A management tool for indicator-supported systems: A public health service application

204 Eu opean Jou nal o Ope a ional Resea ch 61 (1992) 204-214 No h-Holland A managemen ool o indica o -suppo ed sys ems: A public heal h se ice applica ion E. Ca izosa, E. Conde, F.R. Fe n indez and J. Pue o Depa amen o de Es ad[s ica e In es igaci6n Ope a i a, Uni e sidad de Se illa, Se illa, Spain Recei ed Ma ch 1991; e ised Sep embe 1991 Abs ac : We de elop a decision-making me hodology o hie a chical s uc u es. I p o ides di e en decision make s wi h decision-o ien ed in o ma ion based on ob ained sa is ac ion le els. This is specially con enien o public se ices, whe e he main goal is use 's sa is ac ion. Ou me hodology and i s associa ed so wa e (INDI) ha e been implemen ed in he Andalusian Heal h Se ice (SAS), suppo ing esou ce alloca ion decisions in o de o educe he complain s p esen ed agains such an ins i u ion. Keywo ds: Decision Suppo Sys ems; decision heo y; mul ic i e ia decision making 1. In oduc ion Any o ganiza ion in a compe i i e ma ke needs some ools o eac agains unexpec edly inc easing cos s o dec easing quali y. This has gi en an impo an ole o he in o - ma ion depa men : moni o ing he p oduc ion p ocess h ough in o ma ion sys ems gi es he manage he ools o compa e he ou pu s wi h p ese a ge s and check he quali y o hem. Un il he beginning o he 80s, all ha was equi ed we e Managemen In o ma ion Sys ems (MIS), he decisions being ese ed o he man- age s, wi h he only aid o he epo s gi en by he MIS. Howe e , he e has been in he las yea s an inc easing in e es in he de elopmen o no ma i e decision models, suppo ing he mak- ing o non-s uc u ed o semi-s uc u ed deci- sions in o de o sys ema ize he p ocess o con- inuous imp o emen . Mos o he e o s ha e been de o ed o he de elopmen o me hodologies o speci ic deci- sion si ua ions (Valada es e al., 1986; Boldy, 1987; And eu and Co ominas, 1989; Vla6i6, 1989). The de elopmen o ou me hodology HIDS (Hie a chical In o ma ion and Decision Sys em) and i s associa ed so wa e had as a s a ing poin a con ac wi h he Se icio Andaluz de Salud (Andalusian Heal h Se ice), known as SAS. The e, we had o de elop an in e ac i e sys em suppo ing decisions abou he alloca ion o e- sou ces in o de o educe he numbe o com- plain s in public heal h cen e s. We ha e de eloped a uni ied decision-making en i onmen o suppo ing decisions a di e en le els in any hie a chical s uc u e. This en i on- men can be seen as a shell ha he decision make s (DMs) use in o de o de elop hei own DSS p o ile inside he s uc u e. Ou aim is o gi e all he DMs ex emely manageable and meaning ul decision-o ien ed in- o ma ion. The me hodology is based on he anal- ysis o he sa is ac ion le el ob ained h ough he ou pu s o he sys em. This sa is ac ion is mea- su ed by means o obse ed ajec o ies, no mal- ized using sa is ac ion unc ions. This p ocedu e is especially con enien o public se ices, whe e he main goal is o ob ain a high le el o use 's sa is ac ion. This pape is di ided in o ou sec ions. In Sec ion 2, we desc ibe he model and i s unde ly- ing hypo heses, he In o ma ion and Decision P ocesses. In Sec ion 3 we p esen a eal applica- ion o ou me hodology applied o public heal h 0377-2217/92/$05.00 © 1992 - Else ie Science Publishe s B.V. All igh s ese ed E. Ca izosa e al. / Managemen ool o indica o -suppo ed sys ems 205 se ices. Sec ion 4 is de o ed o he desc ip ion o he so wa e a chi ec u e ha has been de el- oped o he model. The pape ends wi h wo ma hema ical appendices dealing wi h some as- pec s o he In o ma ion and Decision P ocesses. 2. The Hie a chical In o ma ion and Decision Sys em (HIDS) 2.1. The model The model we p opose is based on a se o hypo heses we desc ibe below. They do no co e- spond o heo e ical condi ions, bu appea in almos any eal la ge-scale in o ma ion-decision sys em. Due o hei na u e, hese hypo heses a e classi ied in o h ee g oups: - S uc u e hypo heses (S). - Sys em Pa ame e hypo heses (P). - P ese Ta ge s hypo heses (T). S1. The sys em can be ep esen ed h ough a hie a chical s uc u e. $2. Any elemen in he sys em (DM) occupies only one place in he s uc u e. $3. No elemen ac s isola ed om he es . $4. The e a e wo p eo de s on he s uc u e, called he Decision ela ion and In o ma ion e- la ion. Each one is he in e se o he o he . $5. The e exis s only one maximal elemen o he Decision ela ion: The Supe Decision Make (SDM). Fo any DM, he Decision ela ion in- duces exac ly one chain om he SDM o him. PI. Any DM a he lowes le el in he hie a - chy ( e minal DM) is esponsible o a unique se eice cen e . The pe o mance o such a se ice is con olled by a s ochas ic p ocess ha depends on a se o pa ame e s. T1. The pe o mance quali y o a se ice cen- e i a ime is a unc ion o a se V~( ) o nume ical ea u es (which a e pe iodically mea- su ed), and a se o p ese a ge s. T2. The sa is ac ion o a e minal DM is he pe o mance quali y o his associa ed se ice cen- e . The sa is ac ion o any non- e minal DM a ime is a unc ion o he sa is ac ion o hose DMs subo dina ed o him ollowing he Decision ela ion. In a na u al way, he hypo heses desc ibed abo e lead us o a ep esen a ion o he sys em by means o a ma hema ical s uc u e H = (N, F, B), whe e: 1) N is he se o all he DMs in he hie a chy 2) F is he Decision ela ion. I (n, m)~F, we say ha m is subo dina ed o n. 3) B is he In o ma ion ela ion. I (n, m) ~ B, we say ha n in o ms m. 4) (N, F) is an acyclic connec ed dig aph, wi h only one DM wi h ze o ank: he Supe Decision Make (SDM). 5) (N, B) is an acyclic connec ed dig aph, wi h only one elemen wi h maximal ank: he SDM. 6) (n, m) ~ F i (m, n) ~ B. No e ha he hypo heses we imposed a e ex- plici ly used in his o mula ion. In ac , $1 and $2 jus i y he acyclic g aph s uc u e, $3 he con- nec edness, and $4 he exis ence o wo g aphs, one o each di ec ion o low: whe eas he a cs in (N, F) ep esen in di ec ion in which he decisions a e ansmi ed, he ones in (N, B)-s a e he di ec ion o in o ma ion low. Hypo hesis $5 is aken in o accoun in (4) and (5); hypo hesis P1 is needed o explain he non- de e minis ic na u e o he sys ems we a e model- ing. Finally, he T1 and T2 hypo heses allow he e alua ion o sys em pe o mance, and cons i u e he co ne s one o he In o ma ion P ocess we desc ibe below. 2.2. The In o ma ion P ocess (IP) E icien managemen needs e y sha p and belie able knowledge abou sys em pe o mance. Due o he sys em's na u e, only he DMs in he lowes le el in he hie a chy ha e di ec ac- cess o in o ma ion, bu such in o ma ion gi es only e y pa ial knowledge abou he eal pe o - mance o he whole sys em. Howe e , he DMs in he highes le els ( hose wi h a b oade ac ion ield) no only lack di ec access o in o ma ion, bu also need mo e gene al knowledge abou he sys em: as gene al as he kind o he decisions hey ha e o ake. Hence, we ha e o ace wo p oblems: • How should he DMs collec in o ma ion? • How should such in o ma ion be p ocessed and sen o DMs in highe le els in he hie a - chy? The aim o e e imp o ing he quali y o a se ice ad ises agains collec ing in o ma ion abou he se ice h ough me ely desc ip i e a i- 206 E. Ca izosa e al. / Managemen ool o indica o -suppo ed sys ems Figu e 1. Some sa is ac ion unc ions ables. A decision-o ien ed p ocess is mo e sui - able, e alua ing he e icacy o e iciency o pe - o mance agains some p ese and pe iodically ixed a ge s. A powe ul ool o his pu pose is p o ided by Pe o mance Indica o s (PI) (Wes on and B o he s, 1984; Fo uin, 1988). Hence, in- s ead o conside ing ea u es in isola ion, we will use pe o mance indica o s, which a e de ined by a ea u e and i s associa ed a ge . To ge his goal, such PIs mus be easy o unde s and, clea ly de ined and ep esen a i e o he sys em's pe o - mance, which is e lec ed in hypo hesis T1 im- posed o ou model. Fo mally, in o de o measu e a ime he quali y o he se ice associa ed o e minal DM i, a se V/( ) o quan i a i e a iables a e aken. Fo any a iable ~ V/( ), we need a couple (O,,( ), G ( )), whe e Q( ) is he obse ed alue o , and Q( ) is he goal o i . This couple is added o p e ious obse a ions and goals, gi ing us he s ochas ic p ocess {(O~.(s), GL,(s):s ~ T,,}, whe e T~, is he se o ins an s when he a iable has been obse ed. Mo e p ecisely, he quali y should be measu ed h ough he s ochas ic p o- cess {O,,(s):s ~ T,,}, whe e D,~(s) = ~,(O,,(s)- G (s), G~(s)), and is a [0, 1]- alued unc ion, indica ing he le el o ag eemen be ween he obse ed alue and he goal. Hence, De(s)= 1 i a ime s, he p ese goal is eached, and Dc(s) = 0 i he goal is no eached a all. The DMs should ha e a hand a se o unc- ions ~ o i hei eal pe cep ion o ag eemen ; some pa icula ins ances, aken om P ome hEe me hodology (B ans e al, 1984; B ans and Vincke, 1985) a e shown in Figu e 1. Wi h his, we ha e p ocessed he wo-dimen- sional s ochas ic p ocess {(O (s), G~,(s): s ~ T~} in o a one-dimensional p ocess {D~,(s):s ~ T~.} ep esen ing he le el o achie emen h ough ime (S ep 1 in Figu e 2). We a e aced now wi h he p oblem o e alua - ing he e olu ion o such an achie emen (S ep 2 in Figu e 2). This e alua ion should no be done using only he mos ecen obse ed alue (DL( )), because ends o imp o emen o wo sening would no be app ecia ed: he same e alua ion would be ob ained o e y di e en beha io s (Figu e 3). This is he eason why we dis inguish wo di e en pe iods o ime o a a iable : we S ochas ic P ocess O ( ),G ( ) Bidimensionll S ochas ic P o¢Isl -4 '4 By( ) D= i= lon$ P oc=ss N umbe in (0,1) Figu e 2. E alua ing a a iable by a numbe E. Ca izosa e al. / Managemen ool o indica o -suppo ed sys ems 207 Io DMn,, hen DMn ecei es he m- uple (an, .... , anm). This m- uple has also o be p o- cessed in o a scala alue; a p ocedu e ha i s hese needs e y well is he Analy ic Hie a chy P ocess (AHP) (Saa y, 1980; Va gas, 1990). This globalizing p ocess is ecu si ely execu ed and ends eaching he SDM. 2.3. The Decision P ocess (DP) Figu e 3. Di e en ends wi h he same las obse ed alue de ine a sho pe iod as he ime uni y o he obse a ions (week, mon h, qua e .... ), and a long pe iod as he g oup o he sho pe iods o be conside ed in o de o explain he e olu ion o he quali y o (mon h, yea .... ). Wi h he de ini ions abo e, jus he la es long pe iod should be conside ed. The decisi e ole played by he DM should be aken in o accoun in he e alua ing (globalizing) p ocess h ough his a i ude owa ds isk. As has been widely s udied in decision heo y, a neu al a i ude owa ds isk is exp essed by means o he a e age alue, a pessimis ic a i ude by he mini- mum, and an op imis ic a i ude by he maximum (Milno , 1954). Hence, he sui able and simple choice o he globalizing unc ion could ha e he o m qb(a(1), a, a(n)), wi h a(1 ) = min{al,..., an} , a = (l/n) E a i, a n ) = max {a ..... an}, n is he num- be o sho pe iods included in a long pe iod, and a i is he le el o achie emen in he i- h sho pe iod in he long pe iod. A i ing p ocedu e when qb is assumed o be addi i e is desc ibed in Appendix 1. Wi h ha p ocedu e we ha e a scala e alua ion o any a iable o he se ice cen e associa ed o he e minal DMi. The in o ma ion ha has been p ocessed by he e minal DMs has o low owa ds he SDM h ough he dig aph (N, B) (see Figu e 4). The DMs in he hie a chy ecei e meaning ul bu simpli ied in o ma ion. O cou se, i i does no su ice, a d illing p ocess should be a ailable in o de o ob ain mo e echnical da a. Hence, i {DMn¢..., DMn, .} is he se o non- e minal DMs subo dina ed o DM n and an, ep- esen s he le el o achie emen ob ained by The pe o mance measu e we y o op imize is he global sys em sa is ac ion, ob ained using he IP desc ibed abo e. We assume ha he s ochas ic mechanism con- olling he sys em can be modi ied by means o esou ces, and i an unlimi ed amoun o e- sou ces we e a ailable, he o al sa is ac ion would be ob ained. Howe e , his is an u opic si ua ion, so a p ocedu e suppo ing decisions conce ning esou ce alloca ion is needed. In eal sys ems, op imal esou ce alloca ion does no su ice, so an op imal managemen o exis ing esou ces is also necessa y. As a consequence o he IP in he hie a chy, he DMs can de ec and co ec w ong esou ce managemen ; hence, he p ocedu e we p opose deals wi h he o he aspec o he p oblem: he alloca ion o new esou ces. The DP is de eloped h ough he dig aph (N, F). An amoun o a ailable esou ces o he DM can be seen as a low emana ing om him, and ha ing as sinks his subo dina es in (N, F). The p ocess is ecu si ely execu ed, un il eaching he lowes le el in he hie a chy, whose DMs a e he only ones wi h he capabili y o using esou ces in modi ying he sys em pe o - mance. Figu e 4. Agg ega ing sa is ac ions 208 E. Ca izosa e al. / Managemen ool o indica o -suppo ed sys ems The p ocess can be done in di e en ways, depending on he le el o knowledge ha DMs ha e abou he sa is ac ion unc ion. I he e exis s a unc ional dependence be- ween esou ces and ou pu s in he sys em (Vla6i~, 1989), he esou ce alloca ion p oblem is sol ed h ough he ollowing ma hema ical p og amming p oblem: P(F) max (Sij(Oj, Uj, Xj)){,i,j)~F:FF, j,=¢} s. . xj= E Xij Vj/(i,j)~F:FF(j)=#, jEFF 1 R >1 ~ Xlj , j~FF(I) E xik <~ E Xkj i~FTl(k) j~FF(k) Vk~N, k :g 1, FF(k) 4: ~, O <xij < cij 'q(i,j)~F whe e si~(Oj, Bj, x j) is he unc ion measu ing he sa is ac ion o DM/~ N, whose pe o mance de- pends on pa ame e s Oj, has p ese goals Bj and ecei es xj uni s o esou ce. The o al amoun o a ailable esou ces a e R, we suppose ha he e exis s some capaci y Cij in he a cs, and he decisions a iables a e 0 and Xj. P(F) is a mul iobjec i e p oblem, and i he knowledge o a globalizing unc ion is assumed (which is a sensible assump ion due o he AHP ollowed in he IP), p oblem P(F) becomes a scala p oblem, whose op imal solu ion gi es he alues o esou ce alloca ing a iable pa ame e s and global sa is ac ion ob ained o such an amoun o esou ces. When he explici o ms o he sa is ac ion unc ions a e no known, he p ocedu e abo e is in easible. Fo such cases, an in e ac i e me hod- ology is mo e sui able. The i e a i e p ocess we p opose consis s o wo phases (Backwa d and Fo wa d), desc ibed below. In he backwa d phase, he e minal DMs demand an amoun o esou ces hey would like o ecei e, and associa e o such demand he le el o sa is ac ion o be ob ained. This in o ma ion lows un il i eaches he SDM. In he o wa d phase, an o e o esou ces lows om he SDm un il eaching he e minal DMs. These wo phases a e epea ed un il a ce ain equilib ium is ob ained. Compa a i ely, whe eas he backwa d phase looks o op imali y in sa is ac ion, he o wa d phase looks o easibili y. The backwa d phase This phase consis s o h ee s eps: S ep 1. Fixing uppe bounds o any e minal DM and esou ce. In he i s backwa d phase, hese bounds a e de e mined in a ealis ic way, maybe upda ing pas alloca ions. In he ollowing backwa d phases, he bounds a e de e mined based on he o e s done in he p eceding o - wa d phase. S ep 2. Demands and sa is ac ion. Any DM, DMj, gi es a pai ( j, sj), whe e j is a esou ce ec o demand, easible wi h espec o he p e- sen uppe bounds u j, and sj is he le el o sa is ac ion ha would be ob ained wi h such an amoun o esou ces. The p ocess is di e en depending on he kind o DM. A e minal DMj's demand mus be he consequence o a desi ed change in his ec o pa ame e . Such a change may be suppo ed by means o he p ocedu e desc ibed in Appendix 2. A non- e minal DMj's demand o esou ces j equals Y'-i i, and i s associa ed sa is ac ion sj is he agg ega ion o he sa is ac ions o his subo di- na es, ollowing he IP: s= Y~i wisi. Ob iously, his agg ega ion should be supe - ised by DMj in o de o co ec possible e o s in i , due o he ac ha we ha e admi ed a linea globalizing unc ion and he a ibu es may no be mu ually independen (Fishbu n, 1970). S ep 3. Feasibili y es . The p ocess o agg e- ga ion o esou ces and sa is ac ion ends eaching he SDM; he ecei es a pai ( , s), whe e is he amoun o esou ces he sys em desi es, and s is he sa is ac ion ha such esou ces would induce. The SDM has an amoun o o esou ces. I o >/ , he sys em eaches equilib ium, and he DP s ops; i his we e no he case, a o wa d phase s a s, wi h he aim o eaching easibili y. The numbe o i e a ions needed o each equilib ium s ongly depends on how ealis ic he demands made by he e minal DMs a e. Such ealism can be con olled by he SDM h ough a ionally ixing he bounds in S ep 1. The o wa d phase The amoun o esou ces i ha DM i has mus be dis ibu ed among his subo dina e DMs. E. Ca izosa e al. / Managemen ool o indica o -suppo ed sys ems 209 PROPERTIES El MENT5 REOURSIYITY GLOBAL UNDIREDT ELABORATED WEIGHTING BY A.H.P. PARTIAL DIREOT EA iY TO EY/¢UATE WEIGHTIN6 BY A.H.P. lObs' oO "ue¢ O ( l I °(}'1~' =(hi Figu e 5. In o ma ion and Decision P ocesses Such a dis ibu ion should be a unc ion o he couples ( i, sj), Vj ~ F(i), ob ained in he p eced- ing backwa d phase, and should be done in ol - ing DMi. A easible choice o his pu pose could be ob ained by sol ing he ollowing linea ma he- ma ical p og am: max ~ ~sjwi6kj j k s. . Y'~ 6~j <~ 1 Vk = 1 ..... , J O<~6~j Vk=l,..., , j~F(i) whe e 8kj is he ac ion o k- ype esou ce as- signed o DMj and w J is he weigh ha DMi gi es o his subo dina e DMj. The op imal alues o he decision a iables Ski gi e he ac ion o esou ces assignable o e e y DMj. This p ocess is done ecu si ely, and s ops when he lowes le el is eached. Then, a new backwa d phase s a s. In o de o as en he con e gence o equilib- ium, a p uning p ocess could be used, emo ing hose DMs whose demands in a s age we e easi- ble. These wo sec ions ha e been de o ed o de- sc ibe he HIDS. A summa izing diag am is shown in Figu e 5. Fo p ac ical applica ions, all ha is needed i so iden i y he eal s uc u e wi h he elemen s in ou model. This is wha we do in he nex sec ion. 3. A case s udy When his de elopmen was con ac ed, he public heal h se ices in Andalusia (Spain) de- pended on a public ins i u ion called SAS (Se icio Andaluz de Salud). [ EA . DIRECTOR 1 H.I LM. P-k 6. • Figu e 6. SAS s uc u e 210 E. Ca izosa e al. / Managemen ool o indica o -suppo ed sys ems The SAS o ganiza ion Table 1 A simpli ied o ganig am o he adminis a i e s uc u e o his ins i u ion is shown in Figu e 6. The op manage is he SAS di ec o . A he second le el he e a e wo gene al di ec o s: The Hospi al Assis ance Gene al Mange (HAGM) and he P ima y Assis ance Gene al Manage (PAGM). Andalusia is adminis a i ely di ided in o eigh p o inces, each one wi h i s own P o incial Man- age (PM), subo dina e o he wo gene al di ec- o s. E e y cen e has i s own manage (Hospi al o P ima y Assis ance Cen e Manage ). All he cen e s in a p o ince a e unde he esponsibili y o hei P o incial Manage . The complain sys em Ins ead o being ocused on p oduc i i y, pub- lic sys ems a e mainly in e es ed in o e ing high quali y in hei se ices. This is why one o he goals o SAS manage s has always been he con inuous imp o emen o he le el o ob ained sa is ac ion, he la e being measu ed by means o he complain s he use s make. Such complain s a e classi ied acco ding o he ype o pe sonnel, he a ea o ac i i y, he eason o he complain and he answe ob ained o he complain (Table 1). HIDS modeling The hie a chical and adminis a i e SAS s uc- u es coincide, excep o he P o incial Man- age s. Since hese DMs join wo clea ly sepa able asks ( he managemen o he hospi als and he p ima y assis ance cen e s), hey ha e been spli up acco ding o he o ganig am shown in Figu e 7. The main pa ame e s (gi en by he manage s) ha con ol he pe o mance o he di e en elemen s in he sys em a e shown in Table 2. The se o obse ed a iables (ou pu s) h oughou ime shows di e en ypes o p e- sen ed complain s, classi ied ollowing Table 1. The manage s ha e sugges ed ha da a should be collec ed in he cen e s e e y mon h (a sho pe iod). In o de o p ocess such in o ma ion, all ha is needed is (i) he sa is ac ion unc ions associa ed o he di e en a iables and (ii) he Reason: CA. Assis en quali y TP. Poli eness EM. Pe o mance o ins umen s TA. Bu eauc acy PP. Tes s los LI. Cleaning PU. Punc uali y IN. In o ma ion SA. Medical examina ion cancelled LE. Wai ing lis AL. Food IA. Assis en in o ma ion OT. O he s A ea: PL. Floo UR. U gency CE. Ex e nal examina ions QU. Su gical a ea PT. In e nal examina ion LA. Labo a o y and analysis SG. Gene al Se ices S a : ME. Doc o s EM. Nu ses AA. O ice wo ke s CE. A endan s MA. Main enance DI. Di ec o s CL. Res au an , cleaning employees IN. O he s. Resul : a. b. C. d. e. . The use is igh and his p oblem is sol ed. The use is igh and his p oblem emains unsol ed. The use is w ong. The complain is no clea enough. The use needs addi ional in o ma ion. The cen e is no esponsible o he eason o he complain . I ;*s' °zRsc °R 1 N.k E. kl. P.A.E.M. Figu e 7. HIDS modeling E. Ca izosa e al. / Managemen ool o indica o -suppo ed sys ems 211 Table 2 Hospi als P ima y Assis ance Cen e s Numbe o beds X Numbe o examina ion ooms X X Special examina ions X X Assis en ial s a X X Adminis a i e s a X X Gene al se ice s a X X Numbe o ope a ing ooms X Numbe o ambulances X X Numbe o u gency boo hs X Figu e 8. A menu display globalizing unc ions o ajec o ies; we ha e gi en he manage s a small lib a y o sa is ac ion unc ions, aken om decision heo y manuals. The globaliza ion o ajec o ies, done acco ding o Appendix 1, is now being alida ed. Following also manage 's sugges ions, he goals o he a iables a e o be ixed a he beginning o e e y na u al (a long pe iod). Due o he na u e o his sys em, wha manage s ha e o de e mine is he highes numbe o complain s o e e y ype ha is going o be seen as accep able. In he DP, he main esou ces used in o de o imp o e he sa is ac ion le el a e essen ially o economical na u e, al hough in some cases he use s assigned o e e y cen e we e also used as esou ces. Fo his pu pose, he e minal DMs (Hospi al o P ima y Assis ance Cen e Man- age s) could change he pa ame e s associa ed o hei managed cen e (see Table 2). Such a change should be execu ed ollowing he manage 's own expe ience, and, i needed, suppo ed by he p o- cedu e p oposed in Appendix 2: gi en a Heal h Se ice cen e , hose se ices wi h simila pa am- e e s a e de ec ed; by means o a decision p o- cess, which akes in o accoun echnical con- s ain s (uppe bounds o he numbe o beds, dependence be ween he numbe o ope a ing ooms and assis en s a , e c.), a change in he ec o o pa ame e s is p oposed. 4. So wa e a chi ec u e HIDS has been implemen ed in a so wa e a chi ec u e called INDI. INDI is an objec -o i- en ed decision en i onmen ha allows he ep e- sen a ion o decision si ua ions in a e y gene al con ex , and allows he analysis o in o ma ion. One he main ea u es o INDI is i s e olu i e na u e: i pe mi s he addi ion o new ele an elemen s and disca ding o useless ones. The sys em is based on a se o ela ional da a bases, managed by a knowledge base ha de e mines he ela ions among di e en elemen s in he hie a chy. This se o ules desc ibes he p o- cesses o in o ma ion and decision. INDI is a mul i-use sys em, ha uns in a local a ea ne wo k wi h DOS compa ible compu - e s. Some displays a e shown in Figu es 8 and 9. INDI has wo di e en modules: 1) Use in e ace. • Main enance. Allows he ep esen a ion o any hie a chical sys em. The use can c ea e new elemen s and i s associa ed ea u es, and de ine he ela ions among hese elemen s and he es o he hie a chy. These da a a e loca ed in he knowledge-base. • In o ma ion p ocess gene a o . Gene a es he epo s o any DM in he hie a chy, and p ocesses he in o ma ion h ough he IP o ob ain he le el o sa is ac ion o he DMs. ! JUNTA 0E ANOkLUCIA ESTANOAR: ESTANCIA MEDIA I D.A.P:I0.O0 CONSEJERIA DE SALLIO y OE~GLOSE: H.O~ I D.A.N:IO.QO SERVICIOS SCCIALES U.I'IEDIOA: DIAS P lEDICCIQNES. PERI ENERO FEBRERO VAqZO ABRIL P gAS 5 5 5 5 E R ~ 67 0 0 0 I 0 DES -62,00 5.00 5.00 5.00 T BAS 5.00 5.OO S.O0 S.OO A RF~ 67.00 67.00 67.00 67.00 e i~s -~.oo *E,?.oo -62.oo -~.oo PERIO EX~E~O N(~4AL NOW~L NORNAL T.A.H EXTEF6qO EXTE~40 EXTE~6NO EXTEF~O PULSE CL~L~J[ER TECLA PARA CONT[NUAR Figu e 9. A p edic ions display 212 E. Ca izosa e al. / Managemen ool o indica o -suppo ed sys ems "FORWARD PHASE -,Ho,__ I I.OEOISIOH SU,,ORT/ / FREE-TExT NE'NTS "UTIL "HIERARCHY MANAGEME "FORECASTING INOI ATORS RELA ON A ONG DM8 • oN--INE "~1 I'.AIN~ENAHCE~ I ""J'.AIN;~NANC~ ' [ORR[I~RRATI ON I 'MS[TI gRF[[T ION l " SPECIAL FUNCTIONS l • INTRODUCTION OF DATA Figu e 10 G aphical and sc een-edi o epo s a e a ail- able. • Analyze . This is he co ne s one o he DP. I allows in e ac i e analysis (abou he esou ces), p edic i e analysis abou he beha - io o he obse ed a iables and s a is ical anal- ysis (homogenei y in e minal elemen s, clus e analysis). • In e ac i e aid. 2) Sys em in e ace. Allows he con igu a ion o ha dwa e pa ame e s, and he c ea ion o use s and le els o esponsibili y and accessibil- i y o he di e en modules o INDI. An a chi ec u e diag am is shown in Figu e 10. Appendix 1 Ou aim is he i ing o an addi i e globalizing unc ion q~ in o de o agg ega e he achie emen ajec o y ob ained h ough a long pe iod by means o a eal alue q~(a(1), ~, a(n )) ep esen ing he sa is ac ion associa ed o he a iable. By addi i i y we mean ha @ is o he o m q~(a(l ), ~, a(,)) = o a(1 ) +/3~ + 3"a(n ) o some a,/3, 3' >~ 0, a +/3 + 3' = 1, o be es i- ma ed. We assume ha , i he achie emen ajec o y is displayed, he DM is able o sco e he global achie emen (sa is ac ion) in an long pe iod wi h a alue in [0, 1]. E en unde his assump ion, he p ocedu e we p opose is e y use ul, because i a oids ime-con- suming ou inely e alua ions o e e y a iable. The pa ame e s a e i ed in a p elimina y i ing p ocess. Fo any sho pe iod i, le a(1)(i) , ~(i) and a(m(i) be he lowes , a e age and highes achie e- men , espec i ely, ob ained in he long pe iod ending in i. Le also (i) be he sco e in [0, 1] ha he DM p oposes o such a long pe iod. When his p ocess is epea ed du ing k con- secu i e sho pe iods, we ob ain a sample {(a(1)(i), -d(i), a(m(i) , (i)), i= 1 .... , k}. We p opose as pa ame e es ima o s, (a*,/3", 3'*), he op imal solu ion o he p ob- lem: k min E [om(1)(i) +/3~(i) +3"a(m(i ) - (i)] 2 i=1 s. . a+/3+3"=1, a,/3, 3' >/0. Once he DM's sco es ag ee wi h he global- ized alues, he i ing s age ends. F om hen on, he globaliza ion will be au oma ically done as a*ao) +/3"~ + 3"*a(m. O cou se, i a any ime he DM s ops ag ee- ing wi h his globaliza ion, a new i ing s age should s a . Appendix 2 The backwa d s age in he DP s a s a he lowes le el, whe e he sa is ac ion associa ed o esou ce demand mus be de e mined. Le DM n be a e minal DM wi h demand n. In o de o ob ain he associa ed sa is ac ion s n, we p opose a p ocedu e ha shows a heu is ic use o esou ces by modi ying he d-dimensional pa ame e O n associa ed o DM,. The in o ma ion ha DM, has abou sys em pe o mance is summa ized in he de ia ion ec-