka penulis akan menganalisis data tersebut dan meramalkan perolehan nilai air
minum yang disalurkan untuk tahun 2009 – 2011 dengan menggunakan metode pemulusan Smoothing Eksponensial Ganda.
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,1 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,1 21.548.149.420,00+1-0,1 21.473.831.050,00 = 21.481.262.887,00
Maret 2009 = 0,1 21.789.329.725,00+1-0,1 21.481.262.887,00
= 21.512.069.570,80
Universitas Sumatera Utara Universitas Sumatera Utara
Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk
= 0,1 dengan menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,121.481.262.887,00+1-0,121.473.831.050,00 = 21.474.574.233,70
Maret 2009 = 0,121.512.069.570,80+1-0,121.474.574.233,70
= 21.478.323.767,41 Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.481.262.887,00 – 21.474.574.233,70
= 21.487.951.540,30 Maret 2009
= 221.512.069.570,80 - 21.478.323.767,41 = 21.545.815.374,19
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,1 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4
Februari 2009 =
, ,
21.481.262.887,00 – 21.474.574.233,70 = 743.183,70
Maret 2009 =
, ,
21.512.069.570,80 - 21.478.323.767,41 = 3.749.533,71
Universitas Sumatera Utara Universitas Sumatera Utara
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.487.951.540,30 + 743.183,70 1
= 21.488.694.724,00 F
April 2009
untuk m = 1 = 21.545.815.374,19 + 3.749.533,71 1
= 21.549.564.907,90
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt
St St
a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,481,262,887.00
21,474,574,233.70 21,487,951,540.30
743,183.70 Maret
3 21,789,329,725.00
21,512,069,570.80 21,478,323,767.41
21,545,815,374.19 3,749,533.71
21,488,694,724.00 300,635,001.00
90,381,403,826,270,000.00 April
4 22,005,291,800.00
21,561,391,793.72 21,486,630,570.04
21,636,153,017.40 8,306,802.63
21,549,564,907.90 455,726,892.10
207,687,000,183,131,000.00 Mei
5 22,264,141,990.00
21,631,666,813.35 21,501,134,194.37
21,762,199,432.32 14,503,624.33
21,644,459,820.03 619,682,169.97
384,005,991,778,729,000.00 Juni
6 22,481,546,105.00
21,716,654,742.51 21,522,686,249.19
21,910,623,235.84 21,552,054.81
21,776,703,056.66 704,843,048.34
496,803,722,800,268,000.00 Juli
7 22,851,209,020.00
21,830,110,170.26 21,553,428,641.29
22,106,791,699.23 30,742,392.11
21,932,175,290.65 919,033,729.35
844,622,995,674,335,000.00 Agustus
8 22,845,663,820.00
21,931,665,535.24 21,591,252,330.69
22,272,078,739.78 37,823,689.39
22,137,534,091.34 708,129,728.66
501,447,712,615,046,000.00 September
9 22,927,399,070.00
22,031,238,888.71 21,635,250,986.49
22,427,226,790.93 43,998,655.80
22,309,902,429.18 617,496,640.82
381,302,101,426,542,000.00 Oktober
10 22,854,910,720.00
22,113,606,071.84 21,683,086,495.03
22,544,125,648.66 47,835,508.54
22,471,225,446.74 383,685,273.26
147,214,388,919,231,000.00 Oktober
11 22,764,705,655.00
22,178,716,030.16 21,732,649,448.54
22,624,782,611.78 49,562,953.51
22,591,961,157.19 172,744,497.81
29,840,661,523,040,500.00 Desember
12 22,819,191,990.00
22,242,763,626.14 21,783,660,866.30
22,701,866,385.98 51,011,417.76
22,674,345,565.29 144,846,424.71
20,980,486,751,720,300.00 2010
Januari 13
22,977,014,134.00 22,316,188,676.93
21,836,913,647.36 22,795,463,706.49
53,252,781.06 22,752,877,803.74
224,136,330.26 50,237,094,540,662,800.00
Februari 14
22,942,268,240.00 22,378,796,633.23
21,891,101,945.95 22,866,491,320.52
54,188,298.59 22,848,716,487.56
93,551,752.44 8,751,930,385,451,990.00
Maret 15
23,444,261,325.00 22,485,343,102.41
21,950,526,061.60 23,020,160,143.23
59,424,115.65 22,920,679,619.11
523,581,705.89 274,137,802,745,642,000.00
April 16
23,821,534,330.00 22,618,962,225.17
22,017,369,677.95 23,220,554,772.39
66,843,616.36 23,079,584,258.87
741,950,071.13 550,489,908,045,325,000.00
Mei 17
24,200,283,345.00 22,777,094,337.15
22,093,342,143.87 23,460,846,530.43
75,972,465.92 23,287,398,388.74
912,884,956.26 833,358,943,357,364,000.00
Juni 18
24,451,483,354.00 22,944,533,238.84
22,178,461,253.37 23,710,605,224.31
85,119,109.50 23,536,818,996.35
914,664,357.65 836,610,887,149,449,000.00
Juli 19
24,403,585,445.00 23,090,438,459.45
22,269,658,973.98 23,911,217,944.93
91,197,720.61 23,795,724,333.80
607,861,111.20 369,495,130,506,146,000.00
Agustus 20
24,272,090,440.00 23,208,603,657.51
22,363,553,442.33 24,053,653,872.69
93,894,468.35 24,002,415,665.54
269,674,774.46 72,724,483,980,818,800.00
September 21
24,082,631,404.00 23,296,006,432.16
22,456,798,741.31 24,135,214,123.00
93,245,298.98 24,147,548,341.04
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 23,421,572,154.04
22,553,276,082.59 24,289,868,225.50
96,477,341.27 24,228,459,421.98
323,204,229.02 104,460,973,653,456,000.00
Oktober 23
24,612,143,420.00 23,540,629,280.64
22,652,011,402.39 24,429,247,158.88
98,735,319.81 24,386,345,566.77
225,797,853.23 50,984,670,523,114,500.00
Desember 24
20,195,839,321.00 23,206,150,284.67
22,707,425,290.62 23,704,875,278.73
55,413,888.23 24,527,982,478.69
-4,332,143,157.69 18,767,464,338,712,800,000.00
2011 Januari
25 18,547,485,425.00
22,740,283,798.71 22,710,711,141.43
22,769,856,455.98 3,285,850.81
23,760,289,166.96 -5,212,803,741.96
27,173,322,852,155,300,000.00 Februari
26 22,317,670,660.00
22,698,022,484.84 22,709,442,275.77
22,686,602,693.90 -1,268,865.66
22,773,142,306.79 -455,471,646.79
207,454,421,032,716,000.00 Maret
27 23,490,850,795.00
22,777,305,315.85 22,716,228,579.78
22,838,382,051.93 6,786,304.01
22,685,333,828.24 805,516,966.76
648,857,583,732,697,000.00 April
28 23,401,919,900.00
22,839,766,774.27 22,728,582,399.23
22,950,951,149.31 12,353,819.45
22,845,168,355.94 556,751,544.06
309,972,281,818,187,000.00 Mei
29 24,440,969,550.00
22,999,887,051.84 22,755,712,864.49
23,244,061,239.19 27,130,465.26
22,963,304,968.76 1,477,664,581.24
2,183,492,614,660,820,000.00 Juni
30 25,113,931,440.00
23,211,291,490.66 22,801,270,727.10
23,621,312,254.21 45,557,862.62
23,271,191,704.45 1,842,739,735.55
3,395,689,732,958,810,000.00 Juli
31 25,401,258,645.00
23,430,288,206.09 22,864,172,475.00
23,996,403,937.18 62,901,747.90
23,666,870,116.82 1,734,388,528.18
3,008,103,566,665,410,000.00 Agustus
32 25,321,323,110.00
23,619,391,696.48 22,939,694,397.15
24,299,088,995.81 75,521,922.15
24,059,305,685.08 1,262,017,424.92
1,592,687,980,809,830,000.00 September
33 25,080,556,135.00
23,765,508,140.33 23,022,275,771.47
24,508,740,509.20 82,581,374.32
24,374,610,917.96 705,945,217.04
498,358,649,461,600,000.00 Oktober
34 25,109,569,925.00
23,899,914,318.80 23,110,039,626.20
24,689,789,011.40 87,763,854.73
24,591,321,883.52 518,248,041.48
268,581,032,502,130,000.00 Oktober
35 25,282,275,715.00
24,038,150,458.42 23,202,850,709.42
24,873,450,207.42 92,811,083.22
24,777,552,866.13 504,722,848.87
254,745,154,170,497,000.00 Desember
36 25,569,779,015.00
24,191,313,314.08 23,301,696,969.89
25,080,929,658.27 98,846,260.47
24,966,261,290.64 603,517,724.36
364,233,643,619,284,000.00
SE 9,810,307,676.54
SSE
64,932,716,351,400,500,000.00
M SE
1,909,785,775,041,190,000.00
Tabel 4.2 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011 a = 0,1
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,2 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,2 21.548.149.420,00+1-0,2 21.473.831.050,00 = 21.488.694.724,00
Maret 2009 = 0,2 21.789.329.725,00+1-0,2 21.488.694.724,00
= 21.548.821.724,20 Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang
disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk = 0,2 dengan
menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,2 21.488.694.724,00+1-0,2
21.473.831.050,00 = 21.476.803.784,80
Maret 2009 = 0,2
21.548.821.724,20+1-0,2 21.476.803.784,80
= 21.491.207.372,68 Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.488.694.724,00 – 21.476.803.784,80
= 21.500.585.663,20 Maret 2009
= 221.548.821.724,20 - 21.491.207.372,68 = 21.606.436.075,72
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,2 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4
Februari 2009 =
, ,
21.488.694.724,00 – 21.476.803.784,80 = 2.972.734,80
Maret 2009 =
, ,
21.548.821.724,20 - 21.491.207.372,68 = 14.403.587,88
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.500.585.663,20 + 2.972.734,80 1
= 21.503.558.398,00 F
April 2009
untuk m = 1 = 21.606.436.075,72 + 14.403.587,88 1
= 21.620.839.663,60
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt
St St
a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,488,694,724.00
21,476,803,784.80 21,500,585,663.20
2,972,734.80 Maret
3 21,789,329,725.00
21,548,821,724.20 21,491,207,372.68
21,606,436,075.72 14,403,587.88
21,503,558,398.00 285,771,327.00
81,665,251,335,340,900.00 April
4 22,005,291,800.00
21,640,115,739.36 21,520,989,046.02
21,759,242,432.70 29,781,673.34
21,620,839,663.60 384,452,136.40
147,803,445,182,522,000.00 Mei
5 22,264,141,990.00
21,764,920,989.49 21,569,775,434.71
21,960,066,544.27 48,786,388.69
21,789,024,106.04 475,117,883.96
225,737,003,658,631,000.00 Juni
6 22,481,546,105.00
21,908,246,012.59 21,637,469,550.29
22,179,022,474.89 67,694,115.58
22,008,852,932.96 472,693,172.04
223,438,834,893,234,000.00 Juli
7 22,851,209,020.00
22,096,838,614.07 21,729,343,363.04
22,464,333,865.10 91,873,812.76
22,246,716,590.47 604,492,429.53
365,411,097,358,592,000.00 Agustus
8 22,845,663,820.00
22,246,603,655.26 21,832,795,421.49
22,660,411,889.03 103,452,058.44
22,556,207,677.86 289,456,142.14
83,784,858,223,589,600.00 September
9 22,927,399,070.00
22,382,762,738.21 21,942,788,884.83
22,822,736,591.58 109,993,463.34
22,763,863,947.47 163,535,122.53
26,743,736,300,205,500.00 Oktober
10 22,854,910,720.00
22,477,192,334.57 22,049,669,574.78
22,904,715,094.35 106,880,689.95
22,932,730,054.93 -77,819,334.93
6,055,848,888,344,940.00 Oktober
11 22,764,705,655.00
22,534,694,998.65 22,146,674,659.55
22,922,715,337.75 97,005,084.77
23,011,595,784.30 -246,890,129.30
60,954,735,945,595,200.00 Desember
12 22,819,191,990.00
22,591,594,396.92 22,235,658,607.03
22,947,530,186.82 88,983,947.47
23,019,720,422.53 -200,528,432.53
40,211,652,251,619,500.00 2010
Januari 13
22,977,014,134.00 22,668,678,344.34
22,322,262,554.49 23,015,094,134.19
86,603,947.46 23,036,514,134.29
-59,500,000.29 3,540,250,034,624,960.00
Februari 14
22,942,268,240.00 22,723,396,323.47
22,402,489,308.28 23,044,303,338.66
80,226,753.80 23,101,698,081.65
-159,429,841.65 25,417,874,408,049,500.00
Maret 15
23,444,261,325.00 22,867,569,323.78
22,495,505,311.38 23,239,633,336.17
93,016,003.10 23,124,530,092.45
319,731,232.55 102,228,061,067,112,000.00
April 16
23,821,534,330.00 23,058,362,325.02
22,608,076,714.11 23,508,647,935.93
112,571,402.73 23,332,649,339.27
488,884,990.73 239,008,534,163,936,000.00
Mei 17
24,200,283,345.00 23,286,746,529.02
22,743,810,677.09 23,829,682,380.94
135,733,962.98 23,621,219,338.66
579,064,006.34 335,315,123,440,286,000.00
Juni 18
24,451,483,354.00 23,519,693,894.01
22,898,987,320.48 24,140,400,467.55
155,176,643.38 23,965,416,343.92
486,067,010.08 236,261,138,285,539,000.00
Juli 19
24,403,585,445.00 23,696,472,204.21
23,058,484,297.22 24,334,460,111.20
159,496,976.75 24,295,577,110.93
108,008,334.07 11,665,800,227,538,400.00
Agustus 20
24,272,090,440.00 23,811,595,851.37
23,209,106,608.05 24,414,085,094.68
150,622,310.83 24,493,957,087.95
-221,866,647.95 49,224,809,470,435,100.00
September 21
24,082,631,404.00 23,865,802,961.89
23,340,445,878.82 24,391,160,044.97
131,339,270.77 24,564,707,405.51
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,002,975,099.72
23,472,951,723.00 24,532,998,476.43
132,505,844.18 24,522,499,315.74
29,164,335.26 850,558,451,301,988.00
Oktober 23
24,612,143,420.00 24,124,808,763.77
23,603,323,131.15 24,646,294,396.39
130,371,408.15 24,665,504,320.61
-53,360,900.61 2,847,385,714,024,350.00
Desember 24
20,195,839,321.00 23,339,014,875.22
23,550,461,479.97 23,127,568,270.47
-52,861,651.19 24,776,665,804.55
-4,580,826,483.55 20,983,971,272,353,600,000.00
2011 Januari
25 18,547,485,425.00
22,380,708,985.17 23,316,510,981.01
21,444,906,989.34 -233,950,498.96 23,074,706,619.28
-4,527,221,194.28 20,495,731,741,956,400,000.00
Februari 26
22,317,670,660.00 22,368,101,320.14
23,126,829,048.83 21,609,373,591.44 -189,681,932.17
21,210,956,490.38 1,106,714,169.62
1,224,816,253,233,270,000.00 Maret
27 23,490,850,795.00
22,592,651,215.11 23,019,993,482.09
22,165,308,948.13 -106,835,566.74 21,419,691,659.27
2,071,159,135.73 4,289,700,165,514,950,000.00
April 28
23,401,919,900.00 22,754,504,952.09
22,966,895,776.09 22,542,114,128.09
-53,097,706.00 22,058,473,381.39
1,343,446,518.61 1,804,848,548,368,990,000.00
Mei 29
24,440,969,550.00 23,091,797,871.67
22,991,876,195.21 23,191,719,548.14
24,980,419.12 22,489,016,422.09
1,951,953,127.91 3,810,121,013,563,190,000.00
Juni 30
25,113,931,440.00 23,496,224,585.34
23,092,745,873.23 23,899,703,297.44
100,869,678.03 23,216,699,967.25
1,897,231,472.75 3,599,487,261,181,770,000.00
Juli 31
25,401,258,645.00 23,877,231,397.27
23,249,642,978.04 24,504,819,816.50
156,897,104.81 24,000,572,975.47
1,400,685,669.53 1,961,920,344,832,040,000.00
Agustus 32
25,321,323,110.00 24,166,049,739.82
23,432,924,330.40 24,899,175,149.24
183,281,352.36 24,661,716,921.31
659,606,188.69 435,080,324,162,046,000.00
September 33
25,080,556,135.00 24,348,951,018.85
23,616,129,668.09 25,081,772,369.62
183,205,337.69 25,082,456,501.59
-1,900,366.59 3,611,393,182,782.71
Oktober 34
25,109,569,925.00 24,501,074,800.08
23,793,118,694.49 25,209,030,905.68
176,989,026.40 25,264,977,707.31
-155,407,782.31 24,151,578,802,572,100.00
Oktober 35
25,282,275,715.00 24,657,314,983.07
23,965,957,952.20 25,348,672,013.93
172,839,257.72 25,386,019,932.08
-103,744,217.08 10,762,862,577,050,200.00
Desember 36
25,569,779,015.00 24,839,807,789.45
24,140,727,919.65 25,538,887,659.25
174,769,967.45 25,521,511,271.65
48,267,743.35 2,329,775,048,518,180.00
SE 4,712,089,880.73
SSE
60,915,304,961,002,700,000.00
M SE
1,791,626,616,500,080,000.00
Tabel 4.3 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011 a = 0,2
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,3 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,3 21.548.149.420,00 + 1-0,3 21.473.831.050,00 = 21.496.126.561,00
Maret 2009 = 0,3 21.789.329.725,00 + 1-0,3 21.496.126.561,00
= 21.584.087.510,20 Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang
disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk = 0,3 dengan
menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,3 21.496.126.561,00 + 1-0,3
21.473.831.050,00 = 21.480.519.703,30
Maret 2009 = 0,3
21.584.087.510,20 + 1-0,3 21.480.519.703,30
= 21.511.590.045,37 Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.496.126.561,00 – 21.480.519.703,30
= 21.511.733.418,70 Maret 2009
= 221.584.087.510,20 - 21.511.590.045,37 = 21.656.584.975,03
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,3 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4 Februari 2009 =
, ,
21.496.126.561,00 – 21.480.519.703,30 = 6.688.653,30
Maret 2009 =
, ,
21.584.087.510,20 - 21.511.590.045,37 = 31.070.342,07
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.511.733.418,70 + 6.688.653,30 1
= 21.518.422.072,00 F
April 2009
untuk m = 1 = 21.656.584.975,03 + 31.070.342,07 1
= 21.687.655.317,10
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt
St St
a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,496,126,561.00
21,480,519,703.30 21,511,733,418.70
6,688,653.30 Maret
3 21,789,329,725.00
21,584,087,510.20 21,511,590,045.37
21,656,584,975.03 31,070,342.07
21,518,422,072.00 270,907,653.00
73,390,956,453,968,400.00 April
4 22,005,291,800.00
21,710,448,797.14 21,571,247,670.90
21,849,649,923.38 59,657,625.53
21,687,655,317.10 317,636,482.90
100,892,935,269,083,000.00 Mei
5 22,264,141,990.00
21,876,556,755.00 21,662,840,396.13
22,090,273,113.87 91,592,725.23
21,909,307,548.91 354,834,441.09
125,907,480,583,647,000.00 Juni
6 22,481,546,105.00
22,058,053,560.00 21,781,404,345.29
22,334,702,774.71 118,563,949.16
22,181,865,839.10 299,680,265.90
89,808,261,772,883,900.00 Juli
7 22,851,209,020.00
22,296,000,198.00 21,935,783,101.10
22,656,217,294.89 154,378,755.81
22,453,266,723.87 397,942,296.13
158,358,071,051,516,000.00 Agustus
8 22,845,663,820.00
22,460,899,284.60 22,093,317,956.15
22,828,480,613.05 157,534,855.05
22,810,596,050.71 35,067,769.29
1,229,748,443,158,930.00 September
9 22,927,399,070.00
22,600,849,220.22 22,245,577,335.37
22,956,121,105.07 152,259,379.22
22,986,015,468.10 -58,616,398.10
3,435,882,125,686,670.00 Oktober
10 22,854,910,720.00
22,677,067,670.15 22,375,024,435.81
22,979,110,904.50 129,447,100.43
23,108,380,484.29 -253,469,764.29
64,246,921,407,726,000.00 Oktober
11 22,764,705,655.00
22,703,359,065.61 22,473,524,824.75
22,933,193,306.47 98,500,388.94
23,108,558,004.94 -343,852,349.94
118,234,438,555,867,000.00 Desember
12 22,819,191,990.00
22,738,108,942.93 22,552,900,060.20
22,923,317,825.65 79,375,235.45
23,031,693,695.41 -212,501,705.41
45,156,974,801,498,500.00 2010
Januari 13
22,977,014,134.00 22,809,780,500.25
22,629,964,192.21 22,989,596,808.28
77,064,132.01 23,002,693,061.10
-25,678,927.10 659,407,297,194,526.00
Februari 14
22,942,268,240.00 22,849,526,822.17
22,695,832,981.20 23,003,220,663.14
65,868,788.99 23,066,660,940.30
-124,392,700.29 15,473,543,886,673,600.00
Maret 15
23,444,261,325.00 23,027,947,173.02
22,795,467,238.75 23,260,427,107.29
99,634,257.55 23,069,089,452.13
375,171,872.87 140,753,934,191,154,000.00
April 16
23,821,534,330.00 23,266,023,320.12
22,936,634,063.16 23,595,412,577.07
141,166,824.41 23,360,061,364.84
461,472,965.16 212,957,297,573,101,000.00
Mei 17
24,200,283,345.00 23,546,301,327.58
23,119,534,242.48 23,973,068,412.68
182,900,179.33 23,736,579,401.48
463,703,943.52 215,021,347,234,206,000.00
Juni 18
24,451,483,354.00 23,817,855,935.51
23,329,030,750.39 24,306,681,120.62
209,496,507.91 24,155,968,592.00
295,514,762.00 87,328,974,558,223,400.00
Juli 19
24,403,585,445.00 23,993,574,788.35
23,528,393,961.78 24,458,755,614.93
199,363,211.39 24,516,177,628.53
-112,592,183.53 12,676,999,791,571,900.00
Agustus 20
24,272,090,440.00 24,077,129,483.85
23,693,014,618.40 24,461,244,349.30
164,620,656.62 24,658,118,826.32
-386,028,386.32 149,017,915,042,979,000.00
September 21
24,082,631,404.00 24,078,780,059.89
23,808,744,250.85 24,348,815,868.94
115,729,632.45 24,625,865,005.92
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,220,645,137.23
23,932,314,516.76 24,508,975,757.69
123,570,265.91 24,464,545,501.39
87,118,149.61 7,589,571,992,033,410.00
Oktober 23
24,612,143,420.00 24,338,094,622.06
24,054,048,548.35 24,622,140,695.77
121,734,031.59 24,632,546,023.60
-20,402,603.60 416,266,233,766,231.00
Desember 24
20,195,839,321.00 23,095,418,031.74
23,766,459,393.37 22,424,376,670.11
-287,589,154.98 24,743,874,727.35
-4,548,035,406.35 20,684,626,057,451,200,000.00
2011 Januari
25 18,547,485,425.00
21,731,038,249.72 23,155,833,050.27
20,306,243,449.16 -610,626,343.09
22,136,787,515.13 -3,589,302,090.13
12,883,089,494,215,500,000.00 Februari
26 22,317,670,660.00
21,907,027,972.80 22,781,191,527.03
21,032,864,418.57 -374,641,523.24
19,695,617,106.07 2,622,053,553.93
6,875,164,839,680,990,000.00 Maret
27 23,490,850,795.00
22,382,174,819.46 22,661,486,514.76
22,102,863,124.16 -119,705,012.27
20,658,222,895.33 2,832,627,899.67
8,023,780,817,972,160,000.00 April
28 23,401,919,900.00
22,688,098,343.62 22,669,470,063.42
22,706,726,623.83 7,983,548.66
21,983,158,111.89 1,418,761,788.11
2,012,885,011,394,830,000.00 Mei
29 24,440,969,550.00
23,213,959,705.54 22,832,816,956.05
23,595,102,455.02 163,346,892.64
22,714,710,172.49 1,726,259,377.51
2,979,971,438,455,220,000.00 Juni
30 25,113,931,440.00
23,783,951,225.88 23,118,157,237.00
24,449,745,214.75 285,340,280.95
23,758,449,347.65 1,355,482,092.35
1,837,331,702,673,020,000.00 Juli
31 25,401,258,645.00
24,269,143,451.61 23,463,453,101.38
25,074,833,801.84 345,295,864.38
24,735,085,495.70 666,173,149.30
443,786,664,853,224,000.00 Agustus
32 25,321,323,110.00
24,584,797,349.13 23,799,856,375.71
25,369,738,322.55 336,403,274.32
25,420,129,666.22 -98,806,556.22
9,762,735,552,996,290.00 September
33 25,080,556,135.00
24,733,524,984.89 24,079,956,958.46
25,387,093,011.32 280,100,582.75
25,706,141,596.87 -625,585,461.87
391,357,170,107,462,000.00 Oktober
34 25,109,569,925.00
24,846,338,466.92 24,309,871,411.00
25,382,805,522.85 229,914,452.54
25,667,193,594.07 -557,623,669.07
310,944,156,310,156,000.00 Oktober
35 25,282,275,715.00
24,977,119,641.35 24,510,045,880.10
25,444,193,402.59 200,174,469.10
25,612,719,975.38 -330,444,260.38
109,193,409,220,620,000.00 Desember
36 25,569,779,015.00
25,154,917,453.44 24,703,507,352.11
25,606,327,554.78 193,461,472.00
25,644,367,871.69 -74,588,856.69
5,563,497,542,579,510.00 SE
2,553,570,206.00 SSE
58,194,228,132,410,500,000.00 MSE
1,711,594,945,070,900,000.00
Tabel 4.4 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011 a = 0,3
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,4 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,4 21.548.149.420,00 + 1-0,4 21.473.831.050,00 = 21.503.558.398,00
Maret 2009 = 0,4 21.789.329.725,00 + 1-0,4 21.503.558.398,00
= 21.617.866.928,80 Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang
disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk = 0,4 dengan
menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,4 21.503.558.398,00 + 1-0,4
21.473.831.050,00 = 21.485.721.989,20
Maret 2009 = 0,4
21.617.866.928,80+1-0,4 21.485.721.989,20
= 21.538.579.965,04 Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.503.558.398,00 – 21.485.721.989,20
= 21.521.394.806,80 Maret 2009
= 221.617.866.928,80 - 21.538.579.965,04 = 21.697.153.892,56
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,4 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4 Februari 2009 =
, ,
21.503.558.398,00 – 21.485.721.989,20 = 11.890.939,20
Maret 2009 =
, ,
21.617.866.928,80 - 21.538.579.965,04 = 52.857.975,84
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.521.394.806,80 + 11.890.939,20 1
= 21.533.285.746,00 F
April 2009
untuk m = 1 = 21.697.153.892,56 + 52.857.975,84 1
= 21.750.011.868,40
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt
St St
a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,503,558,398.00
21,485,721,989.20 21,521,394,806.80
11,890,939.20 Maret
3 21,789,329,725.00
21,617,866,928.80 21,538,579,965.04
21,697,153,892.56 52,857,975.84
21,533,285,746.00 256,043,979.00
65,558,519,182,152,400.00 April
4 22,005,291,800.00
21,772,836,877.28 21,632,282,729.94
21,913,391,024.62 93,702,764.90
21,750,011,868.40 255,279,931.60
65,167,843,477,701,800.00 Mei
5 22,264,141,990.00
21,969,358,922.37 21,767,113,206.91
22,171,604,637.83 134,830,476.97
22,007,093,789.52 257,048,200.48
66,073,777,370,008,000.00 Juni
6 22,481,546,105.00
22,174,233,795.42 21,929,961,442.31
22,418,506,148.53 162,848,235.40
22,306,435,114.80 175,110,990.20
30,663,858,888,827,400.00 Juli
7 22,851,209,020.00
22,445,023,885.25 22,135,986,419.49
22,754,061,351.02 206,024,977.18
22,581,354,383.93 269,854,636.07
72,821,524,606,960,800.00 Agustus
8 22,845,663,820.00
22,605,279,859.15 22,323,703,795.35
22,886,855,922.95 187,717,375.86
22,960,086,328.19 -114,422,508.19
13,092,510,380,802,000.00 September
9 22,927,399,070.00
22,734,127,543.49 22,487,873,294.61
22,980,381,792.37 164,169,499.25
23,074,573,298.81 -147,174,228.81
21,660,253,626,943,700.00 Oktober
10 22,854,910,720.00
22,782,440,814.09 22,605,700,302.40
22,959,181,325.79 117,827,007.79
23,144,551,291.63 -289,640,571.63
83,891,660,732,814,700.00 Oktober
11 22,764,705,655.00
22,775,346,750.46 22,673,558,881.62
22,877,134,619.29 67,858,579.22
23,077,008,333.58 -312,302,678.58
97,532,963,048,408,300.00 Desember
12 22,819,191,990.00
22,792,884,846.27 22,721,289,267.48
22,864,480,425.06 47,730,385.86
22,944,993,198.51 -125,801,208.51
15,825,944,062,661,500.00 2010
Januari 13
22,977,014,134.00 22,866,536,561.36
22,779,388,185.04 22,953,684,937.69
58,098,917.55 22,912,210,810.92
64,803,323.08 4,199,470,681,754,760.00
Februari 14
22,942,268,240.00 22,896,829,232.82
22,826,364,604.15 22,967,293,861.49
46,976,419.11 23,011,783,855.24
-69,515,615.24 4,832,420,762,821,250.00
Maret 15
23,444,261,325.00 23,115,802,069.69
22,942,139,590.37 23,289,464,549.02
115,774,986.22 23,014,270,280.60
429,991,044.40 184,892,298,263,407,000.00
April 16
23,821,534,330.00 23,398,094,973.81
23,124,521,743.75 23,671,668,203.88
182,382,153.38 23,405,239,535.23
416,294,794.77 173,301,356,150,021,000.00
Mei 17
24,200,283,345.00 23,718,970,322.29
23,362,301,175.16 24,075,639,469.41
237,779,431.42 23,854,050,357.26
346,232,987.74 119,877,281,797,028,000.00
Juni 18
24,451,483,354.00 24,011,975,534.97
23,622,170,919.09 24,401,780,150.86
259,869,743.92 24,313,418,900.83
138,064,453.17 19,061,793,228,541,800.00
Juli 19
24,403,585,445.00 24,168,619,498.98
23,840,750,351.05 24,496,488,646.92
218,579,431.96 24,661,649,894.78
-258,064,449.78 66,597,260,242,192,900.00
Agustus 20
24,272,090,440.00 24,210,007,875.39
23,988,453,360.78 24,431,562,390.00
147,703,009.74 24,715,068,078.88
-442,977,638.88 196,229,188,548,529,000.00
September 21
24,082,631,404.00 24,159,057,286.83
24,056,694,931.20 24,261,419,642.46
68,241,570.42 24,579,265,399.74
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,316,099,832.50
24,160,456,891.72 24,471,742,773.28
103,761,960.52 24,329,661,212.88
222,002,438.12 49,285,082,529,081,400.00
Oktober 23
24,612,143,420.00 24,434,517,267.50
24,270,081,042.03 24,598,953,492.97
109,624,150.31 24,575,504,733.80
36,638,686.20 1,342,393,326,667,300.00
Desember 24
20,195,839,321.00 22,739,046,088.90
23,657,667,060.78 21,820,425,117.02
-612,413,981.25 24,708,577,643.28
-4,512,738,322.28 20,364,807,165,357,400,000.00
2011 Januari
25 18,547,485,425.00
21,062,421,823.34 22,619,568,965.80
19,505,274,680.88 -1,038,098,094.98
21,208,011,135.77 -2,660,525,710.77
7,078,397,057,650,820,000.00 Februari
26 22,317,670,660.00
21,564,521,358.00 22,197,549,922.68
20,931,492,793.32 -422,019,043.12
18,467,176,585.90 3,850,494,074.10
14,826,304,614,679,500,000.00 Maret
27 23,490,850,795.00
22,335,053,132.80 22,252,551,206.73
22,417,555,058.87 55,001,284.05
20,509,473,750.20 2,981,377,044.80
8,888,609,083,236,970,000.00 April
28 23,401,919,900.00
22,761,799,839.68 22,456,250,659.91
23,067,349,019.45 203,699,453.18
22,472,556,342.92 929,363,557.08
863,716,621,227,054,000.00 Mei
29 24,440,969,550.00
23,433,467,723.81 22,847,137,485.47
24,019,797,962.15 390,886,825.56
23,271,048,472.63 1,169,921,077.37
1,368,715,327,271,190,000.00 Juni
30 25,113,931,440.00
24,105,653,210.29 23,350,543,775.40
24,860,762,645.17 503,406,289.93
24,410,684,787.71 703,246,652.29
494,555,853,962,314,000.00 Juli
31 25,401,258,645.00
24,623,895,384.17 23,859,884,418.91
25,387,906,349.44 509,340,643.51
25,364,168,935.10 37,089,709.90
1,375,646,580,449,580.00 Agustus
32 25,321,323,110.00
24,902,866,474.50 24,277,077,241.14
25,528,655,707.86 417,192,822.24
25,897,246,992.95 -575,923,882.95
331,688,318,947,601,000.00 September
33 25,080,556,135.00
24,973,942,338.70 24,555,823,280.17
25,392,061,397.24 278,746,039.02
25,945,848,530.10 -865,292,395.10
748,730,929,016,367,000.00 Oktober
34 25,109,569,925.00
25,028,193,373.22 24,744,771,317.39
25,311,615,429.05 188,948,037.22
25,670,807,436.26 -561,237,511.26
314,987,544,043,505,000.00 Oktober
35 25,282,275,715.00
25,129,826,309.93 24,898,793,314.41
25,360,859,305.46 154,021,997.02
25,500,563,466.27 -218,287,751.27
47,649,542,356,423,800.00 Desember
36 25,569,779,015.00
25,305,807,391.96 25,061,598,945.43
25,550,015,838.49 162,805,631.02
25,514,881,302.48 54,897,712.52
3,013,758,840,342,010.00 SE
1,374,933,882.58 SSE
56,688,673,072,791,900,000.00 MSE
1,667,313,913,905,640,000.00
Tabel 4.5 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011 a = 0,4
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,5 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,5 21.548.149.420,00 + 1-0,5 21.473.831.050,00 = 21.510.990.235,00
Maret 2009 = 0,5 21.789.329.725,00 + 1-0,5 21.510.990.235,00
= 21.650.159.980,00 Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang
disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk = 0,5 dengan
menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,5 21.510.990.235,00 + 1-0,5
21.473.831.050,00 = 21.492.410.642,50
Maret 2009 = 0,5
21.650.159.980,00 + 1-0,5 21.492.410.642,50 = 21.571.285.311,25
Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.510.990.235,00 – 21.492.410.642,50
= 21.529.569.827,50 Maret 2009
= 221.650.159.980,00 - 21.571.285.311,25 = 21.729.034.648,75
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,5 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4 Februari 2009 =
, ,
21.510.990.235,00 – 21.492.410.642,50 = 18.579.592,50
Maret 2009 =
, ,
21.650.159.980,00 - 21.571.285.311,25 = 78.874.668,75
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.529.569.827,50 + 18.579.592,50 1
= 21.548.149.420,00 F
April 2009
untuk m = 1 = 21.729.034.648,75 + 78.874.668,75 1
= 21.807.909.317,50
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt St
St a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,510,990,235.00
21,492,410,642.50 21,529,569,827.50
18,579,592.50 Maret
3 21,789,329,725.00
21,650,159,980.00 21,571,285,311.25
21,729,034,648.75 78,874,668.75
21,548,149,420.00 241,180,305.00
58,167,939,519,893,000.00 April
4 22,005,291,800.00
21,827,725,890.00 21,699,505,600.63
21,955,946,179.38 128,220,289.38
21,807,909,317.50 197,382,482.50
38,959,844,397,862,800.00 Mei
5 22,264,141,990.00
22,045,933,940.00 21,872,719,770.31
22,219,148,109.69 173,214,169.69
22,084,166,468.75 179,975,521.25
32,391,188,249,209,200.00 Juni
6 22,481,546,105.00
22,263,740,022.50 22,068,229,896.41
22,459,250,148.59 195,510,126.09
22,392,362,279.38 89,183,825.63
7,953,754,753,110,410.00 Juli
7 22,851,209,020.00
22,557,474,521.25 22,312,852,208.83
22,802,096,833.67 244,622,312.42
22,654,760,274.69 196,448,745.31
38,592,109,534,855,500.00 Agustus
8 22,845,663,820.00
22,701,569,170.63 22,507,210,689.73
22,895,927,651.52 194,358,480.90
23,046,719,146.09 -201,055,326.09
40,423,244,150,664,200.00 September
9 22,927,399,070.00
22,814,484,120.31 22,660,847,405.02
22,968,120,835.61 153,636,715.29
23,090,286,132.42 -162,887,062.42
26,532,195,104,427,800.00 Oktober
10 22,854,910,720.00
22,834,697,420.16 22,747,772,412.59
22,921,622,427.72 86,925,007.57
23,121,757,550.90 -266,846,830.90
71,207,231,160,539,300.00 Oktober
11 22,764,705,655.00
22,799,701,537.58 22,773,736,975.08
22,825,666,100.07 25,964,562.50
23,008,547,435.29 -243,841,780.29
59,458,813,816,444,400.00 Desember
12 22,819,191,990.00
22,809,446,763.79 22,791,591,869.44
22,827,301,658.14 17,854,894.35
22,851,630,662.57 -32,438,672.57
1,052,267,477,997,230.00 2010
Januari 13
22,977,014,134.00 22,893,230,448.89
22,842,411,159.17 22,944,049,738.62
50,819,289.73 22,845,156,552.50
131,857,581.50 17,386,421,800,316,800.00
Februari 14
22,942,268,240.00 22,917,749,344.45
22,880,080,251.81 22,955,418,437.09
37,669,092.64 22,994,869,028.35
-52,600,788.35 2,766,842,935,359,980.00
Maret 15
23,444,261,325.00 23,181,005,334.72
23,030,542,793.27 23,331,467,876.18
150,462,541.46 22,993,087,529.73
451,173,795.27 203,557,793,539,014,000.00
April 16
23,821,534,330.00 23,501,269,832.36
23,265,906,312.81 23,736,633,351.91
235,363,519.55 23,481,930,417.64
339,603,912.36 115,330,817,289,545,000.00
Mei 17
24,200,283,345.00 23,850,776,588.68
23,558,341,450.75 24,143,211,726.61
292,435,137.93 23,971,996,871.46
228,286,473.54 52,114,714,001,932,200.00
Juni 18
24,451,483,354.00 24,151,129,971.34
23,854,735,711.04 24,447,524,231.64
296,394,260.30 24,435,646,864.55
15,836,489.45 250,794,398,149,644.00
Juli 19
24,403,585,445.00 24,277,357,708.17
24,066,046,709.61 24,488,668,706.73
211,310,998.56 24,743,918,491.93
-340,333,046.93 115,826,582,835,218,000.00
Agustus 20
24,272,090,440.00 24,274,724,074.09
24,170,385,391.85 24,379,062,756.32
104,338,682.24 24,699,979,705.30
-427,889,265.30 183,089,223,356,110,000.00
September 21
24,082,631,404.00 24,178,677,739.04
24,174,531,565.44 24,182,823,912.64
4,146,173.60 24,483,401,438.56
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,365,170,695.02
24,269,851,130.23 24,460,490,259.81
95,319,564.79 24,186,970,086.24
364,693,564.76 133,001,396,178,048,000.00
Oktober 23
24,612,143,420.00 24,488,657,057.51
24,379,254,093.87 24,598,060,021.15
109,402,963.64 24,555,809,824.60
56,333,595.40 3,173,473,970,888,780.00
Desember 24
20,195,839,321.00 22,342,248,189.26
23,360,751,141.56 21,323,745,236.95
-1,018,502,952.31 24,707,462,984.79
-4,511,623,663.79 20,354,748,083,656,200,000.00
2011 Januari
25 18,547,485,425.00
20,444,866,807.13 21,902,808,974.35
18,986,924,639.91 -1,457,942,167.22
20,305,242,284.64 -1,757,756,859.64
3,089,709,177,607,660,000.00 Februari
26 22,317,670,660.00
21,381,268,733.56 21,642,038,853.95
21,120,498,613.17 -260,770,120.39
17,528,982,472.69 4,788,688,187.31
22,931,534,555,265,100,000.00 Maret
27 23,490,850,795.00
22,436,059,764.28 22,039,049,309.12
22,833,070,219.45 397,010,455.16
20,859,728,492.78 2,631,122,302.22
6,922,804,569,228,600,000.00 April
28 23,401,919,900.00
22,918,989,832.14 22,479,019,570.63
23,358,960,093.65 439,970,261.51
23,230,080,674.61 171,839,225.39
29,528,719,382,936,500.00 Mei
29 24,440,969,550.00
23,679,979,691.07 23,079,499,630.85
24,280,459,751.29 600,480,060.22
23,798,930,355.16 642,039,194.84
412,214,327,706,162,000.00 Juni
30 25,113,931,440.00
24,396,955,565.54 23,738,227,598.19
25,055,683,532.88 658,727,967.34
24,880,939,811.51 232,991,628.49
54,285,098,945,802,600.00 Juli
31 25,401,258,645.00
24,899,107,105.27 24,318,667,351.73
25,479,546,858.81 580,439,753.54
25,714,411,500.22 -313,152,855.22
98,064,710,732,701,900.00 Agustus
32 25,321,323,110.00
25,110,215,107.63 24,714,441,229.68
25,505,988,985.59 395,773,877.95
26,059,986,612.34 -738,663,502.34
545,623,769,693,028,000.00 September
33 25,080,556,135.00
25,095,385,621.32 24,904,913,425.50
25,285,857,817.13 190,472,195.82
25,901,762,863.54 -821,206,728.54
674,380,490,995,248,000.00 Oktober
34 25,109,569,925.00
25,102,477,773.16 25,003,695,599.33
25,201,259,946.99 98,782,173.83
25,476,330,012.95 -366,760,087.95
134,512,962,114,441,000.00 November
35 25,282,275,715.00
25,192,376,744.08 25,098,036,171.70
25,286,717,316.45 94,340,572.38
25,300,042,120.82 -17,766,405.82
315,645,175,670,916.00 Desember
36 25,569,779,015.00
25,381,077,879.54 25,239,557,025.62
25,522,598,733.46 141,520,853.92
25,381,057,888.83 188,721,126.17
35,615,663,463,058,100.00
SE
827,618,143.19
SSE
56,488,788,631,150,800,000.00
M SE
1,661,434,959,739,730,000.00
a = 0,5 Tabel 4.6 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,6 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,6 21.548.149.420,00 + 1-0,6 21.473.831.050,00 = 21.518.422.072,00
Maret 2009 = 0,6 21.789.329.725,00 + 1-0,6 21.518.422.072,00
=21.680.966.663,80 Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang
disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk = 0,6 dengan
menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,6 21.518.422.072,00 + 1-0,6
21.473.831.050,00 = 21.500.585.663,20
Maret 2009 = 0,6
21.680.966.663,80 + 1-0,6 21.500.585.663,20
= 21.608.814.263,56 Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.518.422.072,00 – 21.500.585.663,20
= 21.536.258.480,80 Maret 2009
= 221.680.966.663,80 - 21.608.814.263,56 = 21.753.119.064,04
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,6 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4 Februari 2009 =
, ,
21.518.422.072,00 – 21.500.585.663,20 = 26.754.613,20
Maret 2009 =
, ,
21.680.966.663,80 - 21.608.814.263,56 = 108.228.600,36
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.536.258.480,80 + 26.754.613,20 1
= 21.563.013.094,00 F
April 2009
untuk m = 1 = 21.753.119.064,04 + 108.228.600,36 1
= 21.861.347.664,40
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt
St St
a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,518,422,072.00
21,500,585,663.20 21,536,258,480.80
26,754,613.20 Maret
3 21,789,329,725.00
21,680,966,663.80 21,608,814,263.56
21,753,119,064.04 108,228,600.36
21,563,013,094.00 226,316,631.00
51,219,217,467,186,700.00 April
4 22,005,291,800.00
21,875,561,745.52 21,768,862,752.74
21,982,260,738.30 160,048,489.18
21,861,347,664.40 143,944,135.60
20,719,914,173,626,400.00 Mei
5 22,264,141,990.00
22,108,709,892.21 21,972,771,036.42
22,244,648,748.00 203,908,283.68
22,142,309,227.48 121,832,762.52
14,843,222,023,251,100.00 Juni
6 22,481,546,105.00
22,332,411,619.88 22,188,555,386.50
22,476,267,853.27 215,784,350.08
22,448,557,031.68 32,989,073.32
1,088,278,958,512,570.00 Juli
7 22,851,209,020.00
22,643,690,059.95 22,461,636,190.57
22,825,743,929.34 273,080,804.07
22,692,052,203.35 159,156,816.65
25,330,892,287,052,300.00 Agustus
8 22,845,663,820.00
22,764,874,315.98 22,643,579,065.82
22,886,169,566.15 181,942,875.25
23,098,824,733.41 -253,160,913.41
64,090,448,078,062,000.00 September
9 22,927,399,070.00
22,862,389,168.39 22,774,865,127.36
22,949,913,209.42 131,286,061.55
23,068,112,441.39 -140,713,371.39
19,800,252,888,397,200.00 Oktober
10 22,854,910,720.00
22,857,902,099.36 22,824,687,310.56
22,891,116,888.15 49,822,183.20
23,081,199,270.97 -226,288,550.97
51,206,508,299,130,900.00 Oktober
11 22,764,705,655.00
22,801,984,232.74 22,811,065,463.87
22,792,903,001.62 -13,621,846.69
22,940,939,071.35 -176,233,416.35
31,058,217,038,963,300.00 Desember
12 22,819,191,990.00
22,812,308,887.10 22,811,811,517.81
22,812,806,256.39 746,053.94
22,779,281,154.93 39,910,835.07
1,592,874,756,268,510.00 2010
Januari 13
22,977,014,134.00 22,911,132,035.24
22,871,403,828.27 22,950,860,242.21
59,592,310.46 22,813,552,310.32
163,461,823.68 26,719,767,799,192,700.00
Februari 14
22,942,268,240.00 22,929,813,758.10
22,906,449,786.16 22,953,177,730.03
35,045,957.90 23,010,452,552.67
-68,184,312.67 4,649,100,494,509,480.00
Maret 15
23,444,261,325.00 23,238,482,298.24
23,105,669,293.41 23,371,295,303.07
199,219,507.24 22,988,223,687.93
456,037,637.07 207,970,326,428,613,000.00
April 16
23,821,534,330.00 23,588,313,517.30
23,395,255,827.74 23,781,371,206.85
289,586,534.33 23,570,514,810.31
251,019,519.69 63,010,799,263,980,400.00
Mei 17
24,200,283,345.00 23,955,495,413.92
23,731,399,579.45 24,179,591,248.39
336,143,751.71 24,070,957,741.18
129,325,603.82 16,725,111,802,839,200.00
Juni 18
24,451,483,354.00 24,253,088,177.97
24,044,412,738.56 24,461,763,617.38
313,013,159.11 24,515,735,000.10
-64,251,646.10 4,128,274,026,006,990.00
Juli 19
24,403,585,445.00 24,343,386,538.19
24,223,797,018.34 24,462,976,058.04
179,384,279.78 24,774,776,776.49
-371,191,331.49 137,783,004,571,397,000.00
Agustus 20
24,272,090,440.00 24,300,608,879.27
24,269,884,134.90 24,331,333,623.65
46,087,116.56 24,642,360,337.81
-370,269,897.81 137,099,797,227,641,000.00
September 21
24,082,631,404.00 24,169,822,394.11
24,209,847,090.43 24,129,797,697.79
-60,037,044.47 24,377,420,740.21
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,398,927,148.24
24,323,295,125.12 24,474,559,171.37
113,448,034.69 24,069,760,653.32
481,902,997.68 232,230,499,172,371,000.00
Oktober 23
24,612,143,420.00 24,526,856,911.30
24,445,432,196.83 24,608,281,625.77
122,137,071.71 24,588,007,206.06
24,136,213.94 582,556,823,246,161.00
Desember 24
20,195,839,321.00 21,928,246,357.12
22,935,120,693.00 20,921,372,021.24
-1,510,311,503.82 24,730,418,697.48
-4,534,579,376.48 20,562,410,121,584,500,000.00
2011 Januari
25 18,547,485,425.00
19,899,789,797.85 21,113,922,155.91
18,685,657,439.79 -1,821,198,537.09
19,411,060,517.41 -863,575,092.41
745,761,940,235,881,000.00 Februari
26 22,317,670,660.00
21,350,518,315.14 21,255,879,851.45
21,445,156,778.83 141,957,695.54
16,864,458,902.69 5,453,211,757.31
29,737,518,470,023,400,000.00 Maret
27 23,490,850,795.00
22,634,717,803.06 22,083,182,622.41
23,186,252,983.70 827,302,770.97
21,587,114,474.37 1,903,736,320.63
3,624,211,978,489,980,000.00 April
28 23,401,919,900.00
23,095,039,061.22 22,690,296,485.70
23,499,781,636.75 607,113,863.29
24,013,555,754.66 -611,635,854.66
374,098,418,710,736,000.00 Mei
29 24,440,969,550.00
23,902,597,354.49 23,417,677,006.97
24,387,517,702.01 727,380,521.27
24,106,895,500.03 334,074,049.97
111,605,470,861,835,000.00 Juni
30 25,113,931,440.00
24,629,397,805.80 24,144,709,486.27
25,114,086,125.32 727,032,479.29
25,114,898,223.28 -966,783.28
934,669,909,644.34 Juli
31 25,401,258,645.00
25,092,514,309.32 24,713,392,380.10
25,471,636,238.54 568,682,893.83
25,841,118,604.62 -439,859,959.62
193,476,784,075,588,000.00 Agustus
32 25,321,323,110.00
25,229,799,589.73 25,023,236,705.88
25,436,362,473.58 309,844,325.78
26,040,319,132.37 -718,996,022.37
516,955,280,183,979,000.00 September
33 25,080,556,135.00
25,140,253,516.89 25,093,446,792.48
25,187,060,241.30 70,210,086.61
25,746,206,799.36 -665,650,664.36
443,090,806,959,040,000.00 Oktober
34 25,109,569,925.00
25,121,843,361.76 25,110,484,734.05
25,133,201,989.47 17,037,941.56
25,257,270,327.91 -147,700,402.91
21,815,409,018,731,700.00 Oktober
35 25,282,275,715.00
25,218,102,773.70 25,175,055,557.84
25,261,149,989.56 64,570,823.79
25,150,239,931.03 132,035,783.97
17,433,448,249,091,600.00 Desember
36 25,569,779,015.00
25,429,108,518.48 25,327,487,334.22
25,530,729,702.74 152,431,776.38
25,325,720,813.36 244,058,201.64
59,564,405,789,024,200.00 SE
578,975,630.24 SSE
57,524,006,741,146,600,000.00 MSE
1,691,882,551,210,190,000.00
Tabel 4.7 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011 a = 0,6
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,7 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,7 21.548.149.420,00 + 1-0,7 21.473.831.050,00 = 21.525.853.909,00
Maret 2009 = 0,7 21.789.329.725,00 + 1-0,7 21.525.853.909,00
= 21.710.286.980,20 Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang
disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk = 0,7 dengan
menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,7 21.525.853.909,00 + 1-0,7
21.473.831.050,00 = 21.510.247.051,30
Maret 2009 = 0,7
21.710.286.980,20 + 1-0,7 21.510.247.051,30
= 21.650.275.001,53 Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.525.853.909,00 – 21.510.247.051,30
= 21.541.460.766,70 Maret 2009
= 221.710.286.980,20 - 21.650.275.001,53 = 21.770.298.958,87
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,7 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4 Februari 2009 =
, ,
21.525.853.909,00 – 21.510.247.051,30 = 36.416.001,30
Maret 2009 =
, ,
21.710.286.980,20 - 21.650.275.001,53 = 140.027.950,23
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.541.460.766,70 + 36.416.001,30 1
= 21.577.876.768,00 F
April 2009
untuk m = 1 = 21.770.298.958,87 + 140.027.950,23 1
=21.910.326.909,10
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt
St St
a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,525,853,909.00
21,510,247,051.30 21,541,460,766.70
36,416,001.30 Maret
3 21,789,329,725.00
21,710,286,980.20 21,650,275,001.53
21,770,298,958.87 140,027,950.23
21,577,876,768.00 211,452,957.00
44,712,353,024,042,200.00 April
4 22,005,291,800.00
21,916,790,354.06 21,836,835,748.30
21,996,744,959.82 186,560,746.77
21,910,326,909.10 94,964,890.90
9,018,330,503,650,640.00 Mei
5 22,264,141,990.00
22,159,936,499.22 22,063,006,273.94
22,256,866,724.49 226,170,525.64
22,183,305,706.59 80,836,283.41
6,534,504,715,540,580.00 Juni
6 22,481,546,105.00
22,385,063,223.27 22,288,446,138.47
22,481,680,308.06 225,439,864.53
22,483,037,250.14 -1,491,145.14
2,223,513,813,640.54 Juli
7 22,851,209,020.00
22,711,365,280.98 22,584,489,538.23
22,838,241,023.73 296,043,399.76
22,707,120,172.59 144,088,847.41
20,761,595,948,545,700.00 Agustus
8 22,845,663,820.00
22,805,374,258.29 22,739,108,842.27
22,871,639,674.31 154,619,304.05
23,134,284,423.49 -288,620,603.49
83,301,852,759,274,100.00 September
9 22,927,399,070.00
22,890,791,626.49 22,845,286,791.22
22,936,296,461.75 106,177,948.95
23,026,258,978.36 -98,859,908.36
9,773,281,481,235,080.00 Oktober
10 22,854,910,720.00
22,865,674,991.95 22,859,558,531.73
22,871,791,452.16 14,271,740.51
23,042,474,410.70 -187,563,690.70
35,180,138,070,024,400.00 Oktober
11 22,764,705,655.00
22,794,996,456.08 22,814,365,078.78
22,775,627,833.39 -45,193,452.95
22,886,063,192.67 -121,357,537.67
14,727,651,949,107,400.00 Desember
12 22,819,191,990.00
22,811,933,329.83 22,812,662,854.51
22,811,203,805.14 -1,702,224.27
22,730,434,380.44 88,757,609.56
7,877,913,255,121,880.00 2010
Januari 13
22,977,014,134.00 22,927,489,892.75
22,893,041,781.28 22,961,938,004.22
80,378,926.77 22,809,501,580.87
167,512,553.13 28,060,455,455,225,300.00
Februari 14
22,942,268,240.00 22,937,834,735.82
22,924,396,849.46 22,951,272,622.19
31,355,068.18 23,042,316,930.98
-100,048,690.98 10,009,740,567,651,100.00
Maret 15
23,444,261,325.00 23,292,333,348.25
23,181,952,398.61 23,402,714,297.88
257,555,549.15 22,982,627,690.37
461,633,634.63 213,105,612,619,888,000.00
April 16
23,821,534,330.00 23,662,774,035.47
23,518,527,544.42 23,807,020,526.53
336,575,145.80 23,660,269,847.03
161,264,482.97 26,006,233,466,094,300.00
Mei 17
24,200,283,345.00 24,039,030,552.14
23,882,879,649.82 24,195,181,454.46
364,352,105.41 24,143,595,672.34
56,687,672.66 3,213,492,231,914,360.00
Juni 18
24,451,483,354.00 24,327,747,513.44
24,194,287,154.36 24,461,207,872.53
311,407,504.53 24,559,533,559.87
-108,050,205.87 11,674,846,988,390,900.00
Juli 19
24,403,585,445.00 24,380,834,065.53
24,324,869,992.18 24,436,798,138.89
130,582,837.82 24,772,615,377.06
-369,029,932.06 136,183,090,757,102,000.00
Agustus 20
24,272,090,440.00 24,304,713,527.66
24,310,760,467.02 24,298,666,588.30
-14,109,525.16 24,567,380,976.71
-295,290,536.71 87,196,501,069,587,200.00
September 21
24,082,631,404.00 24,149,256,041.10
24,197,707,368.87 24,100,804,713.32
-113,053,098.14 24,284,557,063.14
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,430,941,368.03
24,360,971,168.28 24,500,911,567.78
163,263,799.41 23,987,751,615.18
563,912,035.82 317,996,784,142,665,000.00
Oktober 23
24,612,143,420.00 24,557,782,804.41
24,498,739,313.57 24,616,826,295.25
137,768,145.29 24,664,175,367.19
-52,031,947.19 2,707,323,527,907,630.00
Desember 24
20,195,839,321.00 21,504,422,366.02
22,402,717,450.29 20,606,127,281.76
-2,096,021,863.28 24,754,594,440.54
-4,558,755,119.54 20,782,248,239,887,100,000.00
2011 Januari
25 18,547,485,425.00
19,434,566,507.31 20,325,011,790.20
18,544,121,224.41 -2,077,705,660.09
18,510,105,418.47 37,380,006.53
1,397,264,887,857,640.00 Februari
26 22,317,670,660.00
21,452,739,414.19 21,114,421,126.99
21,791,057,701.39 789,409,336.79
16,466,415,564.33 5,851,255,095.67
34,237,186,194,645,600,000.00 Maret
27 23,490,850,795.00
22,879,417,380.76 22,349,918,504.63
23,408,916,256.89 1,235,497,377.63
22,580,467,038.18 910,383,756.82
828,798,584,675,890,000.00 April
28 23,401,919,900.00
23,245,169,144.23 22,976,593,952.35
23,513,744,336.11 626,675,447.72
24,644,413,634.52 -1,242,493,734.52
1,543,790,680,322,770,000.00 Mei
29 24,440,969,550.00
24,082,229,428.27 23,750,538,785.49
24,413,920,071.04 773,944,833.14
24,140,419,783.83 300,549,766.17
90,330,161,947,346,800.00 Juni
30 25,113,931,440.00
24,804,420,836.48 24,488,256,221.18
25,120,585,451.78 737,717,435.69
25,187,864,904.19 -73,933,464.19
5,466,157,126,935,260.00 Juli
31 25,401,258,645.00
25,222,207,302.44 25,002,021,978.07
25,442,392,626.82 513,765,756.88
25,858,302,887.47 -457,044,242.47
208,889,439,573,942,000.00 Agustus
32 25,321,323,110.00
25,291,588,367.73 25,204,718,450.83
25,378,458,284.63 202,696,472.77
25,956,158,383.70 -634,835,273.70
403,015,824,739,276,000.00 September
33 25,080,556,135.00
25,143,865,804.82 25,162,121,598.62
25,125,610,011.02 -42,596,852.21
25,581,154,757.40 -500,598,622.40
250,598,980,749,188,000.00 Oktober
34 25,109,569,925.00
25,119,858,688.95 25,132,537,561.85
25,107,179,816.04 -29,584,036.77
25,083,013,158.81 26,556,766.19
705,261,830,637,409.00 Oktober
35 25,282,275,715.00
25,233,550,607.18 25,203,246,693.58
25,263,854,520.78 70,709,131.73
25,077,595,779.27 204,679,935.73
41,893,876,091,223,800.00 Desember
36 25,569,779,015.00
25,468,910,492.66 25,389,211,352.93
25,548,609,632.38 185,964,659.35
25,334,563,652.52 235,215,362.48
55,326,266,747,430,200.00 SE
442,210,065.06 SSE
59,521,905,067,986,600,000.00 MSE
1,750,644,266,705,490,000.00
Tabel 4.8 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011 a = 0,7
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,8 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,8 21.548.149.420,00 + 1-0,8 21.473.831.050,00 = 21.533.285.746,00
Maret 2009 = 0,8 21.789.329.725,00 + 1-0,8 21.533.285.746,00
= 21.738.120.929,20 Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang
disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk = 0,8 dengan
menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,8 21.533.285.746,00 + 1-0,8
21.473.831.050,00 = 21.521.394.806,80
Maret 2009 = 0,8
21.738.120.929,20 + 1-0,8 21.521.394.806,80
= 21.694.775.704,72 Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.533.285.746,00 – 21.521.394.806,80
= 21.545.176.685,20 Maret 2009
= 221.738.120.929,20 - 21.694.775.704,72 = 21.781.466.153,68
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,8 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4 Februari 2009 =
, ,
21.533.285.746,00 – 21.521.394.806,80 = 47.563.756,80
Maret 2009 =
, ,
21.738.120.929,20 - 21.694.775.704,72 = 173.380.897,92
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.545.176.685,20 + 47.563.756,80 1
= 21.592.740.442,00 F
April 2009
untuk m = 1 = 21.781.466.153,68 + 173.380.897,92 1
= 21.954.847.051,60
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt St
St a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,533,285,746.00
21,521,394,806.80 21,545,176,685.20
47,563,756.80 Maret
3 21,789,329,725.00
21,738,120,929.20 21,694,775,704.72
21,781,466,153.68 173,380,897.92
21,592,740,442.00 196,589,283.00
38,647,346,190,452,600.00 April
4 22,005,291,800.00
21,951,857,625.84 21,900,441,241.62
22,003,274,010.06 205,665,536.90
21,954,847,051.60 50,444,748.40
2,544,672,641,139,460.00 Mei
5 22,264,141,990.00
22,201,685,117.17 22,141,436,342.06
22,261,933,892.28 240,995,100.44
22,208,939,546.96 55,202,443.04
3,047,309,717,584,970.00 Juni
6 22,481,546,105.00
22,425,573,907.43 22,368,746,394.36
22,482,401,420.51 227,310,052.30
22,502,928,992.72 -21,382,887.72
457,227,887,245,526.00 Juli
7 22,851,209,020.00
22,766,081,997.49 22,686,614,876.86
22,845,549,118.11 317,868,482.50
22,709,711,472.81 141,497,547.19
20,021,555,860,900,300.00 Agustus
8 22,845,663,820.00
22,829,747,455.50 22,801,120,939.77
22,858,373,971.22 114,506,062.91
23,163,417,600.62 -317,753,780.62
100,967,465,095,151,000.00 September
9 22,927,399,070.00
22,907,868,747.10 22,886,519,185.63
22,929,218,308.57 85,398,245.86
22,972,880,034.13 -45,480,964.13
2,068,518,098,524,430.00 Oktober
10 22,854,910,720.00
22,865,502,325.42 22,869,705,697.46
22,861,298,953.38 -16,813,488.17
23,014,616,554.43 -159,705,834.43
25,505,953,550,611,000.00 Oktober
11 22,764,705,655.00
22,784,864,989.08 22,801,833,130.76
22,767,896,847.41 -67,872,566.70
22,844,485,465.21 -79,779,810.21
6,364,818,116,533,580.00 Desember
12 22,819,191,990.00
22,812,326,589.82 22,810,227,898.01
22,814,425,281.63 8,394,767.25
22,700,024,280.71 119,167,709.29
14,200,942,938,540,800.00 2010
Januari 13
22,977,014,134.00 22,944,076,625.16
22,917,306,879.73 22,970,846,370.60
107,078,981.73 22,822,820,048.87
154,194,085.13 23,775,815,887,881,600.00
Februari 14
22,942,268,240.00 22,942,629,917.03
22,937,565,309.57 22,947,694,524.49
20,258,429.84 23,077,925,352.32
-135,657,112.32 18,402,852,123,363,300.00
Maret 15
23,444,261,325.00 23,343,935,043.41
23,262,661,096.64 23,425,208,990.17
325,095,787.07 22,967,952,954.33
476,308,370.67 226,869,663,966,914,000.00
April 16
23,821,534,330.00 23,726,014,472.68
23,633,343,797.47 23,818,685,147.89
370,682,700.83 23,750,304,777.24
71,229,552.76 5,073,649,186,310,590.00
Mei 17
24,200,283,345.00 24,105,429,570.54
24,011,012,415.92 24,199,846,725.15
377,668,618.45 24,189,367,848.72
10,915,496.28 119,148,058,975,542.00
Juni 18
24,451,483,354.00 24,382,272,597.31
24,308,020,561.03 24,456,524,633.58
297,008,145.11 24,577,515,343.60
-126,031,989.60 15,884,062,402,413,900.00
Juli 19
24,403,585,445.00 24,399,322,875.46
24,381,062,412.58 24,417,583,338.35
73,041,851.54 24,753,532,778.69
-349,947,333.69 122,463,136,357,359,000.00
Agustus 20
24,272,090,440.00 24,297,536,927.09
24,314,242,024.19 24,280,831,830.00
-66,820,388.39 24,490,625,189.89
-218,534,749.89 47,757,436,910,515,000.00
September 21
24,082,631,404.00 24,125,612,508.62
24,163,338,411.73 24,087,886,605.50
-150,903,612.46 24,214,011,441.61
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,466,453,422.52
24,405,830,420.37 24,527,076,424.68
242,492,008.63 23,936,982,993.05
614,680,657.95 377,832,311,260,289,000.00
Oktober 23
24,612,143,420.00 24,583,005,420.50
24,547,570,420.48 24,618,440,420.53
141,740,000.11 24,769,568,433.31
-157,425,013.31 24,782,634,817,172,200.00
Desember 24
20,195,839,321.00 21,073,272,540.90
21,768,132,116.82 20,378,412,964.99
-2,779,438,303.66 24,760,180,420.64
-4,564,341,099.64 20,833,209,673,899,500,000.00
2011 Januari
25 18,547,485,425.00
19,052,642,848.18 19,595,740,701.91
18,509,544,994.45 -2,172,391,414.91
17,598,974,661.33 948,510,763.67
899,672,668,807,316,000.00 Februari
26 22,317,670,660.00
21,664,665,097.64 21,250,880,218.49
22,078,449,976.78 1,655,139,516.58
16,337,153,579.54 5,980,517,080.46
35,766,584,549,623,000,000.00 Maret
27 23,490,850,795.00
23,125,613,655.53 22,750,666,968.12
23,500,560,342.93 1,499,786,749.63
23,733,589,493.36 -242,738,698.36
58,922,075,683,781,600.00 April
28 23,401,919,900.00
23,346,658,651.11 23,227,460,314.51
23,465,856,987.70 476,793,346.39
25,000,347,092.56 -1,598,427,192.56
2,554,969,489,928,360,000.00 Mei
29 24,440,969,550.00
24,222,107,370.22 24,023,177,959.08
24,421,036,781.36 795,717,644.57
23,942,650,334.09 498,319,215.91
248,322,040,944,108,000.00 Juni
30 25,113,931,440.00
24,935,566,626.04 24,753,088,892.65
25,118,044,359.44 729,910,933.57
25,216,754,425.93 -102,822,985.93
10,572,566,436,351,800.00 Juli
31 25,401,258,645.00
25,308,120,241.21 25,197,113,971.50
25,419,126,510.92 444,025,078.85
25,847,955,293.01 -446,696,648.01
199,537,895,343,276,000.00 Agustus
32 25,321,323,110.00
25,318,682,536.24 25,294,368,823.29
25,342,996,249.19 97,254,851.80
25,863,151,589.77 -541,828,479.77
293,578,101,486,187,000.00 September
33 25,080,556,135.00
25,128,181,415.25 25,161,418,896.86
25,094,943,933.64 -132,949,926.44
25,440,251,100.99 -359,694,965.99
129,380,468,555,843,000.00 Oktober
34 25,109,569,925.00
25,113,292,223.05 25,122,917,557.81
25,103,666,888.29 -38,501,339.05
24,961,994,007.20 147,575,917.80
21,778,651,513,378,300.00 Oktober
35 25,282,275,715.00
25,248,479,016.61 25,223,366,724.85
25,273,591,308.37 100,449,167.04
25,065,165,549.24 217,110,165.76
47,136,824,075,436,200.00 Desember
36 25,569,779,015.00
25,505,519,015.32 25,449,088,557.23
25,561,949,473.42 225,721,832.38
25,374,040,475.41 195,738,539.59
38,313,575,881,347,200.00 SE
344,835,093.66 SSE
62,182,979,311,960,400,000.00 MSE
1,828,911,156,234,130,000.00
Tabel 4.9 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011 a = 0,8
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk
= 0,9 dengan menggunakan rumus:
′
= α + 1 − α
′
4.1 Februari 2009
= 0,921.548.149.420 + 1-0,921.473.831.050,00 = 21.540.717.583,00
Maret 2009 = 0,921.789.329.725 + 1-0,921.540.717.583,00
= 21.764.468.510,80 Dan tahap selanjutnya untuk menghitung peramalan nilai air minum yang
disalurkan yaitu mencari Pemulusan Eksponensial Ganda untuk = 0,9 dengan
menggunakan rumus:
′′
= α
′
+ 1 − α
′′
4.2 Februari 2009
= 0,921.540.717.583,00 + 1-0,921.473.831.050,00 = 21.534.028.929,70
Maret 2009 = 0,921.764.468.510,80+1-0,921.534.028.929,70
= 21.741.424.552,69 Selanjutnya dicari nilai a
t
dengan menggunakan rumus: a
t
=
′
+
′
−
′′
= 2
′
−
′′
4.3 Februari 2009 = 221.481.262.887,00 – 21.474.574.233,70
= 21.487.951.540,30 Maret 2009
= 221.512.069.570,80 - 21.478.323.767,41 = 21.545.815.374,19
Universitas Sumatera Utara Universitas Sumatera Utara
Tahap selanjutnya adalah dengan menghitung nilai b
t
untuk = 0,9 dengan
menggunakan rumus: b
t
=
– ′
−
′′
4.4 Februari 2009 = 221.540.717.583,00 – 21.534.028.929,70
= 21.547.406.236,30 Maret 2009
= 221.764.468.510,80 – 21.741.424.552,69 = 21.787.512.468,91
Selanjutnya dicari nilai F
t+m
dengan menggunakan rumus: F
t+m
= a
t
+ b
t
m 4.5
F
Maret 2009
untuk m = 1 = 21.547.406.236,30 + 60.197.879,70 1
= 21.607.604.116,00 F
April 2012
untuk m = 1 = 21.787.512.468,91 + 207.395.622,99 1
= 21.994.908.091,90
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt
St St
a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,540,717,583.00
21,534,028,929.70 21,547,406,236.30
60,197,879.70 Maret
3 21,789,329,725.00
21,764,468,510.80 21,741,424,552.69
21,787,512,468.91 207,395,622.99
21,607,604,116.00 181,725,609.00
33,024,196,966,423,700.00 April
4 22,005,291,800.00
21,981,209,471.08 21,957,230,979.24
22,005,187,962.92 215,806,426.55
21,994,908,091.90 10,383,708.10
107,821,393,906,687.00 Mei
5 22,264,141,990.00
22,235,848,738.11 22,207,986,962.22
22,263,710,513.99 250,755,982.98
22,220,994,389.47 43,147,600.53
1,861,715,431,498,980.00 Juni
6 22,481,546,105.00
22,456,976,368.31 22,432,077,427.70
22,481,875,308.92 224,090,465.48
22,514,466,496.98 -32,920,391.97
1,083,752,207,787,540.00 Juli
7 22,851,209,020.00
22,811,785,754.83 22,773,814,922.12
22,849,756,587.54 341,737,494.42
22,705,965,774.40 145,243,245.60
21,095,600,392,341,700.00 Agustus
8 22,845,663,820.00
22,842,276,013.48 22,835,429,904.35
22,849,122,122.62 61,614,982.23
23,191,494,081.96 -345,830,261.96
119,598,570,087,551,000.00 September
9 22,927,399,070.00
22,918,886,764.35 22,910,541,078.35
22,927,232,450.35 75,111,174.00
22,910,737,104.85 16,661,965.15
277,621,082,724,951.00 Oktober
10 22,854,910,720.00
22,861,308,324.43 22,866,231,599.83
22,856,385,049.04 -44,309,478.52
23,002,343,624.35 -147,432,904.35
21,736,461,285,073,500.00 Oktober
11 22,764,705,655.00
22,774,365,921.94 22,783,552,489.73
22,765,179,354.16 -82,679,110.09
22,812,075,570.52 -47,369,915.52
2,243,908,896,512,570.00 Desember
12 22,819,191,990.00
22,814,709,383.19 22,811,593,693.85
22,817,825,072.54 28,041,204.12
22,682,500,244.06 136,691,745.94
18,684,633,407,909,300.00 2010
Januari 13
22,977,014,134.00 22,960,783,658.92
22,945,864,662.41 22,975,702,655.43
134,270,968.56 22,845,866,276.66
131,147,857.34 17,199,760,485,673,500.00
Februari 14
22,942,268,240.00 22,944,119,781.89
22,944,294,269.94 22,943,945,293.84
-1,570,392.47 23,109,973,623.99
-167,705,383.99 28,125,095,819,505,200.00
Maret 15
23,444,261,325.00 23,394,247,170.69
23,349,251,880.61 23,439,242,460.76
404,957,610.67 22,942,374,901.37
501,886,423.63 251,889,982,222,524,000.00
April 16
23,821,534,330.00 23,778,805,614.07
23,735,850,240.72 23,821,760,987.41
386,598,360.11 23,844,200,071.43
-22,665,741.43 513,735,834,772,572.00
Mei 17
24,200,283,345.00 24,158,135,571.91
24,115,907,038.79 24,200,364,105.03
380,056,798.07 24,208,359,347.52
-8,076,002.52 65,221,816,754,194.20
Juni 18
24,451,483,354.00 24,422,148,575.79
24,391,524,422.09 24,452,772,729.49
275,617,383.30 24,580,420,903.09
-128,937,549.09 16,624,891,565,410,000.00
Juli 19
24,403,585,445.00 24,405,441,758.08
24,404,050,024.48 24,406,833,491.68
12,525,602.39 24,728,390,112.79
-324,804,667.79 105,498,072,219,989,000.00
Agustus 20
24,272,090,440.00 24,285,425,571.81
24,297,288,017.08 24,273,563,126.54
-106,762,007.41 24,419,359,094.07
-147,268,654.07 21,688,056,470,897,100.00
September 21
24,082,631,404.00 24,102,910,820.78
24,122,348,540.41 24,083,473,101.15
-174,939,476.66 24,166,801,119.14
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,506,788,367.98
24,468,344,385.22 24,545,232,350.73
345,995,844.81 23,908,533,624.49
643,130,026.51 413,616,231,003,300,000.00
Oktober 23
24,612,143,420.00 24,601,607,914.80
24,588,281,561.84 24,614,934,267.76
119,937,176.62 24,891,228,195.55
-279,084,775.55 77,888,311,941,508,800.00
Desember 24
20,195,839,321.00 20,636,416,180.38
21,031,602,718.53 20,241,229,642.23 -3,556,678,843.31
24,734,871,444.37 -4,539,032,123.37 20,602,812,617,024,200,000.00
2011 Januari
25 18,547,485,425.00
18,756,378,500.54 18,983,900,922.34
18,528,856,078.74 -2,047,701,796.19 16,684,550,798.92
1,862,934,626.08 3,470,525,421,050,050,000.00
Februari 26
22,317,670,660.00 21,961,541,444.05
21,663,777,391.88 22,259,305,496.23
2,679,876,469.55 16,481,154,282.55
5,836,516,377.45 34,064,923,424,240,700,000.00
Maret 27
23,490,850,795.00 23,337,919,859.91
23,170,505,613.10 23,505,334,106.71
1,506,728,221.22 24,939,181,965.77 -1,448,331,170.77
2,097,663,180,226,410,000.00 April
28 23,401,919,900.00
23,395,519,895.99 23,373,018,467.70
23,418,021,324.28 202,512,854.60
25,012,062,327.93 -1,610,142,427.93 2,592,558,638,215,940,000.00
Mei 29
24,440,969,550.00 24,336,424,584.60
24,240,083,972.91 24,432,765,196.29
867,065,505.21 23,620,534,178.88
820,435,371.12 673,114,198,188,097,000.00
Juni 30
25,113,931,440.00 25,036,180,754.46
24,956,571,076.30 25,115,790,432.62
716,487,103.40 25,299,830,701.50
-185,899,261.50 34,558,535,424,866,800.00
Juli 31
25,401,258,645.00 25,364,750,855.95
25,323,932,877.98 25,405,568,833.91
367,361,801.68 25,832,277,536.01
-431,018,891.01 185,777,284,407,923,000.00
Agustus 32
25,321,323,110.00 25,325,665,884.59
25,325,492,583.93 25,325,839,185.26
1,559,705.95 25,772,930,635.59
-451,607,525.59 203,949,357,166,908,000.00
September 33
25,080,556,135.00 25,105,067,109.96
25,127,109,657.36 25,083,024,562.56
-198,382,926.58 25,327,398,891.21
-246,842,756.21 60,931,346,292,036,400.00
Oktober 34
25,109,569,925.00 25,109,119,643.50
25,110,918,644.88 25,107,320,642.11
-16,191,012.47 24,884,641,635.99
224,928,289.01 50,592,735,198,956,000.00
Oktober 35
25,282,275,715.00 25,264,960,107.85
25,249,555,961.55 25,280,364,254.15
138,637,316.67 25,091,129,629.64
191,146,085.36 36,536,825,950,344,100.00
Desember 36
25,569,779,015.00 25,539,297,124.29
25,510,323,008.01 25,568,271,240.56
260,767,046.46 25,419,001,570.82
150,777,444.18 22,733,837,674,320,500.00
SE 266,869,033.35
SSE
65,253,715,250,307,500,000.00
M SE
1,919,230,000,000,000,000.00
Tabel 4.10 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011 a = 0,9
Universitas Sumatera Utara Universitas Sumatera Utara
Tabel 4.11 Perbandingan Ukuran Ketepatan Metode Peramalan
MSE
0,1 1.909.785.775.041.190.000,00
0,2 1.791.626.616.500.080.000,00
0,3 1.711.594.945.070.900.000,00
0,4 1.667.313.913.905.640.000,00
0,5 1.661.434.959.739.730.000,00
0,6 1.691.882.551.210.190.000,00
0,7 1.750.644.266.705.490.000,00
0,8 1.828.911.156.234.130.000,00
0,9 1.919.230.000.000.000.000,00
Dari tabel 4.11 di atas dapat dilihat bahwa yang menghasilkan nilai MSE yang paling kecil atau minimum adalah
= 0,5 yaitu dengan MSE = 1.661.434.959.739.730.000,00.
Universitas Sumatera Utara Universitas Sumatera Utara
Tahun Bulan
Periode Nilai Air Minum Xt St
St a
t
b
t
F
t+1
m=1 e
i
e
i 2
2009 Januari
1 21,473,831,050.00
21,473,831,050.00 21,473,831,050.00
Februari 2
21,548,149,420.00 21,510,990,235.00
21,492,410,642.50 21,529,569,827.50
18,579,592.50 Maret
3 21,789,329,725.00
21,650,159,980.00 21,571,285,311.25
21,729,034,648.75 78,874,668.75
21,548,149,420.00 241,180,305.00
58,167,939,519,893,000.00 April
4 22,005,291,800.00
21,827,725,890.00 21,699,505,600.63
21,955,946,179.38 128,220,289.38
21,807,909,317.50 197,382,482.50
38,959,844,397,862,800.00 Mei
5 22,264,141,990.00
22,045,933,940.00 21,872,719,770.31
22,219,148,109.69 173,214,169.69
22,084,166,468.75 179,975,521.25
32,391,188,249,209,200.00 Juni
6 22,481,546,105.00
22,263,740,022.50 22,068,229,896.41
22,459,250,148.59 195,510,126.09
22,392,362,279.38 89,183,825.63
7,953,754,753,110,410.00 Juli
7 22,851,209,020.00
22,557,474,521.25 22,312,852,208.83
22,802,096,833.67 244,622,312.42
22,654,760,274.69 196,448,745.31
38,592,109,534,855,500.00 Agustus
8 22,845,663,820.00
22,701,569,170.63 22,507,210,689.73
22,895,927,651.52 194,358,480.90
23,046,719,146.09 -201,055,326.09
40,423,244,150,664,200.00 September
9 22,927,399,070.00
22,814,484,120.31 22,660,847,405.02
22,968,120,835.61 153,636,715.29
23,090,286,132.42 -162,887,062.42
26,532,195,104,427,800.00 Oktober
10 22,854,910,720.00
22,834,697,420.16 22,747,772,412.59
22,921,622,427.72 86,925,007.57
23,121,757,550.90 -266,846,830.90
71,207,231,160,539,300.00 Oktober
11 22,764,705,655.00
22,799,701,537.58 22,773,736,975.08
22,825,666,100.07 25,964,562.50
23,008,547,435.29 -243,841,780.29
59,458,813,816,444,400.00 Desember
12 22,819,191,990.00
22,809,446,763.79 22,791,591,869.44
22,827,301,658.14 17,854,894.35
22,851,630,662.57 -32,438,672.57
1,052,267,477,997,230.00 2010
Januari 13
22,977,014,134.00 22,893,230,448.89
22,842,411,159.17 22,944,049,738.62
50,819,289.73 22,845,156,552.50
131,857,581.50 17,386,421,800,316,800.00
Februari 14
22,942,268,240.00 22,917,749,344.45
22,880,080,251.81 22,955,418,437.09
37,669,092.64 22,994,869,028.35
-52,600,788.35 2,766,842,935,359,980.00
Maret 15
23,444,261,325.00 23,181,005,334.72
23,030,542,793.27 23,331,467,876.18
150,462,541.46 22,993,087,529.73
451,173,795.27 203,557,793,539,014,000.00
April 16
23,821,534,330.00 23,501,269,832.36
23,265,906,312.81 23,736,633,351.91
235,363,519.55 23,481,930,417.64
339,603,912.36 115,330,817,289,545,000.00
Mei 17
24,200,283,345.00 23,850,776,588.68
23,558,341,450.75 24,143,211,726.61
292,435,137.93 23,971,996,871.46
228,286,473.54 52,114,714,001,932,200.00
Juni 18
24,451,483,354.00 24,151,129,971.34
23,854,735,711.04 24,447,524,231.64
296,394,260.30 24,435,646,864.55
15,836,489.45 250,794,398,149,644.00
Juli 19
24,403,585,445.00 24,277,357,708.17
24,066,046,709.61 24,488,668,706.73
211,310,998.56 24,743,918,491.93
-340,333,046.93 115,826,582,835,218,000.00
Agustus 20
24,272,090,440.00 24,274,724,074.09
24,170,385,391.85 24,379,062,756.32
104,338,682.24 24,699,979,705.30
-427,889,265.30 183,089,223,356,110,000.00
September 21
24,082,631,404.00 24,178,677,739.04
24,174,531,565.44 24,182,823,912.64
4,146,173.60 24,483,401,438.56
-64,916,937.04 4,214,208,714,655,320.00
Oktober 22
24,551,663,651.00 24,365,170,695.02
24,269,851,130.23 24,460,490,259.81
95,319,564.79 24,186,970,086.24
364,693,564.76 133,001,396,178,048,000.00
Oktober 23
24,612,143,420.00 24,488,657,057.51
24,379,254,093.87 24,598,060,021.15
109,402,963.64 24,555,809,824.60
56,333,595.40 3,173,473,970,888,780.00
Desember 24
20,195,839,321.00 22,342,248,189.26
23,360,751,141.56 21,323,745,236.95
-1,018,502,952.31 24,707,462,984.79
-4,511,623,663.79 20,354,748,083,656,200,000.00
2011 Januari
25 18,547,485,425.00
20,444,866,807.13 21,902,808,974.35
18,986,924,639.91 -1,457,942,167.22
20,305,242,284.64 -1,757,756,859.64
3,089,709,177,607,660,000.00 Februari
26 22,317,670,660.00
21,381,268,733.56 21,642,038,853.95
21,120,498,613.17 -260,770,120.39
17,528,982,472.69 4,788,688,187.31
22,931,534,555,265,100,000.00 Maret
27 23,490,850,795.00
22,436,059,764.28 22,039,049,309.12
22,833,070,219.45 397,010,455.16
20,859,728,492.78 2,631,122,302.22
6,922,804,569,228,600,000.00 April
28 23,401,919,900.00
22,918,989,832.14 22,479,019,570.63
23,358,960,093.65 439,970,261.51
23,230,080,674.61 171,839,225.39
29,528,719,382,936,500.00 Mei
29 24,440,969,550.00
23,679,979,691.07 23,079,499,630.85
24,280,459,751.29 600,480,060.22
23,798,930,355.16 642,039,194.84
412,214,327,706,162,000.00 Juni
30 25,113,931,440.00
24,396,955,565.54 23,738,227,598.19
25,055,683,532.88 658,727,967.34
24,880,939,811.51 232,991,628.49
54,285,098,945,802,600.00 Juli
31 25,401,258,645.00
24,899,107,105.27 24,318,667,351.73
25,479,546,858.81 580,439,753.54
25,714,411,500.22 -313,152,855.22
98,064,710,732,701,900.00 Agustus
32 25,321,323,110.00
25,110,215,107.63 24,714,441,229.68
25,505,988,985.59 395,773,877.95
26,059,986,612.34 -738,663,502.34
545,623,769,693,028,000.00 September
33 25,080,556,135.00
25,095,385,621.32 24,904,913,425.50
25,285,857,817.13 190,472,195.82
25,901,762,863.54 -821,206,728.54
674,380,490,995,248,000.00 Oktober
34 25,109,569,925.00
25,102,477,773.16 25,003,695,599.33
25,201,259,946.99 98,782,173.83
25,476,330,012.95 -366,760,087.95
134,512,962,114,441,000.00 November
35 25,282,275,715.00
25,192,376,744.08 25,098,036,171.70
25,286,717,316.45 94,340,572.38
25,300,042,120.82 -17,766,405.82
315,645,175,670,916.00 Desember
36 25,569,779,015.00
25,381,077,879.54 25,239,557,025.62
25,522,598,733.46 141,520,853.92
25,381,057,888.83 188,721,126.17
35,615,663,463,058,100.00
SE
827,618,143.19
SSE
56,488,788,631,150,800,000.00
M SE
1,661,434,959,739,730,000.00
a = 0,5 Tabel 4.12 Peramalan Nilai Air Minum yang Disalurkan PDAM Tirtanadi Medan Tahun 2009 - 2011
Universitas Sumatera Utara Universitas Sumatera Utara
Dari Tabel 4.12 diperoleh ukuran ketepatan metode peramalan dengan menggunakan
= 0,5 adalah: 1. SE Sum Eror Jumlah Kesalahan:
SE = ∑
SE = 827.618.143,19 2. ME Mean Error Nilai Tengah Kesalahan:
ME = ∑
ME =
. .
,
ME = 24341710,09 3. SSE Sum Square Error Jumlah Kuadrat Kesalahan:
SSE = ∑
SSE = 56.488.788.631.150.800.000,00 4. MSE Mean Square Error Nilai Tengah Kesalahan Kuadrat:
MSE = ∑
MSE = 1.661.434.959.739.730.000,00 5. SDE Standard Deviation of Error Deviasi Standar Kesalahan
SDE =
∑
=
. .
. .
. .
,
= √
1.711.781.473.671.240.000,00
= 1.308.350.669,00
Universitas Sumatera Utara Universitas Sumatera Utara
4.2 Peramalan Nilai Air Minum
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