MODELING AND SCHEDULING INTELLIGENT METHOD S APPLICATION IN INCREASING HOSPITALS EFFICIENCY

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1 MODELING AND SCHEDULING INTELLIGENT METHOD S APPLICATION IN INCREASING HOSPITALS EFFICIENCY 1 NEDA DARVISH, 2 MAHNAZ VAEZI 1 Darvsh, Neda :,PhD student of modelng networkng, Islamc Azad Unversty Tehran Medcal Branch 2 Vaez Mahnaz: MSc of envronmental engneerng, Islamc Azad Unversty Tehran Medcal Branch E-mal: [email protected], [email protected] ABSTRACT Every human cost of each hosptal as the greatest presenter the health care and treatment to all people, the man sources and credts allocated to the health and treatment of a country. Determnng the optmal number of employees for each ward of hosptal, because of ts mportance n qualty of servces offered to customers and costs are among the ssues that any clear standard has not been wrtten for t. In Ths study, the am of modelng of hosptal and use of ntellgent systems to adjust the shft program and to determne optmal number of hosptal staff n order to ncrease effcency and mnmzng ts costs. As, the presence of patent n the hosptal and releasng them can be consdered as a dscrete system wth the characterstcs of Markov processes, n the frst step, usng Markov s chan models a good estmate of the system condtons such as the number of beds needed and occuped beds, whch can be offered n the optmzaton of capacty s benefcal. In second step, to develop the model, an approach s stated for mnmzng the costs wth assst of Petr's network. Fnally, to control and optmze the model wth usng the genetc algorthm s presented for optmal shftng of human resources lke nurses. The results show 42% reducton of human resources costs and 87% savng servce tme for patent. Ths study s applcable and t s n group of descrptve-analyss studes, whch had been desgn as the software and the data collecton tool was the checklst of Bu Al Hosptal s patents records, whch approved by the related experts and studed after observaton, chronoscope and also tme of human resources servces to several patents and the plan shft of nurses and doctors has been studed wth use of ntellgent system s desgnng. Data analyss and plannng s carred out wth the method of Petr net and Markov and genetc algorthm wth use of Matlab and Hpsm software. Comparson of preparaton programs and system desgn show to patents, mprovement of cost reducton about 42% and 87% tme savng servce. Research varous models n operaton, can be used as a sutable tool for schedulng and determnaton the optmal number of staff needed n several parts of a hosptal, whch has a vtal and sgnfcant role. Snce the desgned system n ths study s lmted to the obtaned data from medcal and educatonal center of Bu Al department afflated to Islamc Azad Unversty Tehran medcal branch, to extend and optmum use n other hosptals requre makng changes n programmng based on data. Therefore, t s recommended to 95

2 make these systems usable n other hosptals and ncreasng restrctons, so the prepared program wll be closer to the real world, to be done. Keywords: Hosptal Effcency, Petr's Network, Markov s Chan, Genetc Algorthm, Intellgent Networkng 1. INTRODUCTION One of the strategc areas of nformaton technology development n the country s health, whch acceptance and quck treatment of patents s one of the man components of health care. Ths center n one sde s responsble for the ncreasng trend and the ncreasng patents to receve good servces, and on the other hand always face lmted resources and budgets. Real value human resources needed n the sectons of hosptal s one of the mportant concerns of a hosptal management.tmetable problems program of dfferent staff of the 1980s had been consdered and studed by several researchers. Human resources management polces system can affect on staffs effcency, care qualty, nurses and doctors conscence. Hosptals performance assessment by usng modelng and smulaton can be propounded as a sutable tool for capacty programmng and mprove effcency n provdng health care. So t s essental, hosptals wth human resource plannng and effcent use of labor, tme and cost whle ncreasng effcency reduce plannng problem. The basc ssues, whch can be consdered for runnng optmal hosptal systems are ncludng: 1- dmensons of a hosptal system 2- understandng the performance and dentfy system problems such as patent watng tme 3- mprovng performance 4- study the reacton system aganst large volume of work. 2. PREVIOUS STUDIES REVIEW In order to determne the effcency of hosptal and optmzng the staff numbers by usng ntellgent networks, numerous artcle based on Markov s chan models or Petr network or genetc algorthm have been presented that n the contnuance, some of them are studed. Whereas the tme spent for data processng and plannng staff shft work, takes a lot of tmes from nurse managers, n a research by ANSI and hs colleagues n 1996, wth use of genetc algorthm they have studed reducton of nurse shftng set tme. Implementaton of the software was done n 90 seconds. In 1991, Khan presented a model for mnmzng the human resource. The human resource was the nurses whom were supposed to employ n dfferent wards of hosptal. They tred to present a model of shftng for the staff of the emergency ward. Yet they could not fnd a complete model and method for a complex system lke emergency wards [3]. In 1996, Mourtou n one of the Greece hosptals made a hosptal model by usng Petr's network and Hpsm software. In ths research, a model was presented for patent servces that show the reducton of patent's watng tme up to 23.91%. [7, 12].In 1997, Ptt presented a smulaton model whch could be appled n dfferent wards of a hosptal. The obvous result of ths research was a model n whch, a hosptal was able to have a smlar treatment result wth fewer budgets but less tme 96

3 for patents to stay n hosptal. In 1997, Lo and Kao appled the estmaton method to determne the number needed for staff based on lne programmng for optmzng of nurses number In 1998, Isken and Han Cock studed the tmng model applcablty n dfferent wards of a hosptal wth dfferent demands durng a week, days and a whole day.the ntellgent models as a plannng and decson makng method has been used n health care feld ncreasngly n the last two decays. Genetc algorthm are approprate for plannng and tme table problems solvng, and a plenty software packages for programmng and nurse's shftng problem solvng are based on genetc algorthm. Ths fact s agreeable to the results of Beddoe[28] and Ozcan [25]. The study of researches n ths feld shows that there are varous methods for tmng and nurses' shftng problems solutons. In these methods, a smple model or much related to a specfc problem n a hosptal are generally consdered.gallvan and hs colleagues n 2002 studes by offerng a model based on Markov s chan were studed the varablty n the length of lne snce t s an mportant factor n the hosptal operatons. In ths research, reducng patent watng tme n order to get beds for hosptalzed patents were studed, and a model was presented for optmzng beds and reducng unused beds.in 2006[30], Ms.Saeedeh Ketab worked on quanttatve optmzaton n nurse staff n emergency ward of Chamran Hosptal wth lnear programmng and they were presented an estmaton for reducton n the number of the nurses.in 2008[31], Ms. Asyeh Darvsh presented an ntellgent system to set nurses' shft wth fewer numbers of them accordng to fewer workng tme, nursery rankng and nurses' wll wth help of genetc algorthm n Koodakane Tehran Hosptal. Ths system presents an optmzed shftng schedule n 2 mnutes. In ths research, the condtons of wards of hosptals s studed accordng to the dscrete event tme system (DES based on Markov and Petr net method, and modelng of hosptals s carred out accordng to the patents watng tme and duraton of bedrdden and then wth use of genetc algorthm ntellgent system we wll study the workng tme schedulng regulaton wth less human resources. Rushng and watng, watng for a long tmes for a patent, staff gettng tred of workng, wastng and etc...all of these are sgns of desgnng a flawed system for the patent matters. Petr nets are mathematcal and graphcal modelng tools. These models are sutable tools for descrbng and studyng nformaton processng systems whch states systems behavor [8]. Markov chan models can be used for approprate modelng mode choce for estmaton of certan models. Markov method s memory-less random dscrete events processes. Memory-less means that t s lkely to attend a state depend on prevous state and t does not depends on state s lfetme. Memoryless s equal to the pont that modes countng process has Poason dstrbuton and tme of events happenng had exponentally dstrbuton. Wth use of smulaton modelng can answer to the qualtatve questons [9]. One of the common methods of artfcal ntellgence s genetc algorthm whch s comprehensve searchng technque based on natural genetc acton. Substructural elements of evoluton process n GA (genetc algorthm [10] are ncludng genes 97

4 programs populaton, age renewal, mutaton, competton and selecton. Thus nature wth gradual elmnaton of napproprate speces and hgher prolferaton of optmal speces can promote contnually each generaton n case of dfferent features. In ths artcle, presentaton of a model of a hosptal and presentaton quanttatve benchmark for comparson, study of effcency and extracton of useful varables such as estmated tme for ward occupaton and presentaton shft plan s defned n manner that can mnmze costs of unform algnment of forces. 3. STUDY METHOD Ths study s applcable and carred out for software desgn and acheved accordng to the extracted data. Samples are chosen from general and specfc wards such as emergency and ICU. Data collecton tool shfts nursng program durng the second 6 th month of 1387 and the emergency trage form samples and check lsts of tme-related servces tme to patents, that are collected by the wards personnel durng two august and September months of 1378 and 200 patents and recommended system based on these data was desgned. Analyss of data carred out through revew and pre-processng data and calculatng mathematc functons and modelng and plannng wth Petr-net and Markov method and genetc algorthm by usng of Hpsm and Matlab 7.1 software. 4. FINDINGS Beng desgned ntellgent system, after runnng the desgned software, frstly, we enterng n to graphcal space whch s ncludng three cons: nurse shft(algorthm genetc model,manage tme(petr net model and balance bed( Markov model. Work n process (shown n fgure 1. By mplementng any of these cons we would enter n to another wndow whch we frst receve data and then runs desred applcaton. In ths regard, frst, we want to study Markov (bed balance. Markov development Petr net ng Algorthm genetc Optmzaton Fgure 1: workng n process n a vew Markov chan model can be used by choosng chan model and then we study the amount of the approprate mode n modelng for estmaton occuped beds wth smulated analyss. of specfc models of systems. In ths secton the tme perod of hosptalzaton of patents n wards would analyze and fnally the purpose of the analyss would be the used capacty n rooms Accordngly, the proposed scenaro for hosptal management s ntroduced and evaluated, (shown n fgure 2. Ths scenaro s the usual hosptal, n ths scenaro try to mprove understandng of of ward n order to be able to maxmze the unused space n ward of hosptalzaton. usage of exstng spaces by re-allocatng them Accordngly, you can see: for reducng patents watng tme. Acheved fndngs from hosptal records of patents analyzed by usng technque based on Markov 98

5 P j (1-1 k j / k f = j = + 1 = 0 otherwse K* s the percentage of patents who are n hosptal after ( day whle K s the total percentage of patents who are n hosptal after ( day. hosptalzaton of bed patents Markov The rate of occuped bed Fgure 2: modelng wth Markov method By runnng of ths program we have: patents n one week week's day Fgure3: graph of patent s bedrdden perod n ICU May Jun The Result of study and rate of occuped bed n ICU Table 1: results acheved from markov model analyss of ICU ward Month Saturday Sunday Monday Tuesday Wednesday Thursday Frday May-June 76/19% 90/47% 89/51% 90/46% 83/33% 83/33% 76/19% By observng the acheved results from analyss of beds wth Markov method n ICU ward t can In fgure5 and we desgn the manage tme program wth Matlab software whch shows the be stated that there s no unused bed n ths ward effcency computaton and watng tme. and accordng to the hosptal structure we can ncrease the number of beds n ICU ward. Graph of hosptalzed patents shown n fgure3 and acheved result shown n table 1The second stage of research, for desgnng systems and software package we carry out modelng and graphcal drawng wth modelng Hpsm software, shown Accordng to the fndngs, we would study and analyze the Petr net method. Petr Net can be used to express any feld or a system whch can be descrbed graphcally by a flowchart and use a tool for showng parallel or smultaneous actvtes. A Petr net s a quntuple set of PN= (P, T, F, W, and M n whch: T= s a fnte set of 99

6 transtons, P=s a fnte set of places, F: set of arches, W: s a weght functon, M: s a prmtve markng, M ( p = M ( p I ( p, t + O ( p, t p P, M (p I (p,t (1-2 For stmulaton we use queue theory. Our man purpose n queue theory dscusson s superfcal preparaton of facltes whch affected by queue theory and fndng soluton for mnmzng related costs. Queue theory, mathematc and statstc scence s expanded n a manner that can help managers n analyss of queue or watng and optmzaton of systems. Now the Petr net model would study for a queue system [8]. accordngly, for modelng parts of hosptal wth Petr net, (shown n fgure4 frst we must examne patent process n a hosptal, and then we present a model for ths process. For modelng hosptals wards by Petr net Then a Petr net model would be presented for ths process. Table 2 shown several condtoned of ICU n case of doctors and nurses numbers andtable 3 shown results acheved from Petr net analyss of ICU ward wth desgn the manage tme program wth Matlab. nurse beds doctors Patents dstrbuto Pert net Nurse s effcency Doctor s effcency Ward effcency Bed effcency Fgure 4: modelng wth Petr net Fgure 5: Petr net modelng ICU wth Hpsm 100

7 Computatons are acheved of the followng Bed s effcency percentage general relatons: P= total number of steps,t= tme of one step Nurse_ Performanc e= (( + ( 38 (( nstep nstep j= 31 = 1 9 j= 2 j (( nstep nstep = 1 n( f t s = 0 = 1/ nstep 100 W,5mn n step=t total, PjS= number of genomes n( f t js = 0 n= 1/ nstep n J poston n step I, EjS= number of output N Nurse effcency percentage servce presenters n a system, Tz= output Bed_ Performanc e= (( + ( 58 (( nstep nstep j= 51 = 1 42 j= 10 j (( nstep nstep = 1 n( f t s = 0 n= 1/ nstep n( f t s = 0 = 1/ nstep 100 W j B genomes from j n ( step,tbs= tme of transton actvty of b n ( step,w= number of transton of system Table 2: several condtoned of ICU n case of doctors and nurses numbers Poston nurses beds Table 3: results acheved from Petr net analyss of ICU ward condt Watng n Watng for Watng for Nurses' Beds on recepton/mn bed/mn nurse/mn effcency effcency % 54.25% % 84.32% % 81.86% % 81.56% Intally, the program shft nurse that wll be And fnally we wll study the ntellgent system arranged by supervsor n a form of nonof genetc algorthm whch, n desgned program you can notce the ttle of Nurse Shft genetc perodcally per month. For ths ssue we algorthm (shown n fgure 6, that by choosng consder three shfts workng of 7:00 am, 7:00 ths opton and runnng of program we can to pm and 12:00 pm. Natural workng hours of optmzng the personnel shft program and under-programmng forces n ths study s regulatng the number of work force and 44hours per week. Ths ssue s an optmal multcrtera eventually we can compute the effcency. ssue, because workng shfts program should regulate n a way that weekly table 101

8 complete smultaneously by nurses and n a more complex condton a smple model should be consdered from nurse dstrbuton n dfferent workng shfts. The frst crtera of monotonous dstrbuton of work force s n case of arrangng and second crtera s dstrbuton of number of staff needed durng the week, that by convertng program processng, expendture functon would determne as followng. Workng Shft arrangement physcans nurses Genetc Algorthm Optmal number Optmal arrangement Fgure 6: modelng wth genetc algorthm method For each ( nurse and each (j workng shft we have: a jk 1 shft pattern = 0 else j covers day/nght k Expendture functon of F ( s the purpose of mnmzng expendture functon whch s optmal crtera n ths stage. P F( = 7 a k -1 or 14 a k -8 or 14 a k 1 jk jk jk = = = D N B j days shfts j nght shfts j combned shfts n m, p mn!, x j j 1 jef( x j = 1, jef ( numofnurse f 1 = ( WeekHour NormalWorkHour = 1` Mnmzng the above formula means decreasng the normal hours. each shft whch s ncludng 210 genes. Sutable codng for statng chromosomes s Schedulng table s ncludng 210 rows whch s planned by allocatng numbers to nurses. Samples are ncludng 10 nurses for completed wth arrangement of nurses shft work determnaton chromosomes whch has nonperodcally program. Length of fbers s equal to the number of week days ncludng three shfts multply the number of workng force needed n and less work forces that shown n table 4. Each chromosome whch s ncludng genes s a soluton for ths ssue that nurses shft are dstrbuted n rows of table as one and zero

9 populatons of shft pattern and 100 suggestons, 21 genes, 80-85% cross over of chromosome and about 0.01% mutaton are desgned n ths system. In the present study, compared results n the feld of dfferent rate, we have the percentage of cost reducton mprovement. In regulaton of genetc algorthms strategy and parameters to acheve Run tme about 3 mnutes for optmzng, populaton sze of 400 and stop crtera were consdered up to producton of 400 generatons and for choosng parents we were used rule roulette wheel. Revew and mplementaton of program showed that t s reached to a good convergence. After desgnng system n order to evaluate ts performance, preprocessed data provded to the system and wth mplementaton of system, program was adjusted. Consderng the cost functon defnton and the above descrpton, table 5 shown the results of optmzng the nurse program by genetc algorthm method. Optmzng the arrangement of program by the genetc algorthm s as follows: Nursng program of ICU s adjusted manually by supervsor Table 4- nursng shft schedulng nurse Sat1 Sat2 Sat3 Sun 1 Sun2 Sun3 Mon1 Mon2 Mon3 Tus1 Tus2 Tus Table 5: results of optmzng the nurse program by genetc algorthm method Result Suggeston Shft (1-21 Manual number Nurse number 1,4,3, ,3,7,9 1,2, ,2,6,8,10 5, ,7 4, ,10 1,6,5,3, ,3,6,7,8,10 In ths table 6 results had shown the computaton of ICU effcency wth manual data of the number of physcans and nurses. At the end the optmzed results, we enter the results of genetc algorthm con n nput data of Petr net Icon whch can be seen n table

10 Table 6: computaton ICU effcency wth manual data of physcans and nurses number Ward Bed Physcan Nurse Shft effcency effcency effcency effcency physcans nurses 89.1% 91.66% 95.83% 79.54% % 91.66% 95.83% 83.63% % 91.66% 95.83% 96.36% % 91.66% 93.75% 79.54% Table 7: computaton of ICU effcency wth number of physcans and nurses optmal data Ward Bed Physcan Nurse Shft effcency effcency effcency effcency physcans nurses 86.04% 91.66% 93.72% 72.72% % 91.66% 95.83% 78.42% % 91.66% 95.83% 83.63% % 91.66% 87.50% 81.63% Table 8: statstcal analyss of average and standard devaton comparson Ttle Average Standard devaton optmzed nurse optmzed physcan Effcency of optmzed nurse 83.3% 8.59 Effcency of optmzed physcan 95.1% 1.2 nurses physcans Nurses effcency 84.5% 8.45 Physcan effcency 94% 4.49 Wth observaton of all above results (table 8, we can say that, n ICU whch s an specfc ward by decreasng number of nurses and physcans the physcans and nurses effcency wll decrease because, moreover the watng tme ncrease and as a result, transton tme ncrease from one step to another for, the runnng of ghettos n queue wll carry out wth delay. The bed effcency s dependng on the number of patents, that s why we don t observe any change n that. Operatons research s n a manner that f patents enter n to system a lot, n case of decreasng the servers, they have to wat for 104

11 servces and n contrast f patents enter n to system non-contnuous, the servce facltes durng enterng perods would become useless whch must reman equlbrum n operaton clearly, provdng more and better equpments for presentng servce lead to reduce watng tme and beng n queue and also reduce related costs. By desgnng ntellgent system n ths study, ths balance was acheved n the operaton. Accordng to the acheved results and earler studes t can pont to the ssues whch calculate manually n hosptals at the end of each month that lmted to the cost of occuped bed. about desgnng ntellgent system of nurse shft program we can pont to the studes of Ans and hs colleagues, modelng wth Markov method n order to estmate the number of unused beds, hosptal modelng for estmatng of unused beds by studes of Gallvan and hs colleagues, hosptal modelng wth the Petr net model by Mourtou studes, but the system whch s ntroduce n the present artcle had advantages compared wth exstng nternet servces because, at the same tme we can calculate the effcency of ward and offerng servces to patents, by regulatng shfts programs wth less staffs and wth optmzaton of system we can reduce man problems of hosptals management center. 5. CONCLUSION Acheved results from ths research shows that despte n health system n country effcences such as work force effcency(doctors and nurses s not ncomputable and percentage of bed occupaton and regulatng shft work program prepare manually and wth paper, ths ssue results n tme consumng of managers and wastng costs and errors n carred out computatons. Therefore wth technology mprovement and automaton system there s possblty of makng such automatc data s provded. Usng of ntellgent system consder essentally for preparng optmal program. Studyng of Data showed that the present stuaton of plannng and determnaton of effcency n Iran Hosptals s not desrable. In ths research, Markov methods and Petr net and genetc algorthm as modelng method and developments of model and ntellgent optmzaton for solvng problems, reducng costs and plannng for work force was used successfully and there s the possblty to generalze t wth changes and reforms n programmng. In Acheved results of studes show that, the present research s a sutable base for expandng researches n future n feld of system desgns n a way that can be used n dfferent wards and can provde more facltes to approach the real world. REFERENCES: [1]. S. R. Azm,"Seres of hygene and health rules of Tehran medcal educaton (2002". Tehran. [2]. W. Isken, M.Hancock,"A heurstc approach to nurse schedulng n hosptal unt wth non-statonary: urgent demand and fxed staff sze of socety for health system (1990", [3]. Khan. Z," A note on a networkng model for nursng staff shfts problems. Informaton and decsons technologes (1991"

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