Analysis of time series for postal shipments in Regional VII East Java Indonesia

Transcription

1 Journal of Physics: Conference Series PAPER OPEN ACCESS Analysis of ime series for posal shipmens in Regional VII Eas Java Indonesia To cie his aricle: DE Kusrini e al 2018 J. Phys.: Conf. Ser View he aricle online for updaes and enhancemens. Relaed conen - The Spiriualiy of Mafia Shalawa; A Crisis Soluion of Modern Sociey Mambaul Ngadimah - Impac of climae change in coasal area: A vulnerabiliy assessmen of coasal inundaion due o sea level rise in Cenral Java Indonesia Muh Aris Marfai - Forecasing Hisorical Daa of Bicoin using ARIMA and -Sue Indicaor Dian Uami Suiksno, Ansari Saleh Ahmar, Nuning Kurniasih e al. This conen was downloaded from IP address on 07/10/2018 a 20:58

2 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion Analysis of ime series for posal shipmens in Regional VII Eas Java Indonesia DE Kusrini 1, B S S Ulama 1 and L Aridinani 1 1 Saisika Bisnis Deparmen, Insiu Teknologi Sepuluh Nopember, Surabaya, Indonesia. dwi_endah@saisika.is.ac.id Absrac. The change of number delivery goods hrough PT. Pos Regional VII Eas Java Indonesia indicaes ha he rend of increasing and decreasing he delivery of documens and non-documens in PT. Pos Regional VII Eas Java Indonesia is srongly influenced by condiions ouside of PT. Pos Regional VII Eas Java Indonesia so ha he predicion he number of documen and non-documens requires a model ha can accommodae i. Based on he ime series plo monhly daa flucuaions occur from hen he model is done using ARIMA or seasonal ARIMA and seleced he bes model based on he smalles AIC value. The resuls of daa analysis abou he number of shipmens on each produc sen hrough he Sub-Regional Posal Office VII Eas Java indicaes ha here are 5 pos offices of 26 pos offices enering he erriory. The larges number of shipmens is available on he PPB (Pake Pos Biasa is regular package shipmen/non-documen ) and SKH (Sura Kila Khusus is Special Express Mail/documen) producs. The ime series model generaed is largely a Random walk model meaning ha he number of shipmen in he fuure is influenced by random effecs ha are difficul o predic. Some are AR and MA models, excep for Express shipmen producs wih Malang pos office desinaion which has seasonal ARIMA model on lag 6 and 12. This means ha he number of iems in he following monh is affeced by he number of iems in he previous 6 monhs. Keywords: ARIMA, documens, non-documens, shipmens, pos office. 1. Inroducion The average increase of inerne user households in Indonesia is 3.5% per year as cellular phone users in Indonesia grow by 2% per year (Saisics Indonesia, 2016) encourages shifing he way Indonesians shop from he direc ransacion sysem (in he marke/shop) o indirec ransacion online, i encourages PT. Pos Indonesia o cooperae wih some online shopping service providers such as Maahari mall, Ali Express, ec. (PT. Pos Indonesia Annual Repor, 2015). These condiions affec he magniude of he ypes of documens and non-documens hrough he Pos, which based on he annual repor of PT. Pos Indonesia (2015) delivery of goods hrough packages has increased since 2010 from 14,944,000 unis o 25,241,000 packages in 2014, while sandard leer delivery acually decreased from unis in 2010 o unis in he Year This change indicaes ha he Conen from his work may be used under he erms of he Creaive Commons Aribuion 3.0 licence. Any furher disribuion of his work mus mainain aribuion o he auhor(s) and he ile of he work, journal ciaion and DOI. Published under licence by Ld 1

3 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion rend of increasing and decreasing he delivery of documens and documens in PT. Pos Indonesia is srongly influenced by condiions ouside of PT. Pos Indonesia so ha he predicion he number of documen submissions and non-documens requires a model ha can accommodae i. ARIMA models are, in heory, he mos general class of models for forecasing a ime series which can be made o be saionary by differencing (if necessary), perhaps in conjuncion wih nonlinear ransformaions such as logging or deflaing (if necessary). A random variable ha is a ime series is saionary if is saisical properies are all consan over ime. A saionary series has no rend, is variaions around is mean have a consan ampliude, and i wiggles in a consisen fashion, i.e., is shor-erm random ime paerns always look he same in a saisical sense. The laer condiion means ha is auocorrelaions (correlaions wih is own prior deviaions from he mean) remain consan over ime, or equivalenly, ha is power specrum remains consan over ime. A random variable of his form can be viewed (as usual) as a combinaion of signal and noise, and he signal (if one is apparen) could be a paern of fas or slow mean reversion, or sinusoidal oscillaion, or rapid alernaion in sign, and i could also have a seasonal componen. An ARIMA model can be viewed as a filer ha ries o separae he signal from he noise, and he signal is hen exrapolaed ino he fuure o obain forecass. Based on he above background, he purpose of his reaearch are o obain and analyze he bes ime series model of documen delivery and non-documen and review he forecasing of documens and non-documens based on he ARIMA model obained in he nex period 2. Maerials and Mehods 2.1. ARIMA Model The acronym ARIMA sands for Auo-Regressive Inegraed Moving Average. Lags of he saioneries series in he forecasing equaion are called "auoregressive" erms, lags of he forecas errors are called "moving average" erms, and a ime series which needs o be differenced o be made saionary is said o be an "inegraed" version of a saionary series. Random-walk and random-rend models, auoregressive models, and exponenial smoohing models are all special cases of ARIMA models. A non seasonal ARIMA model is classified as an "ARIMA(p,d,q)" model, where: p is he number of auoregressive erms, d is he number of no seasonal differences needed for saionery, and q is he number of lagged forecas errors in he predicion equaion. The forecasing equaion is consruced as follows. Firs, le y denoe he d h difference of Y, which means: If d=0: y = Y If d=1: y = Y - Y -1 If d=2: y = (Y - Y -1 ) - (Y -1 - Y -2 ) = Y - 2Y -1 + Y -2 Noe ha he second difference of Y (he d=2 case) is no he difference from 2 periods ago. Raher, i is he firs-difference-of-he-firs difference, which is he discree analog of a second derivaive, i.e., he local acceleraion of he series raher han is local rend. In erms of y, he general forecasing equaion is: ŷ = μ + ϕ 1 y ϕ p y -p - θ 1 e θ q e -q (1) Here he moving average parameers (θ s) are defined so ha heir signs are negaive in he equaion, following he convenion inroduced by Box and Jenkins. Some auhors define hem so ha hey have plus signs insead. When acual numbers are plugged ino he equaion, here is no ambiguiy, bu i s 2

4 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion imporan o know which convenion your sofware uses when you are reading he oupu. Ofen he parameers are denoed here by AR(1), AR(2),, and MA(1), MA(2), ec.. To idenify he appropriae ARIMA model for y, we begin by deermining he order of differencing (d) needing o saionary he series and remove he gross feaures of seasonaliy, perhaps in conjuncion wih a variance-sabilizing ransformaion such as logging or deflaing. If we sop a his poin and predic ha he differenced series is consan, we have merely fied a random walk or random rend model. However, he saioneries series may sill have auo correlaed errors, suggesing ha some number of AR erms (p 1) and/or some number MA erms (q 1) are also needed in he forecasing equaion PT.Pos Producs PT. Pos Indonesia (Persero) has an exensive nework of 4,800 online pos offices (hp:// The number of service poins reached 58,700 poins in he form of pos office, posal agency, Mobile Posal Service, and ohers. Innovaion coninues o be carried ou by Pos Indonesia, among ohers, Pos shop developmen which is a reail business developmen implemened o change he image of convenional office ino a modern pos office wih one sop shopping service paern, namely Posal services in he form of mail delivery service, package, financial services, samps, philaely producs and ohers. Online Shopping services Pos Indonesia also provides e-commerce services and oher services hrough mypos and m-pospay applicaions. In general, PT.Pos Indonesia's producs are divided ino hree caegories: 1. Leers and Packages In his caegory here are some producs such as: Admailpos, Express Mail Service (EMS), Philaelic, Pakepos, Posexpress, Special Poskila, Ordinary Leer (Sandard). 2. Financial Services In his caegory here are several producs such as: Bank Channelling, Fund Disribuion, Giropos, Weselpos, Pos Pay. 3. Reail in cooperaion wih ANTAM gold 4. Logisic Inegraion, Cusomized according o cusomer's reques which include services: Transporing, Warehousing, Freigh forwarding, Disribuion of goods and Supply chain managemen. 5. Inernaional pos include: EMS, inernaional fas Package, Expor Package, Inernaional regisered mail, Inernaional Pos Pos, Inernaional air mail. In his research he producs used in he analysis are Admailpos produc, Express Mail Service (EMS), Pakepos, Posexpress, Special Poskila, Ordinary Leer (Sandard). Preparaion of producs based on documen caegory and non documen can no be done direcly because here are several caegories of producs whose daa can no be differeniaed wheher included in he documen or non documen caegory Mehodology for Daa Modelling Sources of daas in his research were aken from he daa delivery noes (documens and nondocumens) or produc services leer and package services received by PT.Pos regional VIII Eas Java for 5 years saring from 2013 o The ypes of producs used for research daa are: 1. PPB is Ordinary Package Shipmen (non documen) 2. SKH is a Special Express Mail (documen) 3. PPKH is a Special Express Package Delivery (non-documen) 4. XP is Express (non documens and documens) 5. EMS is Express Mail Service (documen) 3

5 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion The daas used in his research are in he monhly daa series (wih bag for uni of daa) per each delivery desinaion (26 pos offices hroughou Eas Java), so ha modelling will be done a each delivery desinaion. Afer we were doing he modelling hen we were forecasing for he nex few monhs. 3. Resuls The resuls of he research divided ino hree pars: 1. Descripive analysis of he number of shipmens based on he pos office of desinaion of he producs 2. Time series daa modelling based on producs ype and pos office of producs desinaion 3. Forecasing based on he model obained for each ype of producs and pos office of desinaion of he mail. The resuls can be seen in he secion 3.1, 3.2 and Descripive analysis of he number of shipmens According o Figure 1, here are five pos offices ha have a oal larger produc shipmen han oher pos offices (more han 1,200,000 bags). While he oher 19 pos offices only ge oal shipmens of producs under 200,000 bags) 500, , , , , , , ,000 PPB SKH PPKH EMS EXPRESS 100,000 50,000 - Figure 1. Bar chars he number of bags of shipmen by producs and pos offices desinaion Five pos offices ha ge he mos poss are Pos Office KP Malang, Pos Office KP Kediri, Pos Office KP Madiun, Pos Office KP Jember and Pos Office KP Bliar. The larges number of mails for he five Pos Offices is no only on he oal producs bu also on all ypes of producs, so for Pos 4

6 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion Office Sub-Regional VII Eas Java can make his informaion o provide more space for he producs delivered here han he office anoher desinaion pos Time series daa modeling Based on he ime series plo monhly daa flucuaions occur from and due o he cause of he flucuaion of unknown daa, hen he modeling is done using ARIMA or seasonal ARIMA model and seleced he bes model based on he smalles AIC value. Based on he ACF and PACF plos and esing he significance of he parameers and he coefficien reducion o obain he appropriae model, he corresponding model is shown in full in Table 1. Table 1. The Time series model for he shipmen of producs based on he pos office of desinaion of he mail Producs Pos Office PPB SKH PPKH EMS EXPRESS Probolinggo ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Pasuruan ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Lumajang ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Jember ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Bondowoso ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Siubondo ARIMA (0,0,1) ARIMA (2,1,1) ARIMA (0,0,1) ARIMA (0,0,1) ARIMA (0,0,1) Banyuwangi ARIMA (0,1,0) ARIMA (0,0,1) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Malang ARIMA (0,0,1) ARIMA (0,0,1) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA ([6,10],0,[6,12]) Nganjuk ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Madiun ARIMA (0,1,0) ARIMA (0,0,2) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Ponorogo ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Magean ARIMA (0,0,1) ARIMA (0,0,1) ARIMA (0,0,1) ARIMA (2,0,2) ARIMA (0,0,1) Ngawi ARIMA (0,0,1) ARIMA (0,0,1) ARIMA (0,1,0) ARIMA (0,0,1) ARIMA (0,0,1) Bangkalan ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Sampang ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,0,1) ARIMA (0,1,0) ARIMA (0,1,0) Pamekasan ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,0,1) ARIMA (0,1,0) Sumenep ARIMA (0,0,1) ARIMA (0,0,1) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Gresik ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Lamongan ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Tuban ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Bojonegoro ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Mojokero ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Jombang ARIMA (0,0,1) ARIMA (0,0,1) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Kediri ARIMA (0,1,0) ARIMA (0,0,1) ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (0,1,0) Bliar ARIMA (0,0,1) ARIMA (1,0,0) ARIMA (0,0,1) ARIMA (0,0,1) ARIMA (0,0,1) Tulungagung ARIMA (0,1,0) ARIMA (0,1,0) ARIMA (1,0,0) ARIMA (0,1,0) ARIMA (1,0,0) Mos ime series models are produced in he form of a Random walk where a random walk is defined as a process where he curren value of a variable is composed of he pas value plus an error erm defined as a whie noise (a normal variable wih zero mean and variance one). The implicaion of a process of his ype is ha he bes predicion of y for nex period is he curren value, or in oher 5

7 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion words he process does no allow o predic he change (y y 1 ). Tha is, he change of y is absoluely random. I can be shown ha he mean of a random walk process is consan bu is variance is no. Therefore a random walk process is non saionary, and is variance increases wih. In pracice, he presence of a random walk process makes he forecas process very simple since all he fuure values of y +s for s > 0, is simply y. Pos Office (KP) Table 2. Time series model wihou random walk Producs PPB SKH PPKH EMS EXPRESS Siubondo Z = 792,75 + a Z = 0, 49Z 1+ 0,11Z 2 Z = 476, 74 + a + 0,33a + 0, 40Z 3 + a + 0,76a 1 + 0,32a Banyuwangi Z = 358,89 + a + 0,36a Malang Madiun Magean Ngawi Sampang Sumenep Jombang Z = 9399,84 + a + 0,39 a Z = 863,18 + a + 0, 49 a Z = 793, 42 + a Z a a Z = 160,48 + a + 0,36a Z = 287,6 + a + 0,29a Z = 6837,348 + Z + a 0,58129 a. = 4142, , Z = 3750,65 + a + 0,31a + 0,36a 1 2 Z = 384,99 + a + 0, 46a Z = 353,92 + a + 0,36a + 0, 4a Z = 883,99 + a + 0,33 a Z = 772,58 + a + 0,65 a Z = 339,35 + a + 0,72a Kediri Z = 3854,67 + a + 0, 29a Bliar Tulungagung Z = 7948,82 + a + 0, 47 a Z = ,38Z + a 1 Z = 520,18 + a + 0,5a Z = 160,98 + a + 0,35a 1 Z = 486,05 + a + 0,31 a Z = 4797,11+ a Z = 175,46 + 0,15Z 0,83Z Z = 311,69 + a a + 0,57a 1 0,84a 2 + 0,51a Z = 160,98 + a + 0,35a 1 Z = 153,37 + a + 0,33a 1 Z = 1618,78 + a Z = 287,91+ a + 0,33 a Z = 2879,1+ a + 0, 45a + 0,5a 1 + 0, 49a Z = 504,73 + 0,31Z + a 1 6 Z = 299,81+ 0, 25Z + a 1 Based on Table 2 i can be concluded ha only express shipmen producs wih he desinaion of Malang pos office have a seasonal ARIMA model in which he number of deliveries in he fuure is affeced by shipmen in he previous 6 monhs. The res are AR and MA models in addiion o he previously described random walk model Forecasing The model already obained in he previous secion is used o predic he number of iems by ype of posal produc and pos office. Forecasing is done by using ousampel daa o forecas daa up o 3 monhs ahead. The forecasing resuls are shown in Table 3. Forecasing resuls obained are expeced o provide informaion o he Regional Posal Coordinaor VII Eas Java o make he preparaion of a more adequae place and workforce. 6

8 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion Table 3. Forecasing number of bags for every producs and pos office desinaion for hree monhs in 2017 Pos Office (KP) Monh PPB SKH PPKH EMS EXPRESS Probolinggo Ocober November December Pasuruan Ocober November December Lumajang Ocober November December Jember Ocober 8,363 3,729 5,041 1,699 3,032 November 8,363 3,729 5,041 1,699 3,032 December 8,363 3,729 5,041 1,699 3,032 Bondowoso Ocober November December Siubondo Ocober November December Banyuwangi Ocober November December Malang Ocober 9,400 4,143 5,718 1,922 2,832 November 9,400 4,143 5,718 1,922 1,964 December 9,400 4,143 5,718 1,922 5,540 Nganjuk Ocober November December Madiun Ocober 8,441 3,751 5,162 1,732 3,068 November 8,441 3,751 5,162 1,732 3,068 December 8,441 3,751 5,162 1,732 3,068 Ponorogo Ocober November December Magean Ocober November December Ngawi Ocober November December

9 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion Pos Office (KP) Monh PPB SKH PPKH EMS EXPRESS Bangkalan Ocober November December Sampang Ocober November December Pamekasan Ocober November December Sumenep Ocober November December Gresik Ocober November December Lamongan Ocober November December Tuban Ocober November December Bojonegoro Ocober November December Mojokero Ocober November December Jombang Ocober November December Kediri Ocober 8,773 3,855 5,372 1,800 3,210 November 8,773 3,855 5,372 1,800 3,210 December 8,773 3,855 5,372 1,800 3,210 Bliar Ocober 7,949 3,558 4,797 1,619 2,879 November 7,949 3,558 4,797 1,619 2,879 December 7,949 3,558 4,797 1,619 2,879 Tulung agung Ocober November December TOTAL 179,280 79, ,890 36,565 65,223 8

10 Inernaional Conference on Mahemaics: Pure, Applied and Compuaion 4. Discussion The resuls of daa analysis of he number of shipmens on each produc sen hrough he Sub-Regional Posal Office VII indicaes ha here are 5 pos offices of 26 pos offices enering he erriory. The larges number of shipmens is available on he PPB (non-documen) and SKH (documen) producs. The ime series model generaed mos are random walk models. The random walk model explain ha he number of shipmen is influenced by random effecs in he fuure, ha are difficul o predic, Some models are AR and MA, excep for Express shipmen producs wih Malang pos office desinaion which has seasonal ARIMA model on lag 6 and 12. This means ha he number of iems in he following monh is affeced by he number of iems in he previous 6 monhs. There are several hings ha can be suggesed in his research are: a. The daa uni used is sill in he form of pockes raher han he number of leers for documens or he number of unis of goods for non-documens b. Time unis of daa used also in monhly raher han weekly or daily unis so he models are less sensiive o capure changes in daa behaviour. 5. Acknowlegmen This research was suppored by he Minisry of Research and High Educaion, Indonesia (Kemenrisek Diki) under Research Local ITS (Deparmen Gran 2017) and he Saisika Bisnis Deparmen, Faculy of Vocaion Insiu Teknologi Sepuluh Nopember Surabaya Indonesia. 6. References [1]. Al-Zeaud H A 2011 Modelling and Forecasing Volailiy using ARIMA model European Journal of Economics Finance & Adminisraive Science Issue 35 p [2]. Azad A K and Mahsin M 2011 Forecasing Exchange Raes of Bangladesh using ANN and ARIMA models: A comparaive researchinernaional Journal of Advanced Engineering Science & Technologies vol 10 Issue 1 p [3]. Conreras J, Espinola R, Nogales F J and Conejo A J 2003 ARIMA models o predic Nex Day Elecriciy Prices IFEE Transacions on power sysem vol 18 no 3 p [4]. Daa K 2011 ARIMA Forecasing of Inflaion in he Bangladesh Economy The IUP Journal of Bank Managemen vol 10 no 4 p [5]. Kumar K, Yadav A K, Singh M P, Hassan H and Jain V K 2004 Forecasing Daily Maximum Surface Ozone 6 Concenraions in Brunei Darussalam An ARIMA Modelling Approach Journal of Air and Wase Managemen and Associaion vol 54 p [6]. Liv Q, Liu X, Jiang B, and Yang W 2011 Forecasing incidence of hemorrhagic fever wih renal syndrome in China using ARIMA model Biomed Cenral p [7]. Merh N, Saxena VP and Pardasani KR 2011 Nex Day Sock marke Forecasing: An Applicaion of ANN & ARIMA The IUP Journal of Applied Science vol 17 no 1 p [8]. Uko A K, Nkoro E 2012 Inflaion Forecass wih ARIMA Vecor Auoregressive & Error Correcion Models in Nigeria European Journal of Economic Finance and Adminisraive Science Issue 50 p