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