9 Forecast dengan Double Exponensial Smoothing α = 0,9

4.2. 9 Forecast dengan Double Exponensial Smoothing α = 0,9

Langkah-langkah yang dilakukan sama dengan langkah-langkah sebelumnya, perbedaanya hanya pada penggunaan α = 0,9 Bulan 2 : X t = 262.399 4 , 928 . 267 3 0,1317.69 9 0,9262.39 1 . 1 1 = + = − + = − t t t S X S α α 86 , 904 . 272 3 0,1317.69 8,4 0,9267.92 1 . 2 1 = + = − + = − t t t S S S α α 94 , 951 . 262 6 272.904,8 - 4 2267.928, 2 . 3 = = − = t t t S S a 14 , 788 . 44 86 , 904 . 272 4 , 928 . 267 9 , 1 9 , 1 b . 4 t − = − − = − − = t t S S α α 5. Forecast bulan ke 2 m=1 8 , 163 . 218 14 , 788 . 44 94 , 951 . 262 3 = − + = + = + F m b a F t t m t Dengan demikian dapat kita lihat dari table forecast di bawah ini : Universitas Sumatera Utara Tabel 4.2.9 Jumlah Penumpang Domestik di PT. Persero Angkasa Pura II Bandar Udara Polonia Medan Periode 2006-2008 Bulan Periode Jumlah penumpang t S t S t a b t Forecast m=1 Januari 1 317693 317693 317693 Februari 2 262399 267928,4 272904,86 262951,94 -44788,14 Maret 3 250465 252211,34 254280,692 250141,988 -18624,168 218163,8 April 4 296908 292438,334 288622,57 296254,098 34341,878 231517,82 Mei 5 288737 289107,133 289058,677 289155,59 436,107 330595,976 Juni 6 294128 293625,913 293169,19 294082,637 4110,513 289591,697 Juli 7 337314 332945,191 328967,591 336922,791 35798,401 298193,15 Agustus 8 311797 313911,819 315417,396 312406,242 -13550,195 372721,193 September 9 293032 295119,982 297149,723 293090,24 -18267,673 298856,047 Oktober 10 285932 286850,798 287880,691 285820,906 -9269,033 274822,567 Nopember 11 331132 326703,88 322821,561 330586,199 34940,87 276551,873 Desember 12 329845 329530,888 328859,955 330201,821 6038,394 365527,069 Januari 13 326424 326734,689 326947,215 326522,162 -1912,74 336240,215 Februari 14 263058 269425,669 275177,824 263673,514 -51769,392 324609,422 Maret 15 306916 303166,967 300368,053 305965,881 25190,229 211904,122 April 16 304820 304654,697 304226,032 305083,361 3857,98 331156,11 Mei 17 309035 308596,97 308159,876 309034,063 3933,844 308941,341 Juni 18 345236 341572,097 338230,875 344913,319 30070,999 312967,907 Juli 19 391278 386307,41 381499,756 391115,063 43268,881 374984,318 Agustus 20 353177 356490,041 358991,012 353989,069 -22508,744 434383,945 September 21 309030 313776,004 318297,505 309254,503 -40693,508 331480,326 Oktober 22 362161 357322,5 353420,001 361225 35122,496 268560,996 Nopember 23 336467 338552,55 340039,295 337065,805 -13380,706 396347,496 Desember 24 355296 353621,655 352263,419 354979,891 12224,124 323685,099 Januari 25 369510 367921,166 366355,391 369486,94 14091,972 367204,015 Februari 26 314028 319417,317 324111,124 314723,509 -42244,267 383578,912 Maret 27 336344 334651,332 333597,311 335705,352 9486,187 272479,242 April 28 305705 308599,633 311099,401 306099,865 -22497,91 345191,539 Mei 29 301147 301892,263 302812,977 300971,55 -8286,424 283601,955 Juni 30 304423 304169,926 304034,231 304305,621 1221,254 292685,126 Juli 31 320900 319226,993 317707,717 320746,269 13673,485 305526,876 Agustus 32 316475 316750,199 316845,951 316654,448 -861,766 334419,754 September 33 250020 256693,02 262708,313 250677,727 -54137,638 315792,682 Oktober 34 310832 305418,102 301147,123 309689,081 38438,81 196540,089 Nopember 35 289487 291080,11 292086,811 290073,409 -9060,312 348127,891 Desember 36 312050 309953,011 308166,391 311739,631 16079,58 281013,097 37 327819,211 Universitas Sumatera Utara

4.2.10 Nilai Rata-rata Kesalahan Mean Square Error

n e MSE i ∑ = 2 1. Maka untuk α = 0,1 8 , 295 . 191 . 940 34 .058,52 31.966.504 2 = = = ∑ n e MSE i 2. Maka untuk α = 0,2 8 , 794 . 131 . 931 34 .021,85 31.658.481 2 = = = ∑ n e MSE i 3. Maka untuk α = 0,3 8 , 838 . 242 . 961 34 .517,64 32.682.256 2 = = = ∑ n e MSE i 4. Maka untuk α = 0,4 643 . 683 . 114 . 1 34 .851,66 37.899.243 2 = = = ∑ n e MSE i Universitas Sumatera Utara 5. Maka untuk α = 0,5 766 . 040 . 268 . 1 34 .040,77 43.113.386 2 = = = ∑ n e MSE i 6. Maka untuk α = 0,6 464 . 825 . 464 . 1 34 .788,63 49.804.065 2 = = = ∑ n e MSE i 7. Maka untuk α = 0,7 447 . 745 . 719 . 1 34 .195,34 58.471.345 2 = = = ∑ n e MSE i 8. Maka untuk α = 0,8 360 . 693 . 056 . 2 34 .240,81 69.927.574 2 = = = ∑ n e MSE i Universitas Sumatera Utara 9. Maka untuk α = 0,9 813 . 056 . 511 . 2 34 .656,67 85.375.931 2 = = = ∑ n e MSE i Untuk menentukan nilai α yang optimal, maka diambil dari nilai MSE yang paling minimum yaitu MSE pada α = 0,2. Universitas Sumatera Utara Tabel 4.2.10 Nilai Pemulusan Eksponensial Untuk Penumpang Domestik Periode Jumlah α=0.1 α=0.2 α=0.3 Penumpang Forescast 2 i e Forescast 2 i e Forescast 2 i e 1 317.693 2 262.399 3 250.465 306.634,20 3.154.979.028,64 295.575,40 2.034.948.188,16 284.516,60 1159511462,56 4 296.908 294.847,42 4.245.989,94 275.319,48 466.064.195,79 259.109,18 1428750793,39 5 288.737 294.326,55 31.243.069,20 282.776,08 35.532.519,56 273.747,37 224689067,50 6 294.128 294.396,29 71.980,60 280.305,39 191.064.491,92 278.101,94 256834695,28 7 337.314 294.369,46 1.844.233.258,14 283.033,73 2.946.347.494,15 284.427,43 2796989180,59 8 311.797 301.447,59 107.110.328,75 302.498,04 86.470.657,08 314.311,58 6323087,43 9 293.032 302.946,47 98.296.794,70 306.141,04 171.846.798,63 315.714,82 514510459,25 10 285.932 300.871,37 223.184.895,51 301.192,79 232.891.741,95 304.790,81 355654752,33 11 331.132 297.834,15 1.108.746.748,03 294.859,48 1.315.695.489,52 294.119,75 1369906502,01 12 329.845 303.390,98 699.815.227,07 308.529,07 454.368.999,66 315.274,04 212312991,89 13 326.424 307.951,27 341.241.827,54 317.666,92 76.686.502,67 326.294,65 16731,16 14 263.058 311.223,95 2.319.958.354,07 322.633,87 3.549.283.690,50 329.961,68 4476102932,77 15 306.916 302.631,88 18.353.718,45 300.617,92 39.665.849,47 293.420,54 182127467,60 16 304.820 303.171,00 2.719.201,00 302.568,51 5.069.189,21 299.097,55 32746445,45 17 309.035 303.267,86 33.259.892,25 303.152,40 34.605.041,59 301.325,35 59438780,22 18 345.236 304.120,54 1.690.481.133,24 305.278,78 1.596.579.190,39 305.260,48 1598041879,47 19 391.278 311.376,54 6.384.244.109,15 321.270,32 4.901.075.258,98 329.249,01 3847595848,54 20 353.177 325.880,04 745.123.806,87 350.880.,33 5.274.688,50 370.067,41 285286085,09 21 309.030 331.423,69 501.477.262,24 356.206,25 2.225.598.092,30 369.116,79 3610421851,81 22 362.161 328.185,11 1.154.361.033,34 341.834,86 413.151.967,30 340.728,20 459365001,57 23 336.467 334.933,89 2.350.414,01 352.577,38 259.544.311,52 355.843,55 375450728,66 24 355.296 336.047,76 370.494.820,09 349.558,34 32.920.788,18 348.402,25 47523858,00 25 369.510 340.343,40 850.690.555,56 354.634,10 221.292.549,57 354.979,23 211143189,61 26 314.028 346.530,92 1.056.439.613,51 363.594,66 2.456.853.486,16 366.758,87 2780544229,11 27 336.344 341.785,84 29.613.589,93 347.373,23 121.643.936,45 339.489,29 9892836,60 28 305.705 341.681,62 1.294.317.330,53 344.584,11 1.511.585.116,63 337.225,28 993527988,24 29 301.147 336.028,81 1.216.740.947,93 330.213,87 844.882.699,06 317.653,20 272454638,44 30 304.423 330.326,36 670.984.059,29 318.213,36 190.173.918,61 304.252,74 28987,45 31 320.900 325.797,70 23.987.426,11 311.160,78 94.852.484,12 299.372,60 463428864,65 32 316.475 325.255,20 77.091.982,28 312.968,41 12.296.152,39 307.322,07 83776145,89 33 250.020 323.807,61 5.444.611.094,36 312.672,56 3.925.343.775,77 309.784,32 3571774064,59 34 310.832 310.599,83 53.902,91 286.053,32 613.983.032,10 286.889,05 573264902,59 35 289.487 310.241,89 430.765.458,91 291.900,47 5.824.832,61 295.731,56 38994567,06 36 312.050 306.115,76 35.215.204,38 287.861,91 585.063.891,35 292.458,54 383825500,85 Jumlah 31.966.504.058,52 31.658.481.021,85 32682256517,64 Universitas Sumatera Utara Periode Jumlah α=0.4 α=0.5 α=0.6 Penumpang Forescast 2 i e Forescast 2 i e Forescast 2 i e 1 317693 2 262399 3 250465 273457,80 528668851,84 262399,00 142420356,00 251340,20 765975,04 4 296908 246216,52 2569626144,59 236641,50 3632051022,25 230384,12 4425426610,25 5 288737 274243,82 210052382,46 280101,00 74580496,00 289991,86 1574683,66 6 294128 281423,11 161414179,09 286996,63 50856509,39 292213,71 3664498,55 7 337314 289490,68 2287069840,18 294546,63 1829048364,39 297786,79 1562400222,87 8 311797 327685,78 252453202,78 339515,47 768313523,70 349184,52 1397826589,54 9 293032 322562,93 872075649,48 324690,31 1002248782,01 322514,37 869210065,15 10 285932 303984,15 325880227,94 298995,70 170660127,05 291870,89 35270437,08 11 331132 289863,45 1703093301,64 283981,12 2223205767,68 278865,93 2731741599,66 12 329845 320310,96 90897842,45 325915,19 15443383,06 333568,92 13867616,81 13 326424 331973,84 30800668,53 336415,91 99838345,38 339899,71 181594771,07 14 263058 333095,06 4905189073,07 333977,37 5029556473,84 333187,74 4918180480,35 15 306916 281738,53 633905197,02 268113,39 1505642775,63 253639,68 2838366421,13 16 304820 295347,69 89724637,79 294241,55 111903689,03 296932,18 62217634,45 17 309035 300421,12 74198928,65 301846,20 51678859,82 304937,96 16785745,22 18 345236 306323,38 1514192384,39 308705,81 1334454562,25 311234,42 1156107601,26 19 391278 337842,85 2855315576,13 346704,01 1986840317,08 354891,26 1323994797,08 20 353177 387206,36 1157997410,07 401878,56 2371841946,43 413650,86 3657087952,71 21 309030 375147,89 4371575245,82 374921,06 4341631260,80 369276,97 3629697113,86 22 362161 331973,90 911261247,91 318598,67 1897676856,40 303404,76 3452296178,22 23 336467 355265,04 353366157,46 355256,90 353060417,17 358647,49 491974144,70 24 355296 344198,00 123165604,00 340453,49 220300221,84 337918,39 301981289,57 25 369510 354040,11 239317589,43 354585,01 222755326,50 356674,03 164762010,68 26 314028 369155,41 3039031223,05 372509,64 3420102100,13 376235,65 3869791097,14 27 336344 330268,05 36917144,10 320758,89 242895778,39 310365,87 674863213,01 28 305705 331523,00 666568865,82 328454,48 517538703,77 327924,27 493696101,03 29 301147 308234,94 50238822,56 301711,76 318948,21 296997,92 17214870,88 30 304423 295800,04 74355370,18 291466,39 167873846,34 289714,65 216335509,47 31 320900 294799,80 681220648,84 294601,20 691627039,23 296596,17 590675944,49 32 316475 309161,02 53494303,44 314317,35 4655449,21 320287,28 14533441,84 33 250020 312669,30 3924934414,59 316467,05 4415210586,60 318988,43 4756644645,25 34 310832 261377,19 2445778331,05 250551,46 3633743020,45 238129,78 5285612536,26 35 289487 289744,48 66295,95 294751,70 27717076,62 302447,28 167968760,59 36 312050 286254,71 665397089,37 288476,84 555694108,12 290142,58 479935229,78 Jumlah 37899243851,66 43113386040,77 49804065788,63 Universitas Sumatera Utara Periode Jumlah α=0.7 α=0.8 α=0.9 Penumpang Forescast 2 i e Forescast 2 i e Forescast 2 i e 1 317693 2 262399 3 250465 240281,40 103705708,96 229222,60 451239557,76 218163,80 1043367521,44 4 296908 227444,38 4825194503,50 227822,28 4772836707,92 231517,82 4275875640,43 5 288737 302589,35 191887655,93 316566,41 774475949,63 330595,98 1752173871,77 6 294128 295129,14 1002275,29 294461,19 111016,91 289591,70 20578044,91 7 337314 298872,97 1477712747,48 298539,10 1503492832,79 298193,15 1530440932,89 8 311797 357345,28 2074645809,32 364976,71 2828081822,86 372721,19 3711757287,58 9 293032 317068,66 577761054,84 309102,88 258273215,65 298856,05 33919524,57 10 285932 284589,65 1801900,34 278568,16 54226082,20 274822,57 123419490,71 11 331132 275863,29 3054630166,40 275243,63 3123509865,70 276551,87 2978990260,40 12 329845 343291,59 180810678,98 354271,21 596639518,62 365527,07 1273210043,16 13 326424 341600,14 230315087,94 340564,02 199940081,21 336240,22 96358078,02 14 263058 330898,49 4602331884,21 327681,96 4176256023,00 324609,42 3788577589,84 15 306916 239030,44 4608449130,75 224975,98 6714166426,48 211904,12 9027256901,45 16 304820 303937,02 779652,64 315413,03 112212385,38 331156,11 693590702,55 17 309035 308303,91 534488,68 310238,81 1449169,57 308941,34 8772,04 18 345236 312890,82 1046210944,25 313307,80 1019409671,28 312967,91 1041229821,82 19 391278 362095,69 851607374,00 368617,57 513495124,27 374984,32 265484072,98 20 353177 422721,68 4836462372,76 429532,96 5830231940,34 434383,94 6594567839,94 21 309030 359429,22 2540080925,33 346524,80 1405859984,46 331480,33 504017125,20 22 362161 288863,51 5372522303,19 276826,68 7281945904,83 268561,00 8760960804,98 23 336467 366777,58 918730988,77 379658,48 1865504000,21 396347,50 3585673787,16 24 355296 335556,12 389662879,09 331462,96 568013557,53 323685,10 999249048,15 25 369510 359553,12 99139460,35 362864,13 44167630,96 367204,01 5317567,35 26 314028 379526,46 4290048420,55 382018,97 4622772288,35 383578,91 4837329357,92 27 336344 298741,20 1413970874,00 286008,22 2533690368,40 272479,24 4078707282,71 28 305705 330203,46 600174348,77 335806,05 906073248,71 345191,54 1559186788,24 29 301147 293149,33 63962789,48 289119,85 144652305,88 283601,96 307828588,49 30 304423 289585,53 220150380,89 290574,10 191792072,91 292685,13 137777693,19 31 320900 299516,31 457262138,48 302640,53 333408414,64 305526,88 236332954,29 32 316475 325882,16 88494635,29 330627,17 200283808,11 334419,75 322014191,10 33 250020 319618,83 4843996749,01 318441,25 4681466831,06 315792,68 4326045699,60 34 310832 224477,65 7457073411,47 210367,41 10093133534,78 196540,09 13062640950,98 35 289487 313567,50 579870324,96 328721,31 1539331457,57 348127,89 3438754091,73 36 312050 290362,19 470361129,42 287854,31 585431440,85 281013,10 963289329,09 Jumlah 58471345195,34 69927574240,81 85375931656,67 Universitas Sumatera Utara Grafik Nilai Pemulusan Eksponensial 50000 100000 150000 200000 250000 300000 350000 400000 450000 1 4 7 10 13 16 19 22 25 28 31 34 37 Periode P e n u m p a n g d a n F o re c a s t Periode Penumpang Forescast Grafik 4.2.10 Nilai Pemulusan Eksponensial Untuk Penumpang Domestik Forcast untuk 2009 adalah : Bulan 1 = 296.569,62 + -2.202,191 = 294.367,430 Bulan 2 = 296.569,62 + -2.202,192 = 292.165,239 Bulan 3 = 296.569,62 + -2.202,193 = 289.963,049 Bulan 4 = 296.569,62 + -2.202,194 = 287.760,859 Bulan 5 = 296.569,62 + -2.202,195 = 285.558,669 Bulan 6 = 296.569,62 + -2.202,196 = 283.356,478 Bulan 7 = 296.569,62 + -2.202,197 = 281.154,288 Bulan 8 = 296.569,62 + -2.202,198 = 278.952,098 Bulan 9 = 296.569,62 + -2.202,199 = 276.749,908 Bulan 10 = 296.569,62 + -2.202,1910 = 274.547,718 Bulan 11 = 296.569,62 + -2.202,1911 = 272.345,527 Bulan 12 = 296.569,62 + -2.202,1912 = 270.143,337 Universitas Sumatera Utara Untuk forecast tahun 2010, m yang digunakan adalah m = 13 karena untuk satu kali peramalan m merupakan nilai berkelanjutan dari m sebelumnya. Bulan 1 = 296.569,62 + -2.202,1913 = 267.941,147 Bulan 2 = 296.569,62 + -2.202,1914 = 265.738,957 Bulan 3 = 296.569,62 + -2.202,1915 = 263.536,766 Bulan 4 = 296.569,62 + -2.202,1916 = 261.334,576 Bulan 5 = 296.569,62 + -2.202,1917 = 259.132,386 Bulan 6 = 296.569,62 + -2.202,1918 = 256.930,196 Bulan 7 = 296.569,62 + -2.202,1919 = 254.728,005 Bulan 8 = 296.569,62 + -2.202,1920 = 252.525,815 Bulan 9 = 296.569,62 + -2.202,1921 = 250.323,625 Bulan 10 = 296.569,62 + -2.202,1922 = 248.121,435 Bulan 11 = 296.569,62 + -2.202,1923 = 245.919,244 Bulan 12 = 296.569,62 + -2.202,1924 = 243.717,054 Dan untuk forecast tahun 2011, maka m yang digunakan adalah m = 25. Dapat kita hitung sebagai berikut : Bulan 1 = 296.569,62 + -2.202,1925 = 241.514,864 Bulan 2 = 296.569,62 + -2.202,1926 = 239.312,674 Bulan 3 = 296.569,62 + -2.202,1927 = 237.110,484 Bulan 4 = 296.569,62 + -2.202,1928 = 234.908,293 Bulan 5 = 296.569,62 + -2.202,1929 = 232.706,103 Universitas Sumatera Utara Bulan 6 = 296.569,62 + -2.202,1930 = 230.503,913 Bulan 7 = 296.569,62 + -2.202,1931 = 228.301,723 Bulan 8 = 296.569,62 + -2.202,1932 = 226.099,532 Bulan 9 = 296.569,62 + -2.202,1933 = 223.897,342 Bulan 10 = 296.569,62 + -2.202,1934 = 221.695,152 Bulan 11 = 296.569,62 + -2.202,1935 = 219.492,962 Bulan 12 = 296.569,62 + -2.202,1936 = 217.290,771 Tabel 4.2.12 Forecast dengan Double Eksponensial Smoothing α = 0,2 Bulan 2009 2010 2011 1 294.367,430 267.941,147 241.514,864 2 588.734,859 265.738,957 239.312,674 3 883.102,289 263.536,766 237.110,484 4 287.760,859 261.334,576 234.908,293 5 285.558,669 259.132,386 232.706,103 6 283.356,478 256.930,196 230.503,913 7 281.154,288 254.728,005 228.301,723 8 278.952,098 252.525,815 226.099,532 9 276.749,908 250.323,625 223.897,342 10 274.547,718 248.121,435 221.695,152 11 272.345,527 245.919,244 219.492,962 12 270.143,337 243.717,054 217.290,771 Universitas Sumatera Utara

4.3 Forecast dengan Doble Exponensial Smoothing untuk Penumpang Internasional