Iteratoal Joural of Coputer ad Electrcal Egeerg, Vol. 5, o., August 03 A Methodolog to Iprove Cash Dead Forecastg for ATM etwork Saad M. Darwsh Abstract Developg cash dead forecastg odel for ATM etwork s a challegg task as the chroologcal cash dead for ever ATM fluctuates wth te ad ofte superposed wth o-statoar behavor of users. I order to prove the forecastg precso of ATM cash dead, a Iterval Tpe- Fuzz eural etwork (ITF) has bee utlzed ths paper. The atecedet parts each rule of the ITF are terval tpe- fuzz sets vew of codtos regardg te, locato, cash resdual ad other factors that could lead to cosder cash upload able to keep cash at the rght levels to eet user dead. The eploed ITF has both o-le structure ad paraeter learg abltes. Sulato results for ATM cash forecastg show the feasblt ad effectveess of the proposed ethod. Idex Ters Electroc servces optzato, Fuzz logc, Cash dead forecastg, ATM. I. ITRODUCTIO ATM (Autoatc Teller Mache) s a coputerzed telecoucato devce that provdes facal trasactos a publc space wthout the eed for the hua clerk []. Optal cash aageet ad servces avalablt s oe of the ost portat factors the ATM etwork servces busess. Usg cash aageet optzato ad effcet cash loads routg, baks ca avod of stuck ATMs wth cash ad aage the sste dacall chagg evroet b acheveet the dfferet requreets of ATM etwork partcpats. Recetl, ore baks are turg ther atteto to derve greater effcec how the aage ther cash at ATMs []. Effectve cash aageet starts wth a autoated soluto that uses sophstcated algorths to accuratel predct currec suppl ad dead, allowg baks to forecast dead ad proactvel aage currec throughout ther etwork plus wth reducg of currec trasportato ad servcg costs. These algorths should also be flexble eough to allow the bak to re-forecast future dead, perfor what f aalses ad optze the etwork as the cash dstrbuto evroet evolves. The ke to the ATM s forecastg algorths s to capture ad process the hstorcal data such that t provdes sght to the future. ewl, soe authors attepted to optze the cash b odelg ad forecastg the dead []-[]. However, the hgh varace ad o-statoar of the uderlg stochastc cash dead process ca affect Mauscrpt receved oveber, 0; revsed Februar, 03. S. M. Darwsh s wth the Departet of Iforato Techolog, Isttute of Graduate Studes ad Research, Alexadra Uverst, 63 Horrea Aveue, El Shatb 56, P.O. Box 83, Alexadra, Egpt ( e-al :saad.darwsh@alex-gsr.edu.eg) relablt of such approaches. Furtherore, the dead of cash s ot ol flueced b te, but t follows dfferet tedeces that ake odelg eve ore dffcult. For exaple, how holdas affect the use of ATM depeds o where the teller s located. Ths research proposes rule-based ATM cash dead forecastg ethod as a appled alteratve to te seres-based cash aageet. Te seres ethod has saller calculato, faster speed ad largest applcato rage, but the forecastg accurac caot guaratee to eet cash eeds ad t has o adaptve learg capabltes. I other words, ths work could be terested fdg a set of rules, whch take the wthdrawal affectg put patters of a week ad that f appled to curret operato of ATMs ca lead to the decso of whe ad how upload the ache. The proposed rule-based ethod cobes the erts of eural etwork, provde a ethodolog for solvg a tpes of olear probles that are dffcult to solve b tradtoal techques, ad tpe- fuzz logc cotroller (TFLC) that has bee show to be a powerful paradg to hadle the hgh level of ucertates real-world applcatos [5]. The reag of ths paper s orgazed as follows: Secto brefl overvews extg ATM cash aageet techques. Secto 3 forall defes the proble at had ad the geeratve based soluto. Secto descrbes the proposed rule-based forecastg odel. The experetal results ad a short dscusso are gve Secto 5. Fall, cocludg rearks are derved the last secto, whch also hghlghts drecto for future work. II. EXISTIG METHODS FOR CASH FORECASTIG I the lteratures, techques used for cash dead forecastg ca be broadl classfed to four groups [5-8]: () Te seres ethod that predcts future cash eed based o the past values of varable ad/or past errors. Geerall, techques te seres approach work well uless there s a abrupt chage the evroet or varables that are beleved to affect the cash wthdrawal patter. () Factor aalss ethod, whch s based o the deterato of varous factors that fluece the cash dead patter ad calculatg ther correlato wth actual cash wthdrawal. The purpose s to detere the fuctoal for of ths fluece (depedet varables) ad to use ths to forecast future values of the depedet varables. However, estatg ths fuctoal for s ore dffcult whe the have a o-lear relatoshp. (3) Fuzz expert sste approach that tres to tate the reasog of a hua operator. The dea s to reduce the aalogcal thkg behd the tutve DOI: 0.7763/IJCEE.03.V5.7 05
Iteratoal Joural of Coputer ad Electrcal Egeerg, Vol. 5, o., August 03 forecastg to foral steps of logc. However, expert sstes have bee foud to be feasble ol whe arrowl cofed. I addto, there are a dffcultes to corporate adequate expert kowledge to the rules of fuzz sste. () eural etworks approach that aps the relatoshps betwee varous factors affectg the cash wthdrawal ad the actual cash wthdrawal. The evaluato of ths cash forecastg sste has bee doe o the bass of stadard statstcal easures lke percetage errors. Artfcal eural etworks ethod has better robustess; olear appg ablt ad strog self-learg ablt, but t has slow covergece ad probabl coverges to a local u pot. Soe drawbacks ca be detfed the prevous coercall avalable solutos. For stace, techques based o paraeters are geerall statc ad do ot adapt durg operato, so that o-le cash optzato s ot ade possble. Other techques are largel depedg o lear regresso odels wth seasoalt coeffcets custozed for ever ATM. The developet of such odels s relatvel coplcated ad dffers for varous ATM. III. PROBLEM STATEMET AD SOLUTIO I ATM, whle t would be devastatg to ru out of cash, t s portat to keep cash at the rght levels to eet custoer dead. I such case, t becoes ver ecessar to have a forecastg sste order to get a clear pcture of deads advace. Havg the odels to forecast the dal (or weekl) cash dead for ever ATM, t s possble to pla ad to optze the cash loads for the whole ATM etwork. I geeral, cash wthdrawal s a stochastc process whose characterzato teds to chage over te due to several factors that have a strog ucertat. Cosderg ths obstacle ad to elate the exstg techques drawbacks, the work preseted ths paper proposes a ew forecastg ethod based o ITF. Ths ethod searches for a set of rules whch the cash upload decso could be ade upo codtos regardg wthdrawal affectg factors wth the a to facltate the forecastg operato for whole ATM etwork. Although there are several exaples o the applcatos of eural etworks to the proble of cash forecastg, o work has bee reported o the usg of ITF for ATM cash forecastg. Ths ethod ot ol proves the overall perforace of the forecastg sste but also adapts to the dac ature for ATM cash dead. The fuctoal prcple of the proposed ethod s dscussed below. Proble Forulato ad Methodolog The proble of rule-based cash dead forecastg ca be forulated b IF-THE rules as follow:,t a AD... AD,t IFc ATM c ATM THE UPLOAD a eag that f the ATM uber at te t eets codtos c, c,.., ad c the ths ATM s uploaded wth l cash level. Here, the atecedet parts each rule are codtos o soe factors (e.g. te, cash level, locato, l () etc.) ad the cosequet part are a set of possble recharges to appl whe preses are et. I foral, gve a set of preses, rule specfcatos, R, belog to the space: K R C C... C L () where C s the set of possble outcoes of atecedet ad L s the set of possble recharge levels. I ths case, the a s to fd the subset of K that whe appled to a dstct ATM or to a group of the, zes the dal average ATM cash stock S wth the te terval T that s [9]: T K arg SK (3) K R T S,T S k ATM, A ATMs () ATMA ATM T T t0 t,t S D,T S ATM D 0 ATM ATM,T U ATM,T WATM,T Uc (5) (6) here, S 0 (ATM) s the tal stocked cash, ATM,T L the upload appled to date T, D ATM,T s cash s dal balace at date T, W ATM,T s cash wthdraw at date T ad U c s the extra refll at date T to hadle out-of-servce stuato. Ths artcle utlzes ITF as ea to fd a optal specfcatos subset K. The geeral dea behd use of ITF s that of allowg the etwork to ap the relatoshps betwee varous factors affectg the cash wthdrawal ad the actual cash wthdrawal. owadas; fuzz eural etwork cotrollers that ca cobe the advatages of fuzz logc cotrollers ad eural etworks have bee wdel appled a real word applcatos [0-3]. Oe wa to buld ITF s to fuzzf a covetoal eural etwork. A fuzz euro s bascall slar to a artfcal euro except that t has the ablt to process fuzz forato. Tpe- fuzz logc sste are characterzed b fuzz IF-THE rules but the ebershp fuctos are three desoal ad clude a Footprt of Ucertat (FOU)[]. FOU provdes addtoal degrees of freedo that ake t possble to drectl odel ad hadle ucertates assocated wth the puts ad outputs of real sste. Tpe- fuzz rules are ore coplex tha tpe- fuzz rules because of ther use of tpe- fuzz sets atecedet or cosequet parts. Therefore, ost TF research s ol cocered wth terval tpe- fuzz sstes. The coplete ITF theor ca be foud [], []. Fg. shows the eploed etwork structure, whch has a total of four laers. Ths etwork realzed a terval tpe- fuzz sste whose rule has the for equato. eural etwork s brought forwarded to geerate a fuzz ferece sste structure autoatcall for the put. ote that, whe the algorth s staced, a tal populato of rule specfcato sets s radol geerated. These specfcatos U s 06
Iteratoal Joural of Coputer ad Electrcal Egeerg, Vol. 5, o., August 03 provde the set of codto ad recharge target values requred to buld rules. Detaled atheatcal fuctos of each laer are troduced as follows, ad a ore coplete descrpto for these laers ca be foud [0], [3].,,,,...,, p,..., (8), f f (9) f,,,, (0) f,, (),, A. Laer : Iput Laer Fg.. Geerc structure of ITF Ths laer represets a possble set of rule specfcato that s a pot R. The uber of euros ths laer depeds upo: (a) the uber of cash wthdrawal factors (p) ad (b) wa these factors are ecoded. o weghts to be adusted ths case. The put varables, x,,,..., p, are crsp values that are coded values of: () Caledar effects;() Moth of the ear; (3) Curret avalablt of cash; () Average dal cash dead the last week, ad (5) ATM locato (Lobb- Shoppg ceter- plazas - tourst locato, ad the bak). The et put ad output of the th ode are represeted as: x,,,,...,p I ths scearo, gve the cash lt M, codtos o both curret avalablt of cash S ad cash upload U are reported Table I. Whle, codtos o caledar effects wth respect to the curret date are: () workg da, () weekda, () holda effect, (v) salar da effect ad (v) festval da effect. Oce the ecessar puts (factors) are detfed, t s relatvel sple to tra ITF to for a o-lear odel of the uderlg forecastg sste ad the use ths odel to geeralze ew cases that are ot part of the trag data. () () () (v) (v) (v) (v) TABLE I: CASH STOCK AD UPLOAD STATEMETS Cash stock level S 0. M 0. M S 0. 3M 0. 3M S 0. M 0. 3M S 0. M 0. M S 0. 8M 0. 8M S 0. 9M S 0. 9M B. Laer : Fuzzfcato Laer Cash upload Level U M U 0. 67* M * S S U 0. 5* M S U 0. 33 M U 0. * M S U 0. * M S I ths laer, there are x P odes that perfor the fuzzfcato operato, where s the uber of fuzz rules the rule base. The et output of the ode, perfors a terval tpe - ebershp fucto of the fuzz set s: (7) whch, f, f deote the lower ad upper ebershp fuctos' FOU. For the th fuzz set of the put varable, a Gaussa prar ebershp fucto havg a fxed stadard devato ad a ucerta ea that takes o values [, ] s used because ther ceter paraeter s easl adaptable for a applcatos:,, exp C. Laer 3: Rule Laer () Each ode ths laer correspods to oe fuzz rule the rule base that perfors the fuzz algebrac product operato (fuzz ferece). The rules use the put ebershp values as weghtg factors to detere ther fluece o the fuzz output sets of the fal output cocluso. The output of each ode s a frg stregth F coputed as: F p p 3 3,, D. Laer : Output Laer (3) ode ths laer coputes the output lgustc varable usg the tpe reducto ad de-fuzzfcato processes. Because the output of laer 3 s tpe- terval set, the COS (ceter of set) tpe- reducto ethod s adopted whch the, ad the rght ed pot, left ed pot, tpe reduced set ca be obtaed as :, of the 3 a b 3 l, l, () 3 c d 3 l, l, a 3 3 b r, r, (5) c 3 3 d r, r, The paraeters a l,, b l,,c r,, ad d r, ca be coputed the 07
Iteratoal Joural of Coputer ad Electrcal Egeerg, Vol. 5, o., August 03 forward-propagato dervatves process of the ITF []. The defuzzfed output of the ode ca be represeted as: o (6) The learg procedure of the eploed ITF has two parts: the frst part the put patters are propagated, both cosequet factors ad prese upload level varable are assued to be fxed for the curret ccle through the trag set. I the secod part, pack-propagato s used to odf the paraeters. Here, there s o eed to detere ITF structure advace because the utlzed odel has o-le structure learg ablt that akes t ore sutable for hadlg te-varg sstes tha other ITF sstes, whch adust ther paraeters based o pre-traed ad fxed structure (.e. has o structure learg ad the uber of rules s assged a pror). The utlzed ITF has two tpes of learg: structure ad paraeter learg [][]. I case of structure learg, the frg stregth ca serve as a rule geerato crtero that s, for each pece of cog factors x x, x,... x fds I such that: I arg ax f c x, Q( t ) f c f f (7) where Q (t ) s the uber of exstg rules at te t. I ths, a frg stregth ca be regarded as the degree to whch a put data belogs to cluster (a rule correspods to a cluster the put space). Repeatg the above process for ever cog pece of trag data geerates ew rules, oe after aother, utl the coplete ITF s fall costructed. Regardg paraeter learg, the back propagato ethod s utlzed to adust the paraeters of ITF order to ze the error ter each laer. Readers lookg for coprehesve detals about back propagato pleetato ca refer to [5]. wth Sulk toolbox. Sulk s hghl cofgurable ad extedable sulato software supportg up-to-date features of the recet sulato research. Tests ra o Itel Xeo.66 GHz ache wth GB RAM equpped wth operatg sste Wdows XP professoal platfor. Each test was setup wth ITF s tal ucerta ea stadard devato ad for the ew terval tpe- fuzz set x 0., x 0., 0.. put varable x as B. Executo ad Results Test group s teded for coparg the results offered b the proposed ethodolog wth hstorcal weekl cash wthdrawal actos as perfored b hua the sulator for ATM that facg o statoar of cash dead. Results reported Fg. cofr that ATM cash aageet ca prove b applcato of fuzz eural etwork, leadg to a lower aout of stocked cash. The average geeralzato forecast accurac (per week) of the proposed ethod s about 97.7% whle the u forecast accurac s 9.5%. Valdt of the results are cofred b test group, aed at testg rules foud the past whe the are appled to the future perod wth a horzo of oe oth. Aga, actual cash wthdrawal s coverget to the upload strateg suggested b the ITF-forecastg sste as outled table II. Ths result s accordg to extree heterogeet of ATMs cash dead profles the sulator. For table II, aoe ca affr that rules foud the trag phase are cosstet ad vald whe appled to the specfed te perod. Fg.. Forecastg results for the aalzed data: actual values (sold le) ad predcated values (dashed le). IV. SIMULATIOS AD VALIDATIO I ths secto, a applcato to the cash dead forecastg s vestgated to deostrate the effectveess of the eploed odel. I parallel, the proposed forecaster s copared wth state-of-the-art forecastg approaches A. Experetal Setup To test the potetal of the proposed ethod to accuratel forecast the cash dead ATM etwork, a sulato evroet for ATM etwork was desged. The actvt of ATM etwork, whch cossts of 5 ATMs, was sulated. Dal, weekl ad othl seasoalt alog wth log-ter stles ad specal evets or localzed abrupt chages (holda ad festval effects) were used to tate the custoers oe wthdrawal fro ATMs that are characterzed b dfferet trasacto volues. The realzato of ITF-based forecastg ethod was pleeted usg MATLAB TM prograg evroet Fg. 3. Predctos coparso for dfferet forecastg ethods. Test group 3 aed at assessg the advatages relg forecastg o fuzz eural etwork stead of fuzz logc based-te seres predcato approach establshed b the authors [6]. Ther ethod s based o the cobato of wavelet aalss ad fuzz odelg to deal wth te seres process that has seasoal varatos, log ter ad shot ter fluctuatos. 08
Iteratoal Joural of Coputer ad Electrcal Egeerg, Vol. 5, o., August 03 TABLE II: AVERAGE WEEKLY STOCKED CASH (X0 3 ) OF THE SUGGESTED RULES I THE TESTIG SET. ATM ATM ATM A P A P A P Week 9.7 50. 9.96 0.3 6.6 7. Week 8.7 8.9 7.56 8.3.96 5.6 Week 3 59. 60.5 9.73 9.8 6.0 6. Week 5.8 5.0 8.65 0.0 50.9 5. A: actual wthdrawal, P: predcted Wthdrawal TABLE III: SUMMARY OF EXPERIMETAL RESULT. Forecastg Method MFE ITF 6.566 Fuzz Wavelet-based 9.38 Fg. 3 dsplas the coparso betwee the two ethods ad ther error (.e. devato fro the actual wthdrawal) dcatg that the eploed fuzz eural etwork has a saller dvergece ad has a better predcato tha that for te seres wth a 3% reducto the MFE (ea forecast error) as see table III. Ths suggests that eve wth hghl o-statoar of the uderlg wthdrawal process, the proposed odel exhbts certa regulartes ad rules, whch ca be effectvel odeled to gve reasoable predctos. Furtherore, the ablt to predct cash dead wth reasoable accurac of actual dead provdes target for suppl optzato well te. V. COCLUSIO Optzg cash ATMs s dffcult due to upredctablt of wthdrawals. Therefore, fdg the best atch betwee cash stock ad dead becoes crucal to prove. Ths paper preseted a ethod based o ITF aed at searchg optal strateges to refll ATM cash stocks to eet o-statoar of cash dead. Dfferetl fro approaches based o predcato of future cash dead, the proposed ethod s based o fuzz rules regardg soe factors that f et suggest to upload cash. Such a sste wll help the bak for proper ad effcet cash aageet ad ca be scaled for all braches of a bak b corporatg hstorcal data fro these braches. The perfored sulato of ATM etwork s cash forecastg sste showed good results ad proved that ths ethod s feasble suggestg relable rules able to prove hstorcal cash aageet. However, there are other factors lke festval perod ad arket actvtes that postvel fluece cash dead ad f these are quatfed ad cluded as fluecg varables, the result wll prove wth lesser error. The sste perfors better tha other sstes based o te seres. The future work wll be drected o pleetg coordated route plag techque for reducg the ATM etwork s aageet costs ad buld a adaptve ATM cash aageet ad support sste. REFERECES [] R. Suts, D. Dloas, L. Basta, ad J. Fra, A Flexble eural etwork for ATM Cash Dead Forecastg, Proc. 6th It. Cof. o Coputatoal tellgece, Ma-Mache Sste ad Cberetcs, Spa, Dec. -6, 007, pp. 6-65. [] D. Dloas ad L. Basta, Retal Bakg Optzato Sste Based o Mult-agets Techolog, Proc. 6th It. Cof. o Coputatoal tellgece, Ma-Mache Sste ad Cberetcs, Spa, Dec. -6, 007, pp. 03-08. [3] M. Wager, Forecastg Dal Dead Cash Suppl Chas, Aerca Joural of Ecoocs ad Busess Adstrato, vol., o., pp. 377-383, 00. [] A. R. Bretalla, M. J. Crowderb, ad D. J. Hadb, Predctve-Sequetal Forecastg Sste Developet for Cash Mache Stockg, Iteratoal Joural of Forecastg, vol. 6 pp. 76 776, 00. [5] I. Ad, M. Karakose, ad E. Ak, The Predcto Algorth Based o Fuzz Logc Usg Te Seres Data Mg Method, World Acade of Scece, Egeerg ad Techolog, vol. 5, pp. 9-98, 009. [6] R. Suts, D. Dloas, ad L. Basta, Cash Dead Forecastg For ATM Usg eural etworks Ad Support Vector Regresso Algorths, Proc. 0th EURO M Coferece o Cotuous Optzato ad Kowledge-Based Techologes ((EurOPT-008), Ma 0 3, Lthuaa, 008, pp. 6-. [7] S. D. Tedd ad S. K. g, Forecastg ATM Cash Deads Usg a Local Learg Model of Cerebellar Assocatve Meor etwork, Iteratoal Joural of Forecastg, vol. 7, pp. 760 776, 0. [8] P. Kuar ad E. Wala, Cash Forecastg: A Itroducto of Artfcal eural etworks Face, Iteratoal Joural of Coputer Sceces ad Applcatos, vol. 3, o., pp. 6-77, 006. [9] R. Arese, C. Brtolo, E. Sagaato, ad l. Troao, A Geeratve Soluto for ATM Cash Maageet, It. Cof. of Soft Coputg ad Patter Recogto, Frace, 7-0 Dec. 00, pp. 39-356. [0] C. F. Juag ad R. B. Huag, A Mada Recurret Iterval Tpe- Fuzz eural etwork for Idetfcato of Dac Sstes wth Measureet ose," Proceedgs of the 8th IFAC World Cogress, Ital, Aug. 8-Sep., 0, pp. 8975-8980. [] C. S. Che ad W. C. L, Self-Adaptve Iterval Tpe- eural Fuzz etwork Cotrol for PMLSM Drves, Expert Sstes wth Applcatos, vol. 38, pp. 679-689, 0. [] C. F. Juag, C. F. Lu, ad W. Tsao, A Self Evolvg Iterval Tpe- Fuzz eural etwork for olear Sste Idetfcato, Proceedgs of the 7th IFAC World Cogress, Korea, Jul 6-, 008, pp. 7588-7593. [3] L. Zhao, "Short-Ter Traffc Flow Predcto Based o Iterval Tpe- Fuzz eural etworks," Proc. LSMS /ICSEE00, Sprger, pp. 30-37, 00. [] J. M. Medel, Coputg Dervatves Iterval Tpe- Fuzz Logc Sste," IEEE Tras. o Fuzz Sstes, vol. 0, o., pp. 7-7, 00. [5] C. H. Lee, J. L. Hog, Y. C. L, ad W. Y. La, Tpe- eural etwork Sstes ad Learg," It. Joural of Coputatoal Cogto, vol., o., pp. 79-90, 003. [6] Y. Chea, B. Yaga, ad J. Doga, Te-Seres Predcto Usg a Local Lear Wavelet eural etwork, eurocoputg, vol. 69, pp. 9 65, 006. Saad M. Darwsh receved the B.Sc. degree statstcs ad coputer scece fro the facult of scece, Alexadra Uverst, Egpt 995. He held the M.Sc. degree forato techolog fro the Isttute of Graduate Studes ad Research (IGSR), Departet of Iforato Techolog, Uverst of Alexadra 00. He receved hs Ph.D. degree fro the Alexadra Uverst for a thess age g ad age descrpto techologes. Hs research ad professoal terests clude age processg, web egeerg, securt techologes ad database aageet. He has publshed ourals ad cofereces ad severed as TPC of a uber of teratoal cofereces. Sce Feb. 0, he has bee a Assocate Professor the departet of forato techolog, IGSR. 09