Redesign of a University Hospital Preanesthesia Evaluation Clinic. using a Queuing Theory Approach

Transcription

1 Reesgn of a Unvesty Hosptal Peanesthesa valuaton Clnc usng a Queung Theoy Appoach Maatje. Zonelan Mc ab Fe Boe MD PhD c Rcha J. Bouchee PhD b Annemek e Rooe MD PhD Jack W. van Kleef MD PhD a Dvson I Leen Unvesty Mecal Cente Leen the Nethelans b Depatment of Apple Mathematcs Unvesty of Twente nschee the Nethelans c OR Cente Leen Unvesty Mecal Cente Leen the Nethelans Depatment of Anesthesology Leen Unvesty Mecal Cente Leen the Nethelans Coesponng autho: Maatje Zonelan Dvson I Leen Unvesty Mecal Cente Postbox RC Leen the Nethelans m.e.zonelan@lumc.nl

2 Abstact Backgoun Changes n patent length of stay the uaton of one vst as a esult of the ntoucton of an electonc patent fle system foce an anesthesa epatment to change the outpatent clnc oganzaton. The am of ths stuy s to emonstate how the nvolvement of essental employees combne wth mathematcal technques to suppot the ecson makng pocess esulte n a successful nteventon. Methos The settng s the peanesthesa evaluaton clnc of a unvesty hosptal whee patents consult seveal mecal pofessonals ethe on walk-n o appontment bass. Queung theoy was use to moel the ntal set-up of the clnc an late to moel possble altenatve esgns. Wth the queung moel possble mpovements n effcency coul be nvestgate. Inputs to the moel wee patent aval ates an expecte sevce tmes collecte fom the clnc s loggng system an by obsevaton. The pefomance measues calculate wth the moel wee patent length of stay an employee utlzaton ate. uppote by the moel outcomes a wokng goup consstng of epesentatves of all clnc employees ece f the ntal esgn shoul be mantane o an nteventon was neee. Results The queung moel pecte that thee of the popose altenatves woul esult n bette pefomance. Key ponts n the nteventon wee the escheulng of appontments an the eallocaton of tasks. The nteventon esulte n a shotenng of the tme the anesthesologst neee to ece upon appovng the patent fo sugey. Patent avals ncease shaply ove one yea by moe than 6% howeve patent length of stay at the clnc emane essentally unchange. If the ntal set-up of the clnc woul have been mantane the patent length of stay woul have ncease amatcally. Conclusons

3 Queung theoy poves obust methos to evaluate altenatve esgns fo the oganzaton of peanesthesa evaluaton clncs. Combnng these mathematcal technques wth the essental nvolvement of employees may lea to a successful nteventon that mpoves clnc pefomance.

4 Text Intoucton In the past two ecaes t has become common pactce to pove peopeatve sceenng n an outpatent clnc settng. - Lee 4 was the fst to outlne the concept of the peanesthesa evaluaton clnc PAC. He state that the pupose of the peopeatve sceenng pocess s to examne an teat the patent so that he wll ave n the opeatng theate as stong an as healthy as possble a efnton that stll aequately efnes the pocess. Toay many hosptals opeate a PAC. An accuately pefome sceenng euces the sk of cancellaton on the ay of sugey ue to the physcal conton of the patent nceases the ate of same-ay amssons an euces pe-opeatve mobty esultng n ecease costs an ncease qualty of cae. 56 Congeston s a common phenomenon n outpatent clncs. 7-9 Patents avng fo a peopeatve sceenng ae usually not categoze an theefoe the consultaton tme neee pe patent s ffcult to estmate. Ths nceases the complexty of the PAC oganzaton as compae wth a egula outpatent clnc. In ou own PAC patent watng tmes an length of stay wee ntally sgnfcantly shote than n a compaable clnc 0 but these ncease amatcally afte ntoucton of an electonc patent ata management system snce togethe wth the nfomaton system atonal amnstatve actvtes wee ntouce. Also the wokloa of the staff ncease leang to multple complants about wok stess. The polonge watng tmes togethe wth the low level of job satsfacton fo clnc employees calle fo an evaluaton of altenatve clnc esgns. The am of ths stuy was to exploe possbltes fo a moe effcent opeaton of ou PAC oganzaton. nce all patent movement wthn the PAC was logge we chose to use mathematcal technques to analyze pefomance. The majo avantage of mathematcal moelng s the possblty to execute a thoough analyss of a system whle havng no mpact on the system tself. Usng ou mathematcal moel we 4

5 nvestgate the effect of vaous esgns on selecte pefomance measues such as patent length of stay the total uaton of one clnc vst an staff utlzaton ate the facton of tme clnc staff s occupe wth patent elate actvtes. One of the altenatve esgns we consee was egae as supeo to the ntal esgn by the clnc staff. Ths esgn was mplemente at ou PAC n 007. The pesent stuy was base on a queung moelng appoach. mulaton s a moe common appoach n ths aea. Aleay n 95 Baley use Monte-Calo mulaton to analyze appontment systems fo outpatent clncs. nce then smulaton has been use extensvely fo the stuy of outpatent clncs. Wthn the scope of the PAC smulaton was use to analyze the capacty neee to shoten the watng lst 0 an to stuy the esgn of appontment systems fo the PAC to mnmze patent watng tmes. 7 The choce fo usng smulaton technques s not always suppote by clea agumentaton. mulaton moelng s a poweful tool but t s vey tme-consumng ue to the extensve amount of ata that s neee an the effot t takes to bul the moel nto a smulaton softwae pogam. Moeove t eques etale nfomaton on the nput stbuton such as those of the consultaton tme o the patent aval pocesses. Applcatons of queung theoy n outpatent clnc settngs ae scace. The majoty of papes publshe on ths matte ae covee by Peate n hs extensve bblogaphy on queues n health. An analytcal queung moel eques less ata an can usually be bult n a shote peo of tme. 4 In patcula ou queung moelng appoach eques only mean an vaance of consultaton tmes an patent aval pocesses an poves obust nsght n the unelyng elatonshps of a pocess nstea of focusng on etals as s the case wth smulaton moelng. As can be seen n Appenx ou queung moel conssts of seveal elate fomulas that can be entee nto a speasheet. It enables a bottleneck analyss of the pocesses at the clnc an can easly be ajuste so that t epesents one of the altenatve esgns consee n the eesgn pocess. In ths pape we show that queung theoy s a pope altenatve fo smulaton when eesgnng pocesses n an outpatent clnc. Followng the nteventon an unexpecte ncease of 6% n patent vsts n the fst quate of 008 occue. Howeve ths not cause 5

6 a sgnfcant ncease n watng tmes an n aton esulte n a ecease of employee costs pe patent. Futhemoe the tme neee to appove a patent fo sugey ecease an employee satsfacton ncease. Ths pape escbes the eesgn pocess an poves ectons fo othe PAC manages. 6

7 Methos Intal sevce of the PAC The stuy was pefome at a unvesty hosptal peanesthesa evaluaton clnc wth appoxmately 6000 patent vsts annually. A majoty of patents wee seen on walk-n bass about 70% an the emanng on appontment bass. Walk-n patents ave ectly fom sugcal outpatent clncs wthn the hosptal. Only AA I o II patents wee evaluate on walk-n bass snce fo AA III o IV patents moe tme fo patent contact an atonal nfomaton fom othe specalsts was often eque. It was clnc polcy to maxmze the numbe of walk-n patents although at the same tme these patents pose an uncetan eman on clnc esouces. Although less than 0% of patents wee classfe AA III o IV an theefoe eque an appontment 0% of all patents wee gven an appontment. When walk-n patents wee efee to an appontment t was usually because of ovecowng n the watng oom. Resouces an tasks The clnc was un by the epatment of Anesthesology wth fou anesthesa cae poves attenng: one staff anesthesologst two esents an a nuse pacttone suppote by a secetay an two clnc assstants. The sceenng pocess consste of at most thee steps: an ntake at the secetay an two sepaate contacts wth the nuse an anesthesa cae pove espectvely. All patents woul see the secetay an anesthesa cae pove only aults wee seen by the clnc assstant. Patents etune to the watng oom between vstng each cae pove. Base on a fom complete by the efeng specalst the secetay ece whethe the patent coul be assesse mmeately o ung an appontment at a late tme. nce the secetay s not equppe to make ecsons egang the mecal status of the patent ths poceue esulte occasonally n patents ecevng an appontment they not nee an vce vesa. If the patent eceve an appontment the tme nteval usually one o two weeks was use fo back-offce actvtes to complete the patent s fle. Walk-n patents wee appove fo sugey by the anesthesa cae pove ung the vst. The staff anesthesologst pefome 7

8 the back-offce actvtes consstng mostly of pocessng atonal patent nfomaton that was eque to fnsh the case of appontment patents. Because the staff anesthesologsts also seve as backup manpowe fo the font-offce actvtes they expeence sgnfcant wok stess. Futhemoe the anesthesa cae poves wee unhappy because complcate cases ha to be fnalze by an anesthesa cae pove who ha not seen the patent ntally whch ultmately may esult n an ncomplete unestanng of the mecal conton of the patent. 5 Usng Queung Theoy to Analyze PAC Pefomance The ntal an altenatve esgns wee compae wth a Mult-Class Open Queung Netwok Moel fo a etale escpton see Appenx. An avantage of ths queung moel s that only the fst two moments mean an stana evaton of the aval an sevce tme stbutons ae neee n the calculatons. Ths allows usage of all possble types of stbutons nclung empcal stbutons. Fo the compason two pefomance measues wee calculate wth the queung moel namely patent length of stay an employee utlzaton ate. In the ecent wok by Jang an Gachett 6 the authos befly escbe a suvey hel at the outpatent clnc. Fom the suvey t followe that patents consee the watng tme beng an mpotant contbuto to the length of stay as vey mpotant an unsatsfactoy long. Othe aspects such as the consultaton wth the anesthesa cae pove an the nuse also contbute to the patent s contentment on the clnc vst. 7 Utlzaton ate an watng tme ae elate. As an example conse the sngle seve queue wth Posson avals an geneal sevce tmes. The elatonshp between utlzaton ate an watng tme s escbe by the Pollaczek-Khntchne Fomula 8 : W c whee W enotes the expecte watng tme the expecte sevce tme the utlzaton ate an c the coeffcent of vaaton of the sevce tme. Ths non-lnea elatonshp s shown n Fgue. The utlzaton ate equals the aval ate ve by the sevce ate. The system shoul be able to eal on aveage wth the offee loa an theefoe t s eque that the 8

9 aval ate s stctly smalle than the sevce ate so <. It s appaent that an ncease n the utlzaton ate fom 0.4 to 0.5 has only lttle mpact wheeas an ncease fom 0.8 to 0.9 esults n moe than ouble the ognal watng tme. An ncease fom 0.9 to 0.99 even esults n an ncease of the watng tme by a facto ten. Knowlege of the utlzaton ate of a system s essental snce nceasng ths facto when t s aleay close to one ethe by nceasng the aval ate o eceasng the sevce ate wll esult n a conseable ncease of the watng tme. Inteventon The necessty of an nteventon was felt by all pates nvolve n the PAC. A wokng goup was fome wth epesentatves of all PAC employees. The wokng goup scusse the ntal esgn an evelope fou altenatve esgns whch ae escbe n the subsequent paagaphs. When scussng the ntal esgn the wokng goup entfe all elevant actvtes at the PAC an stanaze the oe of these actvtes n the ntal esgn n seveal flow chats. Ultmately the wokng goup ece upon the planne esgn fom the pesente altenatves. Agan the oe of all actvtes n the new esgn was ocumente n seveal flow chats an mecal potocols. The queung moel esults wee use to suppot the ecson makng pocess an enable a numecal compason of the ntal an altenatve clnc esgns. Altenatve esgn : Clnc Assstant elects at Font Desk Clnc assstants wee convnce that many patents wth an actual AA III o IV scoe wee assgne an eoneous AA I o II scoe by the secetay. These patents wee teate on walk-n bass an consume too much tme n the offce of the anesthesa cae pove esultng n congeston n the watng oom. They suggeste that one of the clnc assstants shoul take ove pat of the font esk task fom the secetay whle the othe clnc assstant pefoms measuements an bloo samplng. Altenatve esgn : Teat all Patents on Appontment Bass 9

10 Deman fo an outpatent clnc s sevces can be ve nto two components: contolle appontment patents an uncontolle walk-n patents eman. 9 In the ntal set-up most AA I o II patents wee seen as walk-n patents. In the secon altenatve all patents ae efee to an appontment snce a clnc wth an appontment-only system wll always pove a bette sevce level than a clnc that allows walk-n avals. 7 Altenatve esgn : Rescheule Appontments Rsng 9 suggeste to scheule appontments such that they complement walk-n avals. Ths esults n a moe homogeneous aval patten thoughout the ay. In the PAC une stuy the numbe of walk-n avals was sgnfcantly lowe n the ealy monng an on Fay aftenoon. In ths altenatve all appontments ae scheule n these peos. Altenatve esgn 4: Regoup mployee Tasks an Amen Patent Flows In ths altenatve the secetay accepts all patents; theefoe all patents ae seen by the clnc assstant on the fst vst. Clnc assstants ae pove wth potocols to a n the ecson whethe the patent can be seen mmeately base on the extent of co-mobty contacts wth mecal specalsts an the equement to obtan atonal mecal nfomaton po to the vst to the anesthesologst. If the patent eques atonal testng these tests ae mmeately pefome an/o equeste an the patent s efee to an appontment scheule when all atonal nfomaton s avalable. Consequently the patent can be appove fo sugey when the appontment takes place. 0

11 Results Moel nput Data fom all PAC vsts ecoe n the fst quate of 007 was use to obtan nput paametes fo the queung moel n 49. Fo the analyss patents wee ve n thee sepaate classes: chlen <6 yeas ol ault patents AA coe I o II an ault patents AA coe III o IV. Ths classfcaton was chosen snce chlen an aults have a ffeent outng moeove the thee classes can be stngushe n consultaton tme at the anesthesologst. An avantage of ths classfcaton s that t s smla to that use by clnc staff. Aval ates fo each patent class an mean an stana evaton of the contact tme at the clnc assstant an anesthesa cae pove wee etemne. Not all egstee contacts wee stoe coectly an theefoe the ecos of 9 patents 87% coul be use fo the latte pat of the ata analyss. The tme patents spent at the secetay was not ecoe an theefoe estmate. The secetay was often stube by co-wokes who nque afte the appoval status of a patcula patent ethe by phone o n peson at the ecepton esk. The anesthesa cae poves wee also stube by co-wokes the nques usually concenng the othe pofessonal esponsbltes. We estmate that 50% of the secetay s tme an % of the anesthesa cae pove s tme was lost ue to these nevtable ntefeences. The numbe of avals pe patent class was use to etemne the stbuton of patents among classes. We foun that the majoty of patents ave between 0 AM an 4 PM. Hence we focuse ou analyss on ths nteval an calculate the aval ate.7 patents/hou by usng patent avals ecoe ung ths nteval. We obseve that wthn ths peo patents fom all classes ave n a homogenously stbute manne. Ths coespons wth the squae coeffcent of vaaton see Appenx of the aval pocess beng equal to fo all patent classes. The avals of patents that wee mmeately efee to an appontment wee not ecoe. Assumng that all appontment patents make the appontment at the ecepton esk we calculate the aval ate of non-amtte patents by multplyng the amtte patent aval ate by the appontment pecentage fo each patent class. A summay of nput ata s gven n Table

12 . eno clnc staff membes scusse an caefully checke all paamete values; atonally they scusse an appove the queung moel esgn. Compason of Intal Desgn an Altenatves Wth the moel we compae each altenatve esgn wth the ntal esgn. If necessay nput paametes wee ajuste see Table fo the mofcatons an Appenx fo an explanaton of the paametes tself. The pefomance measues we chose to compae wee expecte patent length of stay an employee utlzaton ate. The ntal esgn coul be chaacteze by long expecte patent length of stays cause by polonge watng tmes at the secetay an late n the pocess po to the contact wth the anesthesa cae pove Table. These two cae statons also ha hgh utlzaton ates. Compang the pefomance measues of the ntal esgn to those of the altenatve esgns lea to the concluson that all altenatve esgns except altenatve teat all patents on appontment bass woul esult n a bette oveall pefomance. Once the moel esults wee avalable the wokng goup was consulte to make a ecson on the next step to take n the eesgnng pocess. It was appaent to all membes that the ntal esgn coul not be mantane. The fst altenatve of elocatng one nuse to the secetay s staton was not egae as a valuable altenatve snce the expecte ecease n patent length of stay was mnmal. Futhemoe patent watng tme at the emanng clnc assstant ncease substantally whch was also unesable. Base on the pecte ncease n patent watng tme at the secetay n altenatve whch was cause by all patents havng to make an appontment fst an snce ntoucng an appontment-only system was egae as patent unfenly n the sense of one-stop shoppng by the wokng goup altenatve was elmnate. The wokng goup membes ece to mplement altenatve an 4 so that avantages of both altenatves wee nclue. The effects of combnng altenatves an 4 wee agan stue wth the queung moel Table. The queung moel pecte that ths nteventon woul also esult n an mpovement. uppote by the esults all wokng goup membes wee convnce that

13 mplementng a combnaton of the two altenatves woul yel a bette oveall pefomance of the clnc. ffect of nteventon The new esgn was mplemente n the summe of 007. We compae total patent length of stay befoe an afte the nteventon. To mnmze seasonal nfluences an to allow fo leanng effects we use ata fom both the fst quate of 007 an 008. Befoe the nteventon only one clnc assstant was pesent on Fays. nce the nteventon nvolve scheulng the majoty of appontments on Fays one atonal clnc assstant shft was now eque. Ths cause an ncease n total employee capacty fom 7.0 FT total costs: 09K uos to 7.87 FT total costs: 6K uos 6%. Befoe the nteventon total patent length of stay was on aveage mnutes 95% CI: [68.76; 7.8] compae to 77.9 mnutes afte the nteventon 95% CI: [76.4; 79.68]. The ncease n patent length of stay was cause solely by longe contact an watng tmes at the clnc assstant 95% CI of ncease n contact tmes: [5.5; 7.60] 95% CI of ncease n watng tmes: [7.96;.94]. The contact an watng tmes at the anesthesa cae pove not ncease sgnfcantly 95% CI of ncease n contact tmes: [-.50;.46] 95% CI of ncease n watng tmes: [-.0;.8]. Recall that not all patents see the nuse an theefoe the ncease n total patent length of stay was less. In the fst quate of patent contacts wee egstee ung the openng hous of the clnc an ncease of 45 patents 6% compae to the fst quate of 007. Dvng the total pesonnel costs by the numbe of patents fo both quates we see that pesonnel costs ecease fom 7 to 67 uos pe patent -8%. The pecentage of patents seen on walk-n bass ncease fom 7% n 007 to 8% n 008. Ths s consee an mpovement n patent fenlness. Futhemoe n 008 the anesthesologst neee 6.8 ays to ece upon appovng the patent fo sugey compae to 7.9 ays n % CI: [-0.;.]. The staff anesthesologsts wee esponsble fo fnalzng the status of those patents fo whch new nfomaton was obtane n the ays o weeks afte the patent ha vste the PAC. Ths esulte n a conseable expense of tme seveal hous snce they ha to make themselves fully acquante wth the patent s fle befoe

14 they coul appove the patent. Afte the nteventon ths task was mnmal less than 0 mnutes as fo most patents all elevant nfomaton was avalable po to the fst vst to the attenng anesthesa cae pove. 4

15 Dscusson In ths pape we have scusse the pocess of eesgnng ou PAC a faclty wth both walk-n an appontment patents. We emonstate a queung moelng appoach that enables a fast an obust analyss of PAC pefomance. The methoology can be apple to othe peopeatve sceenng clncs as well. The eesgn consste of two pats namely the e-scheulng of appontments to the ealy monng an Fay an the eassgnment of tasks fom the secetay to the clnc assstants. As a consequence all patents wee seen on the walk-n vst by the clnc assstant. Patents equng moe contact tme wth the anesthesa cae pove o backoffce actvtes wee efee to an appontment by the clnc assstant scheule when all eque nfomaton was avalable. Lteatue about the e-esgn of hosptal cae s extensve. 0 Howeve the lteatue on e-esgn of outpatent an peanesthesa evaluaton clncs s lmte. ome stues ae ecate to the esgn of appontment systems 7 othes concentate lagely on watng tmes an patent satsfacton. 0 The concept of e-esgn by eallocatng tasks at the outpatent clnc has eceve less attenton. A possble lmtaton of ths stuy s that all outcomes of the queung moel wee calculate une the assumpton of steay state behavo. The system une stuy wll neve each ths equlbum state ue to nhomogeneous patent avals an estctve openng hous. Une smla estctons queung theoy has been successfully apple n othe aeas such as manufactung. Theefoe we feel that ths appoach mantans ts sutablty. Futhemoe we use the queung moel solely fo compason puposes an not fo pecton of actual patent length of stay an utlzaton ates whch futhe stengthene ou belef n the followe appoach. The moel enable us to analyze the effect of ncease pessue on the clnc. As mentone n the esults secton patent avals ha ncease wth 6% n the fst quate of 008 compae to the same peo n 007. Nevetheless empcal analyss showe that patent length of stay ha only ncease slghtly. The moel shows that the se n patent avals woul have esulte 5

16 n a temenous ncease n patent length of stay an employee utlzaton ate f we ha not change the esgn of ou PAC Table 4. Une the 008 ata the ntal esgn opeates une hgh pessue wth an ncease n length of stay of 5% ue to the 6% ncease n patent avals. In the mplemente esgn ue to ncease effcency the system opeates une moest pessue wth an ncease n length of stay of only 5% Table 4. Ths s n lne wth the elatonshp epcte n Fgue ncatng the typcal elaton between watng tme an loa. By oganzng the pocesses at the clnc moe effcently we euce the loa an move left on the cuve. Theefoe the ncease n patent avals cause an ncease n the loa but only a slght ncease n watng tme an patent length of stay. The majoty of patents vstng ou PAC ae seen on a walk-n bass. nce patents have the oppotunty to go staght fom the sugcal outpatent clnc to the PAC they ae often able to fnalze the ente peopeatve pepaaton wthn one hosptal vst one-stop shoppng avong multple hosptal vsts. Howeve walk-n outpatent clncs ae notoously moe ffcult to hanle n tems of optmzng watng tmes fo patents an peak pessues fo anesthesa cae poves. Dexte 7 states that the best sevce walk-n PACs can pove wll always be wose than appontment PACs. The walk-n PAC eques moe esouces to have acceptable watng tmes fo patents 0 snce moe slack s eque to eal wth unexpecte peaks n patent aval. Appontment systems on the othe han eal wth peaks n eman fo PAC sevces by bulng watng lsts. To allow fo patents that nee to be seen wth some ugency these appontmentonly outpatent clncs wll usually have some unplanne tme slots o a-on manpowe. At the PAC une stuy we use a system that allows both walk-n an appontment patents. The ecease of back-offce actvtes enable the anesthesa cae poves to ecate moe tme to patent contact. Ths explans how 6% moe patents coul be seen wthout an ncease n the numbe of anesthesa cae poves. Although the moel ae n the e-esgn of the PAC the success of the nteventon ele heavly on the nvolvement of the employees. The key to a successful nteventon s the 6

17 combnaton of logstc expetse an the patcpaton of key pesons n the poject. Theefoe the outcomes of the queung moel egang the pefomance of the ntal an altenatve esgns wee scusse n a wokng goup wth epesentatves of all clnc employees. We feel that the nteventon s success was n lage pat the esult of a commtte wokng goup togethe wth the use of mathematcal moelng tools enablng quantfe compasons of altenatve clnc esgns. 7

18 Fgues Fgue Ttle: The Pollaczek-Khntchne Cuve a Fgue Ttle: ngle Class Open Queung Netwok a W Mean watng tme Mean sevce tme 8

19 Appenx : The Queung Moel Wth the mult-class open queung netwok moel we eve measues to analyze pefomance of ou PAC. Thee ae many books that gve an ntoucton to Queung Theoy see fo example Taylo an Kaln. 4 The extensve bblogaphy by Peate poves many examples of Queung Theoy applcatons n health cae. The pape by Jang an Gachett 6 gves an example of a mult-class open queung netwok moel apple to an outpatent clnc. A queung netwok moel epesents a set of connecte queues. At the PAC thee ae thee sepaate queues whee the employees act as seves. The secetay staton s a sngle seve queue wheeas the clnc assstant an anesthesa cae pove staton ae mult-seve queues. Patents ente the queung netwok va the secetay staton an fnally epat fom the system. Futhemoe f upon aval at a staton an employee s avalable patents ae seve mmeately; othewse they jon the queue n fst come fst seve scplne. We use the appoxmate ecomposton metho 5 to analyze the moel. The appoxmate ecomposton metho has as avantage that only the mean an squae coeffcent of vaaton CV of the aval pocess an contact tmes ae neee the CV equals the vaance ve by the squae mean. Fst we ntouce some notatons. Thee ae stnct patent classes whee ae patents efee to an appontment by the secetay aults AA I o II aults AA III o IV an 4 ae chlen. To evaluate altenatve esgn 4 we also ntouce to epesent patents aults wth AA I o II aults wth AA III o IV an chlen espectvely who etun fo the appontment. These nexes only exst when altenatve esgn 4 s evaluate an theefoe the bnay vaable equals f altenatve esgn 4 s evaluate an 0 othewse. We have statons [..] epesentng the secetay clnc assstant an anesthesa cae pove espectvely. The numbe of seves.e. employees at staton equals s. An effectve capacty of e fo the secetay an e fo the anesthesa cae s ntouce. nce the secetay s stube whle hanlng patents e s taken nto account when calculatng the mean tme a patent spens 9

20 0 at ths staton. The anesthesa cae pove s not stube whle teatng patents an theefoe e s only use n calculatng the utlzaton ate. The aval ate of patent class at staton s ζ wheeas s the mean sevce tme fo patent class at staton. The CV of avals at staton of patent class s CV A an CV s the CV of the sevce tme fo patent class at staton. Fnally a s the facton of patents of class who ae efee to an appontment n altenatve esgn 4. In the moel analyss we follow the thee steps fom the appoxmate ecomposton metho. tep : Reucton to a ngle Class Open Queung Netwok Fgue gves the ngle Class OQN esultng fom the aggegaton of the patent flows. The aggegate aval ntenstes at staton a λ λ λ The utlzaton ates pe patent class fo staton an ae....4 fo an fo...4 fo s e a s e s s e Aggegatng the utlzaton ates ove all patent classes fo staton gves 4 4 Fo stablty t s eque that < fo all. tep : Analyss of the ngle Class Open Queung Netwok The aval pocess at staton has CV whee 4 A A w CV Q w CV. 4 4 λ λ Q v v w The mean contact tme an CV at staton ae

21 4 4 CV CV λ λ The aval pocess at staton has CV CV A P CVD P whee CV D s the CV of the epatue pocess at staton an P s the poton of the aggegate flow out of staton to staton CV D CVA CV P. λ taton has mean contact tme an CV CV CV λ λ The aval pocess at staton has CV CV A w Q w w QCV Q CV wth 4 v CV CV D 4 4 a λ CV P CV 4 v Q Q CV P CV D A CV D s D P CV P Q P a λ P 4 4 a λ a λ whee CV s the CV of the patent flow fom staton to staton CV the CV of the patent flow fom staton to staton an CV D s the CV of the epatue pocess at staton. P s the poton of aggegate flow out of staton to staton an P s the poton of aggegate flow out of staton to staton. taton has mean contact tme an CV 4.

22 CV CV a CV a λ λ tep : Pefomance Measues pe Patent Class We ae nteeste n the watng tmes fo patents pe staton an the utlzaton ates pe employee at each staton. The latte s gven by the aggegate utlzaton ates eve n step whle the mean watng tmes ae obtane by usng the CV s an mean sevce tmes calculate n step. The mean watng tme at the thee sevce statons s equal fo all patent classes.. fo!!! whee 0 / / / / s s n n s c M M Q c M M Q A Q A Q s s n s G s G s s W W CV CV W e CV CV W Patent length of stay fo each patent class can now be calculate by ang the mean watng an length of stay of all cae statons the patent calls at on hs vst to the PAC.

23 Refeences. Conway JB Golbeg J Chung F. Peamsson anaesthesa consultaton clnc. Can J Anaesth 99;9:05-7. Lew Pavln DJ Amunsen L. Outpatent peanaesthesa evaluaton clncs. ngapoe Me J 004;45: Polla JB. conomc aspects of an anesthesa peopeatve evaluaton clnc. Cu Opn Anaesthesol 00;5: Lee JA. The Anaesthetc Out-Patent Clnc. Anaesthesa 949;4: van Kle WA Moons KG Rutten CL chuuhus A Knape JT Kalkman CJ Gobbee D. The effect of outpatent peopeatve evaluaton of hosptal npatents on cancellaton of sugey an length of hosptal stay. Anesth Analg 00;94: Pake BM Tetzlaff J Ltake DL Maue WG. Reefnng the peopeatve evaluaton pocess an the ole of the anesthesologst. J Cln Anesth 000;: Dexte F. Desgn of appontment systems fo peanesthesa evaluaton clncs to mnmze patent watng tmes: a evew of compute smulaton an patent suvey stues. Anesth Analg 999;89:95-8. Dunnll MG Poune R. Mecal outpatents: changes that can beneft patents. Cln Me 004;4: Hape PR Gamln HM. Reuce outpatent watng tmes wth mpove appontment scheulng: a smulaton moellng appoach. O pectum 00;5:07-0. wa GM Razzaq e Rooe A. Boe F Hollmann MW Dzoljc M Lemae LC. Patent flow n the peopeatve assessment clnc. u J Anaesthesol 008;5:80-6. Baley NTJ. A stuy of Queues an Appontment ystems n Hosptal Out-Patent Depatments wth pecal Refeence to Watng-Tmes. Jounal of the Royal tatstcal ocety ees B-tatstcal Methoology 95;4: e Bun AM van Rossum AC Vsse MC Koole GM. Moelng the emegency caac n-patent flow: an applcaton of queung theoy. Health Cae Manag c 007;0:5-7. Peate J. Queues n health. Health Cae Manag c 00;5:8 4. Geen L. Queueng Analyss n Healthcae. In: Hall RW e. Patent Flow: Reucng Delay n Healthcae Delvey. e. New Yok NY: pnge 006: Gbby GL chwab WK. Avalablty of ecos n an outpatent peanesthetc evaluaton clnc. J Cln Mont Comput 998;4: Jang L Gachett R. A queueng netwok moel to analyze the mpact of paallelzaton of cae on patent cycle tme. Health Cae Manag c 008;: wa GM e Haes JC Oot FJ Lemae LC Hollmann MW Peckel B. ettng potes fo mpovng the peopeatve assessment clnc: the patents' an the pofessonals' pespectve. B J Anaesth 008;00:-6

24 8. Cohen JW. The ngle eve Queue. 8 e. Amsteam the Nethelans: Noth- Hollan Publshng Company Rsng J Baon R Avell B. A ystems Analyss of a Unvesty-Health-evce Outpatent Clnc. Opeatons Reseach 97;: lkhuzen G Lmbug M Bakke PJ Klaznga N. vence-base e-engneeng: e-engneeng the evence--a systematc evew of the lteatue on busness pocess eesgn BPR n hosptal cae. Int J Health Cae Qual Assu Inc Leaesh Health ev 006;9: Hepne DL Bae AM Huwtz Gustafson M Tsen LC. Patent satsfacton wth peopeatve assessment n a peopeatve assessment testng clnc. Anesth Analg 004;98: Buzacott JA hanthkuma JG. tochastc Moels of Manufactung ystems. e. nglewoo Clffs NJ: Pentce Hall 99. lkhuzen G Buge MP Jonkes R Lmbug M Klaznga N Bakke PJ. Usng busness pocess eesgn to euce wat tmes at a unvesty hosptal n the Nethelans. Jt Comm J Qual Patent af 007;:-4 4. Taylo HM Kaln. An Intoucton to tochastc Moelng. e. an Dego CA: Acaemc Pess Btan GR Moabto R. uvey Open Queueng Netwoks: Optmzaton an Pefomance valuaton Moels fo Dscete Manufactung ystems. Poucton an Opeatons Management 996;5:6-9 4

25 Table Ttle: ummay of Input Data Patent class N Appontment Aval evce Tme evce Tme evce Tme Pecentage ate ecetay Clnc Assstant Anesthesa Cae Pove b D c D D Chlen 74 5% n74 Aults AA 90 5% I o II n7 n90 Aults AA 7 78% III o IV n86 n7 Defee to appontment b Mean sevce tme n mnutes c tana evaton of sevce tme n mnutes 5

26 Table : Ajustment of Input Paametes fo valuaton of Altenatve Desgns Altenatve Ajustment xplanaton e s e f ζ.7 One clnc assstant moves to secetay staton No stubance ung welcomng of patents The secetay gves all patents an appontment the fst tme they ave at the PAC thus aval ate nceases. CV A 0 CV A 0 CV A4 0 g ζ.9 ζ 0.07 ζ h ζ 0 We assume that appontment patents ave on tme. Theefoe the stana evaton of the aval tme equals 0 whch esults n an CV equal to 0. Appontments ae escheule outse the nteval 0AM 4 PM an theefoe the facton of patents wth an appontment s emove fom the aval ates. No patents ae efee to an appontment by the secetay Consultaton tme at secetay eceases wth.5 mnutes snce pat of tasks ae eallocate to clnc assstants; consultaton tmes at clnc assstants nceases wth these.5 mnutes an wth an atonal.5 mnutes neee to etemne upon atonal testng. CV A5 0 CV A6 0 CV A7 0 We assume that appontment patents ave on tme. Theefoe the stana evaton of the aval tme equals 0 whch esults n an CV equal to 0. All othe paamete values eman constant e Clnc assstant selects at font esk f Teat all patents on appontment bass g Rescheule appontments h Regoup employee tasks an amen patent flows 6

27 We assume that the ato between expectaton an vaance of the contact tme at the clncal assstants an theefoe also the CV emane constant. 7

28 Table Ttle: Results of Analytcal Moel Desgn ecetay Clnc Assstant Anesthesa Cae Pove Patent length of stay j k W l W W Intal Altenatve I m Altenatve II n Altenatve III o Altenatve IV p Altenatve III IV j Mean patent length of stay n mnutes fo the most common goup of patents ault AA I/II walk-n k Occupaton ate l Mean watng tme n mnutes m Clnc assstant selects at font esk n Teat all patents on appontment bass o Rescheule appontments p Regoup employee tasks an amen patent flows 8

29 Table 4 Ttle: Results of Analytcal Moel wth 008 Data q Desgn ecetay Clnc Assstant Anesthesa Cae Pove Patent length of stay s W t W W Intal Altenatve III IV u q Aval ates: Chlen 0.87 Aults AA I o II. Aults III o IV 0.4 efee to appontment 0.88 Mean patent length of stay n mnutes fo the most common goup of patents ault AA I/II walk-n s Occupaton ate t Mean watng tme n mnutes u Rescheule appontments egoup employee tasks an amen patent flows 9

30 Fgue Fgue 0