Researches on how to Plan the Medical Service of Hospital

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1 Iteratoal Joural of Maageral Studes ad Research (IJMSR) Volume 4, Issue 7, July 06, PP 6-46 ISSN (Prt) & ISSN (Ole) Researches o how to Pla the Medcal Servce of Hosptal Sh Jahe*, Yag Yag, Xg Cheghao, Ja Dogxue Qush Hoors College, Taj Uversty, Taj, Cha College of Electrcal ad Electroc Egeerg, Shadog Uversty of Techology, Zbo, Cha *shjahe_006@6.com bstract: I recet years, the agg tred of the populato s gradually creasg. Meawhle, the resdets health awareess s also rsg ad medcal formato reform cotues to deepe ad Cha's medcal servce s udergog rapd developmet as well. Researches o how to pla the medcal servce of hosptal ca ot oly avod the waste of resources, but also effectvely cotrbute to the developmet of Cha s medcal ad health servces. We solve the problem from two aspects. Oe s the queue rules of patets. Itroduce weght ovato boldly ad desg a ew Queug system combe M/M// / /PS wth M/M/C/ / /FCFS. The other s dex system of evaluato whch s from the perspectve of both patet ad hosptal. Based o combg psychology ad mathematcs such as fuzzy math formulas, scetfc ad reasoable weght of dcates s obtaed by alytc Herarchy Process The we acheve to evaluate the model of mult-level correctly ad arrage the teral resources of hosptals reasoable. mog them, combg the HP, Delph method ad queug theory based model to obta the objectve fucto by f s a great ovato. I addto, takg the factors such as seaso ad holdays, whch result movemets, to cosderato, related dcators are mproved to a fucto of tme subtly. d the as a bass, hosptals wll get reasoable suggesto about collectg formato varables. t last, hosptals acheve to make optmal use of resources wth the hosptal, ad mprove patets satsfacto as hgh as possble by a full rage of reforms. Keywords: queug theory,aalytc herarchy process,delph method,olear programmg. INTRODUCTION s s kow to all, dffcult hosptalzato has always bee a uspeakable pa to patets ad hosptals. Searchg to the bottom, besdes the shortage ad ureasoable dstrbuto of medcal resources, the resource dscordace wth the hosptal s also vtal mportace. log wth the developmet of the Iteret ad mprovemet of formato degree, hosptals ca obta a great amout of formato through moder methods. By meas of medcal bg data, hosptal are able to get fully tegrated resources, as well as ufed coordato, provdg patets wth more humazed,persoalzed ad effectve medcal servce. Nevertheless, hosptals are also cofroted wth daze prevoulg the age of bg data, these data characterzed by large amout, fe tmeless ad certtude. How to tegrate a sea of fo effcetly to pull together relyg o the aalyss ad statstcs of dsease cure rate through bg data, hosptals ca reder patets best therapy procedure, accordg to ther dagostc fo. Besdes, t ca arrage advace to get rd of troubles rsg from coflct ad watg a le. Image below dagrams a process of patet s vst to hosptalzato-----geeral patets, after clc dagoss, partly leave the hosptal, others receve a operato or osocomal treatmet. The latter usually eed to queue at fastgum, watg for ther arragemet. There are aother sort of specal patets called selectve operated patets, who have completed dagoss but eed electve surgery. Selectve operated patets queug fo. Classcally, selectve operated patets fall to RC Page 6

2 Sh Jahe et al. categores: sck people who are hosptal a day before ther operato appotmet, ad drectly operatve patets. Oce the operato s performed, selectve operated patets are eedless to be fxed wards ad queue up. I practce, dsease s ofte suffcet some departmets, whch results that the stuato of watg for beds s serous, ad lots of patets eed to le up to be hosptal. O the cotrary, some departmets has may empty beds, ad bed occupacy rates are very low. For ths reaso, from the holstc perspectve, hosptals ca cetralzed the wards ad beds. t preset, there s o suffcet codtos of all dsease of pathologcal for large samples to make vestgatos. broad also mperfect ths regard. Wth the establshmet of data systems, dsease research, treatmet optos, ad user servces ca be promoted smultaeously. However, hosptals ca oly focus o the maagemet of health care resources order to adapt to the arrval of the age of bg data. I order to mprove the effcecy of hosptal resources, please try to aalyze ad solve the followg problems: Problem oe: formato systems are ot yet uder fully perfect codtos, order to meet servce requremets. What data do hosptals eed to collect? Please expla the reasos. The expla how to orgaze ad descrbe ths formato order to mprove effcecy. Problem two: I order to mprove Ward resource utlzato effcecy, t s must to descrbe the whole process of hosptalzed patets from admsso to dscharge correctly. But whe the patets arrve at hosptal ad how hosptal resource s dstrbuted are ucerta. So how to reflect ths ucertaty s the key to develop a deploymet strategy. Try to buld a mathematcal model to descrbe the process for patets from admsso to dscharge. Problem three: Please gve a reasoable method of cotrol ad optmzato ad establsh a model o overall allocato of resources of hosptal ward to help mprove the effcecy of hosptal servces ad hosptal resource use. Problem four: as the seasos, holdays, ad may other factors, the umber of patets hosptalzed s wth great volatlty. s a result, the hosptal loads wave fercely, whch leadg to the mbalace of all aspects of hosptal work, serously affectg the effectveess of servces. Please make a reasoable methods of cotrol, whch uder the codto of balacg hosptal work to mprove servce satsfacto ad effcet use of hosptal beds as hgh as possble. I the ed, you have to provde a medcal servce proposal to the hosptal accordg to your study perspectve.. MODEL HYPOTHESIS Hypothess :the umber of hosptal workers s suffcet ad oce the patet s scheduled for surgery, t ca be carred out o schedule. Hypothess :The patet's codto s requred for surgery ad hosptalzato. Hypothess :Oce patets eter the hosptal referral, they ever gve up treatmet or accdetal pass away. Hypothess 4:The fluece of medcal strumet s ot cosdered. Hypothess 5:The data used are real ad relable. Hypothess 6:Patet source s ulmted, ad the arrval of the patet s radom. Hypothess 7:The mpact of sudde major dseases s ot cosdered, such as SRS, etc. Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 7

3 Researches o how to Pla the Medcal Servce of Hosptal. SYMBOL DESCRIPTION k C (t) ] (t) W t L V (t) o The posto of the patet the team Number of operato room / servce desk The proporto of the total patets the Departmet of the T dsease Servce tme for the T dsease The watg tme for oe patets The umber of beds the Departmet Operato tme of the T dsease Operato room utlzato 4. PROBLEM NLYSIS 4.. Backgroud of alyss. Wth the developmet of socety ad the pheomeo of agg populato, how to realze the reasoable allocato of medcal resources s becomg a hot topc. The hosptal s a complex system ad the patet to the hosptal tme s relatvely radom ad hard to cotrol. What s more, State of resources whe they reach the hosptal s ucertaly ad coordato of teral resources s dffcult. Thus, the pheomeo of queug s easy to occur. The watg tme of the hosptal bed ad the operato ca reduce the patet's satsfacto wth the hosptal. However, the watg tme of the hosptal bed ad the operato ca reduce the patet's satsfacto wth the hosptal. But f we bldly crease the umber of the beds, the hosptal bed utlzato rato wll decrease. Thus, I the case of the total umber of beds ad the operato room, we should ratoally allocate of resources to reduce patets' watg tme ad mprove the utlzato rate of hosptal bed.. t preset, the domestc hosptal maagemets rely o experece ad geeral practce ad they use scetfc ad quattatve methods, whle the queug theory operatos research s a scece to solve the above problems. The queug theory s a effectve method to study the above problems quattatvely ad scetfcally. The hosptal's medcal resources maly clude ward, operato room ad some other resources ad the allocato of resources s determed by the maagemet of the hosptal. s for the maager of the hosptal, the rato of ward dfferet departmets ad reasoable arragemet of operato room s very essetal for the tegrato of medcal resources ad the maxmzato of the beefts of medcal sttutos.. I ths paper, the aalyss of the rato of hosptal wards ad operato room ad the order of the patet queug. The cocluso wll be used to acheve a w-w stuato of patet satsfacto ad hosptal resource utlzato. 4.. Problem alyss 4... alyss of problem Queug servce system s maly dvded to three parts: put process, queug dscple, ageces, the form s //B/C, ccordg to the relevat lterature reports, the tme of arrval of the patets to the tme of T ad the servce tme of the operato room are ot subject to the specfc dstrbuto. s a result, we ca oly do the geeral dstrbuto. The, Queug system should be recorded as G/G/K, whch follow the rules ad characterstcs of the type of the queug system. But accordg to the theory of queug Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 8

4 Sh Jahe et al. theory, G/G/K queug system s extremely dffcult to solve. Thus, We use ths set of mathematcal models, M/M/C / / ad M/M// / mxed queug system. Oe s a queug system whose put process s Posso flow, servce tme obeys the complex expoetal dstrbuto, ad system has C servce desk parallel servces, system capacty s fte ad system source s fte watg for system. The other oe s a queug system whose put process s Posso flow, servce tme obeys the complex expoetal dstrbuto, ad system has oe servce desk parallel servce, system capacty s fte ad system source s fte watg for system. The, we get the effectve resource utlzato of beds, R ( Z X K ), ( Z Y ) mog the formula, K stads for the tme to observe the patet's hosptalzato; Z stads for the tme whe patet dscharges. X stads for the tme whe the patet takes the operato. Y stads for the tme whe the patet s hosptalzed. I addto, we use the aalytc herarchy process to defe the weght of dfferet patets, ad to pla the queue order of dfferet patets. Fally, we use fuzzy psychology to defe the overall level of the system. From the perspectve of queug system, we eed to kow the data matrx of each dsease (operato tme, preoperatve preparato tme, postoperatve recovery tme, the severty of the lless, the proporto of all patets), the umber of operato room, the umber of varous departmets. From a psychologcal pot of vew, we eed to kow the patet's satsfacto ad the utlzato rate of hosptal beds for effectve resources for ths system, the weght of each alyss of problem The patet etered the two queue after the dagoss of the dsease. Oe s the M/M// / queug system whch uses PS queug rules. The patet's weght s made up of two parts: oe s the durato whe you are the queue, ad the other s the dstace to do the most approprate operato of the hosptal bed. The servce desk of the queug system s the hosptal bed. Wheever the other patets the Departmet of the hosptal dscharge, there s a patet mmedately added. Thus, the servce of ths system s Uts. The patet eters the ward by ths queue rule, but also try to meet the hosptal watg for the operato tme before eterg the ward (The patet's operato tme ad the operato tme of all patets the cohort ). Ths system represets the whole process of the patet from the clc to the ward. The other s M/M/C/ / queug system whch uses FCFS queug rules. The queue s sorted accordg to queue.the servce desk of the system s the operato room. L (the umber of uts the beds) of the cohort dcates the team from admsso to the preparato for the operato. There s o practcal sgfcace after L. Ths system represets a procedure for patets from outpatet to surgery alyss of problem The evaluato dex of the system s dvded to two parts: oe s the satsfacto of the patets, ad the other s the effectve utlzato of the resources of the hosptal. For patet satsfacto, there are two parts; oe s the legth of tme for the patet to be hosptalzed, ad the other s the durato from the hosptal to the preparato of the operato. The utlzato rate of hosptal resources s made up of Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 9

5 Researches o how to Pla the Medcal Servce of Hosptal two parts: the utlzato rate of hosptal bed ad the utlzato rate of operato room. The bed utlzato rate s obvously determed by the formula Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 40 R ( Z X K ) ( Z Y ) metoed prevously. ccordg to the umber of beds, t s clear that the umber of beds, the shorter the patets from the dagoss, the hgher the patet satsfacto, the patet from the hosptal to the preparato of the operato tme, the patet satsfacto s reduced; the utlzato rate of the operato room, the umber of beds, the hgher the utlzato rate of operato room. t the same tme, the umber of hosptal beds s a fxed value, so we eed to be accordace wth the weght rato of each departmet to get the best bed umber, so as to get the best system alyss of problem4 The cdece of dfferet dseases, data wth tme chagg, we ca dvde the fucto of each varable s set to t, a relatvely short perod of tme, ca be regarded as a costat, wth the chage of tme, the correspodg data s also a costatly chagg hosptal ca collect correspodg data, the accordg to the problem of three establshed model calculated hosptal ow the evaluato dex ad the best evaluato dex. If the dfferece betwee the two s ot more tha 0%, the umber of hosptal beds wthout chage; f the dfferece betwee the two s more tha 0%, the hosptal accordace wth the problem of three of the method to re plag the umber of departmets. Ths method ot oly ca mprove the resource utlzato, but also balace the work testy of the hosptal. 5. THE ESTBLISHMENT ND THE SOLUTION 5.. The Establshmet of Model For patets to sort, take the patet's put process to accout. The put process s to descrbe how the customer accordg to the rules of the arrval queug system. For customer sources, the source may be lmted, ad t may be fte; for the arrval type, the customer may be a sgle arrval, ad t may be a batch arrval; for the customers to arrve at the tme, some are subject to Posso dstrbuto, some are subject to the K Erlag dstrbuto, ad some are equally spaced tme. Posso dstrbuto s the most wdely used dstrbuto model, whch ca descrbe the customer arrval system from two perspectves: frst, the umber of customers arrvg at a certa tme (such as the ut tme), the two s the tme of the customer arrval system. I probablty theory, the probablty dstrbuto of radom varable N s P{ N } e ( 0,,...; 0).! N s called Posso dstrbuto. I the Posso dstrbuto, the umber of customers arrvg at a queug system wth the ut tme s a radom varable that obeys the Posso dstrbuto. The, the umber of customers the queue system to reach the queug system N (t), the the probablty dstrbuto of the expresso should be ( t) t P{ N } e ( 0,,...; 0; t 0).!

6 Sh Jahe et al. We called N (t) for the Posso process, also kow as Posso flow. It satsfes the followg three codtos: o aftereffect, amely the umber of customers arrvg the do ot wat to had over the tme terval s depedet of each other; statoarty, amely [t, t + t+δt]. For ths model, practcal terms, the patets are dvdually comg ad are depedet of each other, a certa perod of tme to reach umber follows a Posso dstrbuto, arrval process s statoary (varace value s ot affected by the tme to reach the tme terval ad expected), so for the umber of smooth team, we ca stck weghted assgmet came to a optmzato of the queug rules for the team. Frst, what s the ormal ad reasoable queug rules? t frst, we eed to cosder how log the patet has bee led up. Because our model the queue s ot the FCFS model, for a log tme already led up the team, we also eed to make t raked the forefrot of the team. Therefore, the queue order we troduce frst weght ɑ, of the weght of the dcators for the patet who has raked the log team, we wll the quatfcato for the patet team posto K. Relatvely speakg, the patet's posto weghted value ɑ k s smaller, the posto of the patet a team should be more frot. I addto, we also wat to cosder the use of teral resources the hosptal whe the patet s hosptalzed. Frst, we assume that each departmet of the allocato of the operato room as a fxed value, ths value should be the Departmet of patets wth log-term operato. The, the utlzato rate of our bed utlzato rate dcates that the ward utlzato rate ca be determed to descrbe. Through smulato, we fd that ths fucto solves up very trouble, so we used Matlab smulato whch ca make the approxmato for a polyomal fucto o the ut quatty. The we gve hm a weght ɑ. Relatvely speakg, f the weghted value s smaller, the team should be depedg o the moth before. 5.. The Establshmet of Model 5... Establshmet of evaluato system For the allocato of beds, we have the followg evaluato system. Hosptal agle Bed utlzato rate, x, the hgher the bed utlzato s, the more reasoable the overall allocato of hosptal resources are, ad vce versa. Operato room utlzato rate, x, the hgher the utlzato rate of the operato room s, the more reasoable the overall allocato of hosptal resources are, ad vce versa. ccordg to the dfferece of the degree of the hosptal resource utlzato, the weghted value of beta ad beta was gve. Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 4

7 Researches o how to Pla the Medcal Servce of Hosptal Patet agle Watg tme for admsso to the ward(patets the outpatet servce to eter the hosptal watg tme), otes x, watg for the shorter the ward, the hgher the patet servce satsfacto, ad vce versa. Watg tme for the operato (patets admtted to the hosptal after the operato of the watg tme), otes x4, watg for the shorter operato tme, the hgher the patet servce satsfacto, ad vce versa. Based o the mpact of the two o the patet's servce satsfacto, the sze of the dfferece, gvg dfferet weghtsβ β4. I order to establsh a reasoable dex evaluato system, from two aspects of hosptal ad patets, a comprehesve evaluato dex s set up. y. x x x 4x Establshmet of Weghted Value t preset, we use HP to determe the utlzato rate of the ward x, operato room utlzato x, watg for admsso to the ward x, watg for the tme x4of the operato of the correspodg weght of β β β β4. I estmatg the mpact of each dex o the comprehesve assessmet dcators, the dcators, x ad xj.we use the followg e levels to quattatvely express the results of ths comparso, ad remember t as x/xj. I problem solvg: The mportace compared x wth xj x/xj equal mddle Slghtly mportat mddle 4 mportat 5 mddle 6 much more mportat 7 mddle 8 far more mportat 9 The we get verse matrx We regard t as matrx M. ccordg to the propertes of hosptal servces as well as the "people-oreted", chersh lfe, determed to wat for stay ward tme x, awatg surgery tme x4 ad ward utlzato x, operatg Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 4

8 Sh Jahe et al. room utlzato rate x, betwee the relatve mportace of; accordg to the psychology kowledge ad hosptalzato costs, etc. determe watg for the arrval of the ward x ad wat for the relatve mportat degree betwee the operato tme X4. The accordg to the hosptal stuato determe ward utlzato (x4) ad operatg room utlzato betwee x relatve mportat degree. x/x= x/x= x/x= x4/x=4 x4/x=4 x4/x=4 The we get matrx : The matrx s ormalzed, ad each colum s summed, ad each elemet of the matrx s dvded by the colum's ad the obtaed matrx B s as follows.97% 9.00% 4.4% 5.69% β=.97% β=9.00% β=4.4% β4=5.69% 5... Evaluato Idex Formula Hosptal agel ()The value of x s a costat ad t equals to.i aother word, x=. () Patet agel x j j ( t) L V ( t ) Referrg to the related psychology ad the theory of fuzzy psychology, patets' satsfacto s quatfed by the patet watg tme, ad the quattatve crtera must be see the appedx. ()The satsfacto of patets before admsso V ( t ). t, v ( t ) x e. Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 4

9 Researches o how to Pla the Medcal Servce of Hosptal (4)The satsfacto of patets before operato x 4 tj w e. 6. MODEL TESTING Model establshed above ca be a good smulato of the radom arrval of patet. Multple recordg ad averagg y ca approxmately elmate the radom oses. The y chages based o the chages of L. The fucto ca be obtaed by fttg method, whose dervato ca be obtaed as well as the correspodg L of extreme value. However, the process of rug the program, ths model eed to calculate the average of a large umber of radom umbers, so the procedure s too log. It s ecessary to adopt a smplfed model. I ths model, the radom umber of Posso dstrbuto s replaced by the Lambada parameter, so the step of multple operatos s elmated. Meawhle,the Idvdual the same departmet s represeted of the expectatos of the varous parameters of the Departmet, whle, fact, the dfferece betwee the dvdual s gored. Thus, the eta parameter s costat a certa departmet. So the model, each secto of the Departmet s the FCFS model. Each departmet of the FCFS mode s set at ths tme whe the hosptal has a total of C operatg table, L beds, N departmet. V, lambada_, ad mu_ ca be obtaed by statstcs. The umber of beds to be optmzed for each of the departmets of the hosptal bed umber L. They are N vectors. Frst we determe the allocato of resources each departmet of the Departmet (or the allocato of operatos for log tme) C. To make ratoal use of the operato room, C ca be expressed as a fucto of the operato room eeds for each departmet. d ths eed ca be used to characterze the patet's operatg tme the ut tme. Because of ths tme, the research of the dvdual departmets of the FCFS M/M/C queue, here s ot to prove the referece to the theory of queug theory. It s easy to kow that full use of the hosptal bed, we deem.. I ths model, order to esure the We ca kow from the lttle formula, Wth the same dea of calculatg the utlzato rate of a model of the operato room, here s the dfferece method. W ad eta_ as the judgmet dex, they are ormalzed by the weght obtaed by Delph method, we ca get a comprehesve evaluato dex beta. Beta s ormalzed ad multpled by L to obta a deal soluto for the L obtaed the curret state of L. Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 44

10 Sh Jahe et al. Note that L s a fucto of L, L,, the dervato of the L. So the evaluato dex s troduced. Y dex gves the dstace of the deal combato of the L_ of the Departmet. L_ s the optmal soluto for the L_ to chage y. Ths s the cotet of the olear programmg, whch ca be easly mplemeted usg the fmco fucto matlab. Here o loger. It s dcated that the upper boud of L_ should be L_q olear programmg due to the exstece of the assumpto. mu_=[.6,.58,,]' v_=[.06,.,0.9,0.48]'; lambada_=[.59,.5,.97,0.98]'; The advatages of ths model are aalyzed. total of 4 clcs, a total of 00 beds, operato room. ssumg the weght of Telf s [0.8, 0.], ths cotext, the matlab program ca be easly obtaed by usg the model. t ths tme the measuremet y =.65e- Obvously, ths model ca gve a gve weght uder the codto of Delph dstrbuto of each departmet the best umber of beds. 7. THE DVNTGE ND THE DISDVNTGE 7.. dvatages. The data questo sought fully covers multple dcators whch mpact our assessmet, ad these dcators ca reflect the qualty of patets Queug models ad bed arragemet models may ways.. I questo, the ovelty of the model s reflected by usg aalytc herarchy process to reforce Queug dscple, whch make the rotatos of patets more properly, ad acheve to maxmze team effectveess.. Issue troduces the related psychology ad mathematcs kowledge, makg the dstrbuto of beds all departmets more scetfc ad systematc. 4. I questo, as the umber of beds calculated may ot be tegers, the umber of hosptal beds of some lless after roudg may be less tha deal stuatos, order to avod the pheomea of shortage of bed, the system, beds shared betwee dfferet dseases, s set up. Dsadvatages:. I the model of Questo, t s dffcult to sequece electve patets reasoably.. I the model of Problem, the mpact of death caused by the falure of the operato s t cosdered. 8. MODEL REFINEMENT. Lambada Ca be descrbed as a varable about tme, so that you ca make a dyamc aalyss.. I ths model, plag o operatg room C ca be mproved to teger programmg.. The best soluto x should be a teger programmg model. 4. Whe actually take the data to the mathematcal to test the model, we ca fd easly that sometmes these compoets of the optmal soluto obtaed s less tha the umber of beds l. Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 45

11 Researches o how to Pla the Medcal Servce of Hosptal ccordg to the study, as the resource avalable s fxed, t wll product waste. I such cases beds utlzato metrcs should be joed. REFERENCES [] Wag Ku, L Hog. Patet satsfacto survey o applcato of hosptal maagemet [j]. The people's Lberato rmy hosptal admstrato joural, 00,6: [] Su Hoghua, Zeg Chao. Research o smulato optmzato based o queug theory hosptal [j]. Moder educatoal equpmet, 00,5:59-6 [] Lu Bje. pplcato of queug theory hosptal maagemet [j]. Cha dgtal medce, 006, (): 4-45 [4] Wu Yuhua, Du Gag. Maagemet Scece [M]. Edto. Taj: Taj Uversty Press, 009 Iteratoal Joural of Maageral Studes ad Research (IJMSR) Page 46