Perolehan Nilai Air Minum Yang Disalurkan Pdam Tirtanadi Medan Tahun 2012 – 2013

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KEMENTERIAN PENDIDIKAN DAN KEBUDAYAAN UNIVERSITAS SUMATERA UTARA

FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM Jl. Bioteknologi No. 1 Kampus USU MedanTelp.(061)8211050

Fax.(061)8214290, Medan 20155

SURAT KETERANGAN

Hasil Uji Program Tugas Akhir

Yang Bertanda tangan di bawah ini menerangkan bahwa Mahasiswa Tugas Akhir Progam D3 Statistika:

Nama : Dony Mukhtar Harianja

NIM : 102407080 Pogram Studi : D3 Statistika Judul Tugas Akhir : Perolehan Nilai Air Minum yang Disalurkan PDAM Tirtanadi

Medan Tahun 2012 -2013

Telah melakukan test program Tugas Akhir mahasiswa tersebut di atas pada tanggal

Dengan Hasil: Sukses / Gagal

Demikian diterangkan untuk digunakan melengkapi syarat pendaftaran Ujian Meja Hijau Tugas Akhir Mahasiswa bersangkutan di Jurusan D3 Statistika FMIPA USU Medan.

Medan, Juli 2013

Dosen Pembimbing

Drs. Faigiziduhu Bu’ulölö, M.Si NIP. 19531218 198003 1 003

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DAFTAR PUSTAKA

Assauri, Sofjan. 1984. Teknik dan Metode Peramalan. Jakarta: Fakultas Ekonomi Universitas Indonesia.

BPS. 2009. Medan Dalam Angka 2011. Badan Pusat Statistik. Bagoes, Ida. 1993. Demografi Umum. Edisi ke-2. Pustaka Pelajar.

Deanto. 2002. Proyeksi Bisnis Dengan Microsoft Excel. Jakarta: Alex Media Komputindo.

Hadi, Sutrisno. 1974. Statistika. Yogyakarta: Andi Yogyakarta. http://www.pdamtirtanadi.co.id/pengolahan.htm.20Maret2012. http://www.pdamtirtanadi.co.id/sejarah.htm .21Maret2012. http://pdf.usaid.gov/pdf_docs/PNADJ481.pdf.22Maret2012.

Makridakis, Spyros; wheelright, Steaven. C. 1993. Metode dan Aplikasi Peramalan. Erlangga.

Pratiwi. 2009. Panduan Penulisan Skripsi dan Tugas Akhir. Yogyakarta: Tugu Publisher.

Sianipar, Pandapotan. 2004. Menggunakan Microsoft Office Excel 2003. Jakarta: Penerbit Elex Media Komputindo.

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BAB 3

SEJARAH SINGKAT TEMPAT RISET

3.1Sejarah Singkat Badan Pusat Statistik (BPS)

1. Pada bulan Februari 1920 di kantor Statistik untuk pertama kalinya didirikan oleh Direktur Pertanian, Kerajinan dan Perdagangan dan berkedudukan di Bogor.

2. Pada bulan Maret 1923 dibentuk suatu komisi yang bernama Komisi untuk Statistik yang anggotanya merupakan wakil dari tiap-tiap departemen.

3. Pada bulan September 1924 nama lembaga tersebut diganti menjadi Kantor Pusat Statistik dan dipindahkan ke Jakarta. Komisi ini juga pernah melakukan sesuatu kegiatan statistik yang bersifat monumental yaitu Sensus Penduduk 1930, yang merupakan sensus penduduk yang pertama kali dilakukan di Indonesia.

3.1.1 Masa Pemerintahan Jepang

Pada Juni 1942 Pemerintah Jepang baru mengaktifkan kembali kegiatan statistik yang utamanya diarahkan untuk memenuhi kebutuhan perang/militer. Dan tugas serta fungsi kegiatan statistik pada saat itu lebih terkonsentrasi untuk keperluan militer.

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3.1.2 Masa Pemerintahan RI

Setelah Proklamasi Kemerdekaan Republik Indonesia tanggal 17 Agustus 1945 kegiatan statistik ditangani oleh lembaga baru yaitu Kantor Penyelidikan Perangkaan Umum Republik Indonesia (KAPPURI). Perkembangan berikutnya KAPPURI dilebur menjadi Kantor Pusat Statistik (KPS) dan berada di bawah dan bertanggung jawab kepada menteri Kemakmuran.

Dengan Keputusan Presiden RI Nomor 172 Tahun 1957, terhitung mulai 1 Juni 1957 KPS diubah menjadi Biro Pusat Statistik, dan urusan statistik yang semula menjadi tanggung jawab dan wewenang Menteri Perekonomian dialihkan menjadi wewenang dan berada di bawah Perdana Menteri. Berdasarkan Keppres ini pula secara formal nama Biro Pusat Statistik dipergunakan.

3.1.3 Masa Orde Baru Sampai Sekarang

BPS telah mengalami empat kali perubahan stuktur organisasi :

1. Peraturan Pemerintah No.16 Tahun 1980 tentang organisasi BPS 2. Peraturan Pemerintah No.6 Tahun 1980 tentang organisasi BPS

3. Peraturan Pemerintah No.2 Tahun 1992 tentang kedudukan, tugas, fungsi, susunan dan tata kerja BPS

4. Undang-undang No.16 tahun 1997 tentang statistik 5. Keputusan Presiden RI No.86 tahun 1998 tentang BPS

6. Keputusan kepala BPS No.100 tahun 1998 tentang organisasi dan tata kerja BPS

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Pada tanggal 19 Mei 1997 menetapkan tentang statistik sebagai pengganti UU No.6 dan 7 tentang sensus dan statistik. Pada tanggal 17 Juli 1998 dengan keputusan presiden RI No.89 tahun 1998, ditetapkan BPS sekaligus mengatur tata kerja dan stuktur organisasi BPS yang baru.

3.2 Visi dan Misi Badan Pusat Statistik

Visi

BPS Pelopor Data Statistik Terpecaya Untuk Semua.

Misi

Dalam menunjang pembangunan nasional BPS mengemban misi mengarahkan pembangunan statistik pada penyediaan data statistik yang bermutu dan handal, efektif dan efisien, peningkatan kesadaran masyarakat akan kegunaan BPS dan pengemban ilmu pengetahuan statistik dalam kehidupan masyarakat.

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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

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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

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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 = (0,1)(21.481.262.887,00)+(1-0,1)(21.473.831.050,00) = 21.474.574.233,70

Maret 2009 = (0,1)(21.512.069.570,80)+(1-0,1)(21.474.574.233,70) = 21.478.323.767,41

Selanjutnya dicari nilai at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.481.262.887,00) – 21.474.574.233,70

= 21.487.951.540,30

Maret 2009 = 2(21.512.069.570,80) - 21.478.323.767,41 = 21.545.815.374,19

Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,1 dengan

menggunakan rumus:

bt = _{( – )}( ′− ′′ ) (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

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Selanjutnya dicari nilai Ft+m dengan menggunakan rumus:

Ft+m = a _t+ b_t (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.487.951.540,30 + 743.183,70 (1)

= 21.488.694.724,00

FApril 2009 untuk m = 1 = 21.545.815.374,19 + 3.749.533,71 (1)

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Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

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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 at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.488.694.724,00) – 21.476.803.784,80

= 21.500.585.663,20

Maret 2009 = 2(21.548.821.724,20) - 21.491.207.372,68 = 21.606.436.075,72

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Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,2 dengan

menggunakan rumus: bt =

( – )(

′₋ ′′_{) (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 Ft+m dengan menggunakan rumus:

Ft+m = a

t + bt (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.500.585.663,20 + 2.972.734,80 (1)

= 21.503.558.398,00

FApril 2009 untuk m = 1 = 21.606.436.075,72 + 14.403.587,88 (1)

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Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

(15)

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 at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.496.126.561,00) – 21.480.519.703,30

= 21.511.733.418,70

Maret 2009 = 2(21.584.087.510,20) - 21.511.590.045,37 = 21.656.584.975,03

(16)

Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,3 dengan

menggunakan rumus: bt =

( – )(

′₋ ′′_(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 Ft+m dengan menggunakan rumus:

Ft+m = a

t + bt (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.511.733.418,70 + 6.688.653,30 (1)

= 21.518.422.072,00

FApril 2009 untuk m = 1 = 21.656.584.975,03 + 31.070.342,07 (1)

(17)

Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

(18)

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 at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.503.558.398,00) – 21.485.721.989,20

= 21.521.394.806,80

Maret 2009 = 2(21.617.866.928,80) - 21.538.579.965,04 = 21.697.153.892,56

(19)

Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,4 dengan

menggunakan rumus: bt =

( – )(

′₋ ′′_{) (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 Ft+m dengan menggunakan rumus:

Ft+m = a

t + bt (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.521.394.806,80 + 11.890.939,20 (1)

= 21.533.285.746,00

FApril 2009 untuk m = 1 = 21.697.153.892,56 + 52.857.975,84 (1)

(20)

Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

(21)

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 at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.510.990.235,00) – 21.492.410.642,50

= 21.529.569.827,50

Maret 2009 = 2(21.650.159.980,00) - 21.571.285.311,25 = 21.729.034.648,75

(22)

Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,5 dengan

menggunakan rumus: bt =

( – )(

′₋ ′′_{) (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 Ft+m dengan menggunakan rumus:

Ft+m = a

t + bt (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.529.569.827,50 + 18.579.592,50 (1)

= 21.548.149.420,00

FApril 2009 untuk m = 1 = 21.729.034.648,75 + 78.874.668,75 (1)

(23)

Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

(24)

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 at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.518.422.072,00) – 21.500.585.663,20

= 21.536.258.480,80

Maret 2009 = 2(21.680.966.663,80) - 21.608.814.263,56 = 21.753.119.064,04

(25)

Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,6 dengan

menggunakan rumus: bt =

( – )(

′₋ ′′_{) (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 Ft+m dengan menggunakan rumus:

Ft+m = a

t + bt (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.536.258.480,80 + 26.754.613,20 (1)

= 21.563.013.094,00

FApril 2009 untuk m = 1 = 21.753.119.064,04 + 108.228.600,36 (1)

(26)

Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

(27)

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 at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.525.853.909,00) – 21.510.247.051,30

= 21.541.460.766,70

Maret 2009 = 2(21.710.286.980,20) - 21.650.275.001,53 = 21.770.298.958,87

(28)

Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,7 dengan

menggunakan rumus: bt =

( – )(

′₋ ′′_{) (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 Ft+m dengan menggunakan rumus:

Ft+m = a

t + bt (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.541.460.766,70 + 36.416.001,30 (1)

= 21.577.876.768,00

FApril 2009 untuk m = 1 = 21.770.298.958,87 + 140.027.950,23 (1)

(29)

Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

(30)

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 at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.533.285.746,00) – 21.521.394.806,80

= 21.545.176.685,20

Maret 2009 = 2(21.738.120.929,20) - 21.694.775.704,72 = 21.781.466.153,68

(31)

Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,8 dengan

menggunakan rumus: bt =

( – )(

′₋ ′′_{) (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 Ft+m dengan menggunakan rumus:

Ft+m = a

t + bt (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.545.176.685,20 + 47.563.756,80 (1)

= 21.592.740.442,00

FApril 2009 untuk m = 1 = 21.781.466.153,68 + 173.380.897,92 (1)

(32)

Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

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Tahap pertama dalam perhitungan ini adalah perhitungan Pemulusan Eksponensial Tunggal untuk  = 0,9 dengan menggunakan rumus:

′_{= α} _{+ (1}_{− α )} ′ _(4.1)

Februari 2009 = (0,9)(21.548.149.420) + (1-0,9)(21.473.831.050,00) = 21.540.717.583,00

Maret 2009 = (0,9)(21.789.329.725) + (1-0,9)(21.540.717.583,00) = 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 = (0,9)(21.540.717.583,00) + (1-0,9)(21.473.831.050,00) = 21.534.028.929,70

Maret 2009 = (0,9)(21.764.468.510,80)+(1-0,9)(21.534.028.929,70) = 21.741.424.552,69

Selanjutnya dicari nilai at dengan menggunakan rumus:

at = ′+ ( ′− ′′) = 2 ′ − ′′ (4.3) Februari 2009 = 2(21.481.262.887,00) – 21.474.574.233,70

= 21.487.951.540,30

Maret 2009 = 2(21.512.069.570,80) - 21.478.323.767,41 = 21.545.815.374,19

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Tahap selanjutnya adalah dengan menghitung nilai bt untuk  = 0,9 dengan

menggunakan rumus: bt =

( – )(

′₋ ′′_{) (4.4)}

Februari 2009 = 2(21.540.717.583,00) – 21.534.028.929,70 = 21.547.406.236,30

Maret 2009 = 2(21.764.468.510,80) – 21.741.424.552,69 = 21.787.512.468,91

Selanjutnya dicari nilai Ft+m dengan menggunakan rumus:

Ft+m = a

t + bt (m ) (4.5)

FMaret 2009 untuk m = 1 = 21.547.406.236,30 + 60.197.879,70 (1)

= 21.607.604.116,00

FApril 2012 untuk m = 1 = 21.787.512.468,91 + 207.395.622,99 (1)

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Tahun Bulan Periode Nilai Air Minum (Xt) S't S''t at bt Ft+1(m=1) ei ei 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

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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.

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