An Alternative Forecasting Using Holt-Winter Damped Trend for Soekarno-Hatta Airport Passenger Volume

Transcription

1 An Alernaive Forecasing Using Hol-Winer Damped Trend for Soekarno-Haa Airpor Passenger Arum Handini Primandari Program Sudi Saisika, FMIPA, UII ABSTRACT Locaed in he capial ciy of Indonesia, Soekarno-Haa Airpor is considered as he main airpor. Since here are some aviaion companies providing low cos fligh, he number people coming and leaving rough his airpor has increased. The passenger volume can be considered as seasonal daa since i shows incremen in paricular monhs, such as long holiday. Knowing in advance he volume of passenger will help he governmen o improve is service effecively. There is a simple and accurae mehod for forecasing seasonal daa ha is called Hol-Winer Exponenial Smoohing (HWE). However, HWE always encouners over forecasing problem when i is employed o forecas in some fuure periods (m>1). In order o solve his problem, we add he damped parameer ha will be damping he exponenially growh on HWE. This mehod called HWE damped rend. We employed he domesic passenger volume daa of Soekarno-Haa Airpor from January 2008 ill December This daa colleced from prior research. As he resul, HWE damped rend ouperforms radiional HWE on eiher raining daa se or esing daa. Keywords hol-winer, hol-winer damped rend, rus-region-reflecive algorihm Inroducion The availabiliy of infrasrucure such as ransporaion funcion o faciliae eiher permanen or emporary migraion. Basically, ransporaion is divided ino hree including land, air, and waer ransporaion. Among he ypes of ransporaion, air ransporaion is he fases in erm of ime for ravelling. Alhough here are several issues regarding fligh safey, as he echnology become more sophisicaed he aviaion acciden risk can be minimalized (BBC, 2014). In he early of 90 s, aviaion is considered as luxurious ransporaion service which can be afforded only by high class sociey. However, in he early of 2000s commercial aviaion indusries are more arisen providing low cos fligh. As he resul, fligh no only can be afforded by high class sociey, bu also by middlelow sociey. One of aviaion company which jargon is we make people fly, has been proofing is exisence providing low cos fligh. Because of economical reason (Arum Handini Primandari) 1

2 menion above, aircraf became he op choice for long disance ravel. Soekarno-Haa (Soea) Airpor locaed in Tangerang, Jakara is one of Indonesian inernaional airpor under Angkasa Pura II, Inc. Since i is locaed in he capial ciy of Indonesia, Soea Airpor is considered as main inernaional airpor. In aemp o improve is service, he governmen buil erminal 3 ulimae which is launched on June, 15 h The reason why he erminal 3 ulimae was buil is he high densiy volume of passengers (Akhir, 2016). The predicion of passenger volume can be calculaed inuiively, for example when Eid or long holiday is coming, he passenger volume will increase significanly. However, he accuracy of his ype of predicion is no measurable. Because of his reason, we need o calculae he predicion using scienific mehod. The accurae forecasing will help he governmen and relaed insiuion o fulfill he need of passenger effecively. The daa of passenger volume can be considered as seasonal daa since i shows incremen in paricular monhs, such as long holiday. There is a simple mehod for forecasing seasonal daa ha is Hol- Winer Exponenial Smoohing (HWE). Beside is simpliciy, HWE is considered having high accuracy (Li, 2013; Taylor, 2012). However, HWE always encouner over forecasing problem when i is employed o forecas in some fuure periods (m>1). Thus, he predicion value is far from acual daa. The growh facor in HWE rigger he over forecasing problem. In order o solve his problem, we add he damped parameer ha will be damping he exponenially growh. This mehod called HWE damped rend (Hyndman, e. al., 2008; Taylor, 2003). HWE mehod consiss of some parameers for fiing daa. In aemp o obain he opimum fiing curve, we also need he opimum parameers. The value of is parameers are obained by using rus-region-reflecive algorihm. This algorihm generaes gradiens of objecive funcion ieraively. In his paper, passenger volume in Soea Airpor is prediced by employing HWE damped rend. We conduc he research by using rus-region-reflecive algorihm in aemp o obain opimum (Arum Handini Primandari) 2

3 parameers. As he comparison, he resul of HWE damped rend will be compared wih he radiional HWE. Mehod 1. Daa We used domesic passenger volume daa of Soekarno-Haa Airpor from January 2008 ill December 2015 (Primandari and Sario, 2016). Passenger volume is he number of deparure and arrival. We spli up he daa ino wo differen purpose, ha are daa for building model (raining se) and daa for forecasing (esing se). 2. Hol-Winer Exponenial wih Damped Trend The classic Hol-Winer Exponenial Smoohing have hree parameers for level (α), growh (β), and seasonal (γ). Adding he damp parameer (ϕ) ino HWE o dampening rend, we have he formula of addiive HWE mehod wih damped rend express as follow (Hyndman, e al. 2008): Level : y s 1 b m 1 1 Growh : b 1 b 1 1 Seasonal : s y b s m The predicion formula defines as follow: Forecas : 2 h yˆ h... b smh (1) Where y is he acual daa a ime and m is he lengh of seasonaliy (e.g. he number of monhs or quarers in a year). The, b, s respecively as level, growh, and season facor a ime. 3. Trus-Region-Reflecive Algorihm There are several non-linier opimizaion algorihms o solve opimizaion problems including newon mehod, gauss-newon mehod, and levenberg-marquard mehod. The rusregion opimizaion mehod in combinaion wih he inerior reflecive Newon algorihm can be a powerful approach o solve consrained non-linear minimizaion problems. The rus-region mehod approximaes an objecive funcion f(x) wih quadraic funcion q(s), which is a (Arum Handini Primandari) 3

4 reflecion of funcion f(x) in a neighborhood N around he curren poin x, in which x is a consrain vecor. The neighborhood N is called rus-region. Mahemaically, he rus-region-reflecive mehod sub problem is saed as follow (Le and Faahi, 2016): 1 T T min sqs min s s Hs s g such 2 ha Ds, (2) where g is he gradien of funcion f(x) for curren x, H is a symmeric marix of second derivaives (Hessian marix), D is a diagonal scaling marix, Δ is he rusregion radius > 0, and is he second norm. A rial sep s is compued by minimalizing he area N in equaion (2). If f(x+s) < f(x), he curren poin x is updaed o be x+s, oherwise he vecor x remains unchanged and he area N is shrunk ino nex sep. 4. Error Measuremen Error is he difference beween prediced value and acual value. The error measuremens are used o measure he accuracy of forecasing. We employ wo ype of measuremens ha are he absolue error and relaive error. The absolue error is he maximum error. We use RMSE (Roo Mean Squared Error) as absolue error measuremen given as follow (Li 2013): n 1 RMSE y y ˆ 2. (4) n 1 Where n is he amoun of daa, acual daa a ime and y is he y ˆ is he predicion a ime. The relaive error compares he error by acual daa. We use MAPE (Mean Absolue Percenage Error) o measure relaive error. n 1 y ˆ y MAPE 100% n, (5) y where argumen. i1 Numerical Resul is he absolue value of is The number of arriving passengers in Soekarno Haa Airpor from January 2008 o December 2015 flucuaed around 1 million people and so did he number of deparing passengers. The average of arrival is people, while he average of deparure is people. According o his average, people end o (Arum Handini Primandari) 4

5 come o he capial. Below is he graph of arrival and deparure. (a) (b) Figure 1. (a) The Number of Arrival; (b) The Number of Deparure of Soea Airpor from January 2008 o December 2015 Even hough he number people coming o he capial is greaer han he people who is leaving, bu he boh are proporional. I can be seen from he graph ha arrival and deparure barely have he same paern. The red marks on he graph are he monh in which Eid was held. Because of abou 85% Indonesia ciizen are muslims (Republika, 2016), once in every year here are massive movemen ino homeown o celebrae Eid called mudik. Bu, according o he graph, his mudik do no always (Arum Handini Primandari) 5

6 increasing he volume of fligh occupan. Thus, Eid do no affec he seasonal. The fligh occupan during he observed years summed up monhly presened in Fig.3. Figure 2. The Comparison of Number of Arrival and Deparure Figure 3. Passenger Monhly Recapiulaion According o Fig.3., he lowes number of passengers is on February, whereas he highes is on December. Meanwhile, he passenger volume of ohers monhs flucuaes around he average. This figure also explains ha from January 2008 o December 2015, February become he monh wih low volume of passenger on average. Thus we can clearly see he seasonal paern (Arum Handini Primandari) 6

7 We work on passenger volume daa from January 2008 o July 2015 o obain fiing curve of HWE damped rend. The opimum parameers obained from rusregion-reflecive algorihm are 0,9093; 0,4888; 0,118, and 0,8284. The separaely graph of level, growh, and seasonal paern are presened below. (a) (b) (c) Figure 4. The Level, Growh, and Seasonal Facors on Training Daa (Arum Handini Primandari) 7

8 Figure 5. The Comparison of Fiing Daa wih Acual Daa Based on Fig.5. he HWE damped rend performs well enough for fiing he acual daa, even hough i canno follow every poins perfecly. The comparison beween HWE damped rend and radiional HWE is given below. Table 1. Training Daa Performance Comparison No Iem HWE Mehod HWE Damped Trend 1. Alpha (α) 0,9196 0, Bea (β) 0,5250 0, Gamma (γ) 0,1091 0, Phi (ϕ) - 0, RMSE , ,60 6. MAPE 8,28% 7,87% According o boh RMSE and MAPE, we can see ha HWE damped rend ouperform radiional HWE. We use passenger volume daa from Augus o December 2015 for checking he forecasing performance obained in fiing daa. Table 2. Forecasing Comparison of Tesing Daa Mehod No Monh Acual HWE Daa HWE Damped Trend 1 Aug Sep Oc Nov Dec According Table 2., he forecas values of HWE always increase exponenially rough he periods. Therefore, is value is far from he acual value. On he oher way, HWE damped rend predicion values sill follow he rend of he acual values, eiher downward or upward. Thus, (Arum Handini Primandari) 8

9 he forecasing value of HWE damped rend is more plausible han radiional HWE. The comparison is shown on he graph in Fig. 6. Figure 6. The Forecasing Performance Comparison On November, we can clearly see ha HWE forecasing coninue o rise, whereas he HWE damped rend slide down o acual daa. Conclusion The HWE wih damped rend ouperformed radiional HWE boh raining and esing daa se. Alhough, he opimum parameers of HWE damped rend and HWE did no show much difference, he value of RMSE and MAPE of HWE damped rend are significanly smaller han HWE. Moreover, he esing daa se graph indicaed ha HWE forecasing do no encouner over forecasing. So ha, adding he damped parameer in Hol-Winer Exponenial Smoohing was successfully damping he rend o rise exponenially. Thus he damped parameer reduces he error measuremen of esing daa forecasing. We can employ HWE damped rend o predic he nex passenger volume. References Akhir, D. J., HOT BISNIS: Terminal 3 Ulimae, Bandara Modern di Indonesia, Rerieved from Okezone:hp://economy.okezone.co m/read/2016/06/10/320/ /ho -bisnis-erminal-3-ulimaebandara-modern-di-indonesia. Diakses anggal Juni 20, BBC, AirAsia QZ8501: Does bad weaher cause plane crashes?, Rerieved from BBC: hp:// Diakses angal 30 Desember, Hyndman, R. J., e. al., 2008, Forecasing wih Exponenial Smoohing: The (Arum Handini Primandari) 9

10 Sae Approach, Deblik, Berlin, Germany: Springer. Le, T. M., & Faahi, B., 2016, Trus-Region Reflecive Opimisaion o Obain Soil Visco-Plasic Properies, Inernaional Journal for Compuer- Aided Engineering and Sofware, 33(2), Journal of Forecasing, 19, Taylor, J. W., 2012, Densiy Forecasing on Inraday Call Cener Arrivals Using Models Based on Exponenial Smoohing, Managemen Science, 53(3), Li, X., 2013, Comparison and Analysis beween Hol Exponenial Smoohing and Brown Exponenial Smoohing Used for Freigh Turnover Forecas, Proceedings Third Inernaional Conference on Inelligen Sysem Design and Engineering Applicaions (ISDEA) 2013, ISBN: , Held in Hongkong China by IEEE. Primandari, A. H., & Sario, A. P., 2016, Grey Double Eksponenial Smoohing dengan Levenberg- Marquard unuk Peramalan Penumpang di Bandara Soekarno Haa, Yogyakara: Laporan Peneliian Tidak Dipublikasi. Republika, 2016, Januari 9, Persenase Uma Islam di Indonesia Jadi 85 Persen, Rerieved from Republika News: hps://m.republika.co.id/beria/nasi onal/umum. Diakses 9 Januari, 2016 Taylor, J. W., 2003, The Exponenial Smoohing wih a Damped Muliplicaive Trend, Inernaional (Arum Handini Primandari) 10