Load balancing location of emergency medical service stations

30 2015, XVIII, 3 Ekonomika a managemen DOI: 10.15240/ ul/001/2015-3-003 In oduc ion The quali y and e i ciency o an eme gency medical sys em (EMS) depends mainly on he numbe o ambulances ope a ing in a gi en egion and he deploymen o s a ions whe e he ambulances a e kep . Speci ying he p ope numbe o ambulances is a sensi i e issue balancing be ween wo opposing aspec s. On one hand, he main ole o he EMS – o sa e li es and educe human su e ing caused by inju ies o illnesses – equi es a dense ne wo k o eme gency s a ions. On he o he hand, he e is a jus i i ed equi emen on he e i ciency o public expendi u es. In he Slo ak Republic he e is one ambulance a e e y s a ion. The numbe and loca ions o s a ions in he whole s a e e i o y a e de i ned by he Regula ions o he Minis y o Heal h o he Slo ak Republic No. 10548/2009-OL, 11378/2010- OL and 14016/2010-OL. In acco dance wi h he Regula ions, 273 s a ions a e cu en ly deployed in he a ea o he Slo ak Republic. The s a is ical compu a ions ha alloca e each municipali y o he nea es s a ion sugges ha he e a e signi i can di e ences in popula ion in he egions se ed by indi idual ambulances, he e o e some ambulances a e used less equen ly han he o he s. The accessibili y o he eme gency se ice in egions se ed by o e loaded ambulances de e io a es, since he p obabili y ha he nea es ambulance will be busy a he momen o an eme gency call is high. Assuming ha he numbe o ambulances is gi en, we wan o in es iga e whe he loca ing ambulances di e en ly migh esul in a mo e e en dis ibu ion o hei wo kload and, consequen ly, in a be e pe o mance o he sys em. To design a new deploymen o s a ions, a ma hema ical p og amming model cons aining he popula ion alloca ed o one s a ion can be used. Ou o he abundan numbe o loca ion models, a capaci a ed p-median model has been chosen, since i maximises he e i ciency o he sys em, bu i simul aneously inc eases he ai ness o he deli e y o he EMS se ice. The e i ciency c i e ion means ha wi h a limi ed numbe o esou ces he bes possible le el o he se ice is p o ided o as many people as possible. In a p-median model, he o al a el ime o ambulances o po en ial pa ien s is a su oga e o e i ciency. Besides e i ciency, equi y (o ai ness) is a co e pe o mance dimension in a heal h ca e sys em [17]. Fai ness is achie ed when each cus ome ecei es he se ice o equi ed and/ o accep able quali y. This demand is ha d o mee in a de e minis ic ma hema ical model because o he s ochas ic na u e o he eal sys em. De e minis ic models o he EMS sys ems a e based on an implici assump ion ha he e is always an ambulance a ailable o espond o a call. Bu in he eal sys em his may no be ue because he a i ing calls a e s ochas ic e en s, and ea ing a pa ien is also a andom a iable. Mo eo e , he a el ime o an ambulance may be a ec ed by he a i c and wea he condi ions. The e o e, he nea es ambulance may happen o be busy when an acciden occu s. Then ano he ambulance mus be dispa ched o se e he call, o he se ice mus be pos poned. Thus he eal se ice le el becomes lowe han he compu ed one. Howe e , we can limi he popula ion alloca ed o one s a ion in he p oblem o mula ion and so inc ease he p obabili y ha he nea es ambulance will be a ailable a he momen o an eme gency call. The es o he pape is o ganized as ollow: Sec ion 1 e iews he li e a u e on loca ion models in public se ice sys ems. A ma hema ical p og amming model o he capaci a ed p-median p oblem is o mula ed in Sec ion 2. Sec ion 3 desc ibes wo heu is ic LOAD BALANCING LOCATION OF EMERGENCY MEDICAL SERVICE STATIONS Ľudmila Jánošíko á, Lýdia Gáb išo á, B uno Ježek EM_3_2015.indd 30EM_3_2015.indd 30 25.8.2015 10:51:1525.8.2015 10:51:15 31 3, XVIII, 2015 Business Adminis a ion and Managemen me hods sol ing he p oblem and a new heu is ic me hod based on p e iously de eloped app oaches. The nume ical e alua ion o he solu ions is p esen ed in Sec ion 4. The las sec ion p o ides conclusions and p esen s some pe spec i es o u u e esea ch. 1. Li e a u e Re iew We ecommend he excellen pape by ReVelle and Eisel [21] as an in oduc ion o he loca ion analysis. The au ho s dis inguish wo basic ypes o loca ion p oblems: con inuous loca ion p oblems, which a e o he mos pa plana p oblems and end o be non-linea op imiza ion p oblems, and disc e e loca ion p oblems, which a e mos o en ne wo k p oblems, in ol e ze o- one a iables and esul in in ege p og amming op imiza ion p oblems. Ano he classi i ca ion o loca ion p oblems di e en ia es be ween he p i a e and public sec o s. Rega ding disc e e loca ion models in he public sec o , we e e o [18] o he o e iew o basic models and [4] o he case s udy in he Slo ak Republic. Ambulance loca ion and eloca ion models a e su eyed in [5]. In his e iew pape , he models a e classi i ed in o wo main ca ego ies: de e minis ic and p obabilis ic models. De e minis ic models a e used a he planning s age. They igno e s ochas ic conside a ions ega ding he a ailabili y o ambulances. They can be u he di ided in o co e ing and alloca ion models. In co e ing models, a maximum alue is p ese o ei he dis ance o a el ime. I a se ice is p o ided by a acili y loca ed wi hin his limi , hen he se ice is conside ed accep able, and a cus ome is conside ed co e ed by he se ice, i he has a acili y si ed wi hin he p ese dis ance o ime. The e a e wo ypes o objec i e: we may wan o co e all cus ome s wi h minimum numbe o acili ies o , gi en a limi ed numbe o acili ies, o maximize co e age o he popula ion. In he o me case, he p oblem is called a Loca ion Se Co e ing P oblem (LSCP), in he la e case we a e aced o a Maximal Co e ing Loca ion P oblem (MCLP). The concep o co e age o loca ion o ambulances is used o example by A inghie i e al. [2]. The au ho s p opose he Lowe -P io i y Calls Co e age model o p o ide a lowe bound on he numbe o ambulances needed o gua an ee a desi ed le el o he eme gency se ice. In he alloca ion models, he goal is o assign demand zones o ambulance loca ions in o de o minimise he o al a el ime om he ambulance loca ions o po en ial pa ien s. One o possible models o his ype is so-called p-median model ha is sol ed in [7] and [22] o op imise ambulance loca ions in he ci y o Niiga a (Japan). P obabilis ic models e l ec he ac ha ambulances ope a e as se e s in a queuing sys em and hey canno always answe a call. P obabilis ic models ha e been de eloped o example by Chan a e al. [6] o Ingol sson e al. [12]. The basic concep in hei app oach is so- called busy ac ion o ambulances, which is he p obabili y ha he ambulance will be occupied a he momen o he call ecep ion, and i will no be able o espond o he call. The p oblem is ha he busy ac ion o an ambulance depends on he loca ion o ambulances, mo e speci i cally on he egion ha is se ed by each ambulance, howe e , his is in ac he ou pu om he loca ion model. So he models ha deal wi h he busy ac ions as exogenous inpu s canno gi e a ealis ic ou pu ei he , e en i hey a e sol ed epea edly in an i e a i e p ocess, whe e he busy ac ions o ambulances a e adjus ed acco ding o he ou pu o he p e ious i e a ion. The way o cope wi h a empo al una ailabili y o he nea es ambulance is o in ol e a edundan ambulance. The concep o backup co e age was i s in oduced by Hogan and ReVelle [11]. Backup co e age means ha a cus ome has a leas wo ambulances kep a disposal in hei neighbou hood. Pi kul and Schilling [20] and A az e al. [1] u he expand he backup co e age o mula ion and conside wo kload capaci ies o acili ies. Mos s udies published so a deal wi h ambulance loca ion in an u ban a ea like Milano, I aly [2], Auckland Region, New Zealand [10], Belo Ho izon e, B azil [23], Niiga a, Japan [7], [22]. Howe e , ou goal is o design a me hodology applicable in a la ge-scale e i o y including bo h u ban and u al a eas. The me hodology comp ises a sui able ma hema ical p og amming model and a simula ion model ha is used o e alua e he pe o mance o he sys em in a dynamic en i onmen . The compu e simula ion pe o med wi h he solu ions o di e en de e minis ic op imisa ion models [15] sugges s ha he p-median model o ambulance loca ion in a la ge-scale e i o y ou pe o ms backup co e age models in e ms o expec ed a e age a el ime, pe cen age o escue calls accessible wi hin 15 minu es and he numbe o calls ha EM_3_2015.indd 31EM_3_2015.indd 31 25.8.2015 10:51:1525.8.2015 10:51:15 32 2015, XVIII, 3 Ekonomika a managemen ha e o be pu on hold. Howe e , he p-median model leads o signi i can di e ences in he wo kload o indi idual ambulances. The e o e, i seems easonable o limi he popula ion alloca ed o one s a ion. This es ic ion esul s in a ai dis ibu ion o ambulances’ wo kload and, which is mo e impo an , in be e a ailabili y o he ambulances. This way he p oblem o s a ion loca ion becomes a weigh ed capaci a ed p-median p oblem. 2. P oblem Fo mula ion The goal in he weigh ed capaci a ed p-median p oblem is o i nd he loca ion o a i xed numbe o p s a ions in o de o minimise he o al a el ime needed o each all po en ial pa ien s. The model o he load balancing s a ion loca ion p ese es he cu en numbe o s a ions and looks o a new s a ion loca ion in he conce ned egion. The demand zones a e indi idual illages and ci ies. We suppose ha he demand (i.e. he numbe o eme gency calls) in a municipali y is p opo ional o he numbe o i s inhabi an s. The e o e, in he objec i e unc ion he a el ime o an ambulance om i s base s a ion o a municipali y will be mul iplied by he numbe o inhabi an s. We assume de e minis ic a el imes (de i ned by he dis ance and he a e age speed o a gi en oad ype). The a e age speed is based on he analysis by Ježek e al. [16]. The inpu s o he ma hema ical p og amming model a e as ollow: I he se o candida e loca ions, J he se o municipali ies, p he numbe o s a ions o be loca ed, ij he sho es a el ime o an ambulance om si e i  I o si e j  J, bj he numbe o he inhabi an s o a municipali y j  J, Q he capaci y limi o an ambulance. The decision on opening a s a ion (o mo e s a ions) in a candida e loca ion i  I can be modelled by he nonnega i e in ege a iable yi. The alue o yi is he numbe o s a ions loca ed in cen e i (o cou se, i may be ze o). The assignmen o he municipali y j o he cen e i is modelled by a bina y a iable xij. The a iable xij akes alue o 1, i he municipali y j will be se ed by an ambulance loca ed in he cen e i, o he wise xij = 0. A e hese p elimina ies, he model o he weigh ed p-median p oblem can be w i en as: Minimise  IiJj jij b ij ij x ij (1) Subjec o 1  Ii ij x o j  J (2) iij yx  o i  I, j  J (3) Jj ijj xb    Qyi o i  I (4) py Ii i    (5)   0 Zy i o i  I (6)  1,0 ij x o i  I, j  J (7) The basic sys em c i e ion (1) is he o al a el ime o ambulances o all po en ial pa ien s (o inhabi an s o municipali ies). Cons ain s (2) ensu e ha e e y municipali y j will be assigned o exac ly one cen e i. Cons ain s (3) ensu e ha i he municipali y j is assigned o he cen e i, hen a leas one s a ion mus be open in ha cen e. Cons ain s (4) limi he o al numbe o pe sons se ed by one cen e. Cons ain (5) limi s he o al numbe o he s a ions ha can be si ed. The emaining obliga o y cons ain s (6) and (7) speci y he de i ni ion domains o he a iables. The capaci a ed p-median p oblem is known o be NP-comple e. As a consequence, i canno be sol ed o op imali y e en o mode a e- sized p oblem ins ances [13]. Howe e , we ace a la ge-scale p oblem ins ance consis ing o all 2,916 municipali ies in Slo akia (by he adminis a i e di ision alid in 2003). E e y municipali y is ega ded as a candida e loca ion, as well as a demand zone, i means I = J and |I| = |J| = 2,916. To ge a su i cien ly good solu ion in a easonable ime, a decomposi ion echnique can be used. In ou p e ious esea ch wo decomposi ion heu is ic me hods we e de eloped. Bo h o hem exploi a ma hema ical p og amming app oach o sol e a subp oblem. The p ima y esea ch aimed a he possibili y o using he p oposed me hods o p ac ical la ge- scale p oblem ins ances was p esen ed in [9] and [14]. ij ij ij ij EM_3_2015.indd 32EM_3_2015.indd 32 25.8.2015 10:51:1525.8.2015 10:51:15 33 3, XVIII, 2015 Business Adminis a ion and Managemen 3. Solu ion Me hods – Decomposi ion Heu is ics Using Ma hema ical P og amming The p inciple o a decomposi ion echnique is simple: i he p oblem canno be op imised as a whole, op imise i in pa s. The app oach can be used o e e y p oblem ha can be di ided in o subp oblems. Then e e y imp o emen o he subp oblem co esponds o an imp o emen o he solu ion o he whole p oblem. Loca ion p oblems mee his condi ion. 3.1 Lop Heu is ic The i s decomposi ion heu is ic is based on he app oach p oposed by Tailla d and published o me ly unde he name o POPMUSIC [24], and la e in [25] as local op imiza ion me hod (LOPT). In his pape he la e no a ion is used. To make he p oblem ac able, i s size is educed be o e he op imiza ion. The goal is o elimina e he a iables which a e less likely o belong o a good o op imal solu ion. The educ ion is pe o med in se e al s eps. Fi s , he se I o 2,916 possible loca ions o s a ions is educed. A new se I con ains 2,282 candida e loca ions and consis s o all he municipali ies wi h he exis ing EMS s a ions de i ned by he o i cial egula ions, and all he o he municipali ies wi h a leas 300 inhabi an s. Second, one o mo e s a ions a e placed a p io i in la ge ci ies wi h mo e han 25,000 inhabi an s, since 25,000 pe sons is a capaci y limi o one ambulance (acco ding o he analysis o he Slo ak EMS sys em [3]). The numbe o s a ions kj ha mus be open in he municipali y j  J we ge by di iding he numbe o inhabi an s by he capaci y limi : kj = [bj /25,000]. A he same ime, he demand o he municipali y j is adjus ed o he new alue ¯bj = bj – kj • 25,000. The o al numbe o s a ions placed in la ge ci ies be o e he op imiza ion is  Jj j kk (k = 50 in he case s udy). The numbe o s a ions o be loca ed (p = 273) is educed by his alue leading o he new numbe p¯ = p – k = 223 . The se Ī and pa ame e s ¯bj and p¯ a e he inpu s o he Lop heu is ic. Since ¯bj < 25,000 o e e y j  J, he heu is ic places one s a ion a he mos in he candida e loca ion j. Fu he elimina ion o a iables conce ns he a iables x and is based on he assump ion ha pa ien s will no be se ed by he ambulances ha a e oo a away. Tha is why only hose a iables xij emain in he model o which he coe i cien ij is less han he p ede i ned h eshold. The h eshold is de i ned by he alue limi = α • max / √p¯ whe e max = max { ij : i  Ī, j  J} and α is a pa ame e . In he Slo ak oad ne wo k we ha e max = 279 minu es. Thus o α = 1.5 we ge he h eshold limi = 26 minu es. All hese measu es educe he numbe o a iables by 94%. Howe e , we s ill ha e 431,569 bi alen a iables, and he use o a decomposi ion heu is ic is jus i i ed. The Lop heu is ic s a s wi h he ini ial loca ion o p¯ = 223 s a ions ha is compu ed by an IP sol e unning in a limi ed ime. The ini ial loca ions a e deno ed as empo a y and inse ed in o he se C. Then a empo a y s a ion is andomly selec ed. This selec ed s a ion, oge he wi h a ew o i s closes s a ions and municipali ies alloca ed o hem in he cu en solu ion, o m a subp oblem wi h s a ions, which is conside ably smalle han he ini ial loca ion p oblem (see Fig. 1). The loca ion o s a ions is op imized by using an IP sol e . I a be e loca ion is ound, all hese s a ions emain empo a y; o he wise he i s s a ion is emo ed om C. Then a new s a ion is andomly selec ed and he p ocess epea s un il C is emp y. 3.2 Decomp Heu is ic The second heu is ic deno ed as Decomp is also based on he domain decomposi ion. Bu in con as o he Lop heu is ic, he decomposi ion is pe o med a he beginning o he solu ion p ocess. The e i o y is decomposed in o adminis a i e egions. I means ha he se I ( emembe I = J) is di ided in o a ew disjunc i e subse s. Each subse includes all municipali ies o one o eigh Slo ak adminis a i e egions. The size o he subse s anges be ween 87 (B a isla a Region) and 664 municipali ies (P ešo Region). The subse s de i ne eigh sepa a e p-median p oblems (1) – (7) co esponding o he pa icula egions. The cons an p in e e y p oblem is se in o de o p ese e he cu en numbe o s a ions in he gi en egion. The p oblems a e sol ed sepa a ely. By he union o hei solu ions we ob ain loca ions o all s a ions in he Slo ak Republic. The Decomp heu is ic consis s o he ollowing ou phases: 1. The loca ion o p s a ions is compu ed by sol ing he uncapaci a ed p-median EM_3_2015.indd 33EM_3_2015.indd 33 25.8.2015 10:51:1525.8.2015 10:51:15 34 2015, XVIII, 3 Ekonomika a managemen p oblem (1) – (3), (5), (7) wi h he a iables yi  {0,1} o i  I. Ad in e im he cons ain s (4) a e elimina ed. Le  Jj ijji xbB be he numbe o inhabi an s o he nea es municipali ies j which a e se ed by he ambulance in he cen e i. 2. The alue Bi ep esen s he demand alloca ed o he cen e i. I can be g ea e o less han he capaci y limi Q o an ambulance. To p o ide addi ional capaci y in he cen es wi h high demand, s a ions wi h small demand (Bi << Q) can be closed and eloca ed o he cen es wi h high demand (Bi >> Q). In his s ep we decide on he numbe p1 o s a ions which can be eloca ed. 3. The new loca ion o p – p1 s a ions is compu ed ega dless o he capaci y cons ain s. Le I* deno e he se o new s a ion loca ions wi h he demand Bi alloca ed o hem. 4. Now ee p1 s a ions can be eloca ed among he cen es i  I* by sol ing a new ma hema ical p og amming p oblem (8) – (11). The a iable zi indica es how many o eloca ed s a ions will be placed a he cen e i  I*. We in oduce a new a iable w ha ep esen s a lowe bound on he numbe o s a ions in a cen e i ha sha e he demand Bi. The ma hema ical model maximizes he alue w and esul s in a new numbe yi o s a ions ha consis s o one s a ion loca ed in phase 3 and zi eloca ed s a ions. Maximise w (8) Subjec o 1 * pz Ii i   (9) wBz ii  1 o i  I* (10)  0 Zzi o i  I* (11) The abili y o he Decomp me hod o i nd a be e s a ion loca ion is limi ed due o he ac ha he numbe p o s a ions o each subp oblem is bound by he exis ing EMS s a ions in he gi en egion. The e o e in he ollowing esea ch we ied o imp o e ou solu ion by he adjus men o he inpu pa ame e s o he Decomp heu is ic. We used he esul s o he Lop me hod as inpu da a o he Decomp me hod as ollow: om he Lop solu ion we iden i i ed he numbe o s a ions o each o he Slo ak egions and hen ound an imp o ed loca ion in he egion by he Decomp me hod. Fo he ime being, we call his p ocedu e Lop -Decomp. The Lop , Decomp and Lop -Decomp p ocedu es we e implemen ed in he isual de elopmen en i onmen Xp ess-IVE using Fig. 1: A subp oblem wi h se e al cen es and municipali ies alloca ed o hem Sou ce: own ij EM_3_2015.indd 34EM_3_2015.indd 34 25.8.2015 10:51:1525.8.2015 10:51:15 35 3, XVIII, 2015 Business Adminis a ion and Managemen he sol e Xp ess-Op imize 2.2.3 [8]. The expe imen s we e pe o med on a pe sonal compu e equipped wi h he In el Co e i7 p ocesso wi h 1.60 GHz and 8 GB o RAM. The compu a ion ime did no exceed 25 minu es o Decomp and 217 minu es o he Lop me hod. 4. E alua ion o he Al e na i e Deploymen s Each o h ee desc ibed me hods (Lop , Decomp and new Lop -Decomp) esul s in a di e en loca ion o 273 s a ions. Each loca ion is ep esen ed by he componen s o he ou pu ec o y*. The alue yi > 0 indica es he numbe o s a ions loca ed in he cen e i  I. The ec o y* is he inpu o he e alua ion o he al e na i e deploymen s and hei compa ison mu ually and wi h he cu en si ua ion in he Slo ak Republic. The e alua ion is based on he assump ion ha e e y municipali y is se ed by i s closes ambulance. The assignmen o municipali ies o cen es can be quickly compu ed by sol ing he ollowing alloca ion p oblem: Minimise  IiJj ij ij x (12) Subjec o 1  Ii ij x o j  J (13) iij yx  o i  I, j  J (14)  1,0 ij x o i  I, j  J (15) He e yi a e no any mo e a iables bu cons an s ha gi e he numbe o s a ions loca ed in he cen e i  I. The op imal solu ion o he p oblem (12) – (15) associa es each cen e i wi h he subse o municipali ies  1,  ijixJjJ . Then he numbe o pe sons (po en ial pa ien s) se ed by he cen e i is   i Jj ji bB and he sha e o one ambulance loca ed ain his cen e is Bi / yi. Table 1 p esen s he basic cha ac e is ics o he p oposed deploymen s o s a ions. The column Numbe o cen es gi es how many cen es we e chosen om 2,916 candida e loca ions. The column Numbe o di e en ly loca ed s a ions indica es how much he solu ion o he model di e s om he cu en deploymen o s a ions. We can see ha in all solu ions abou 37% o 273 s a ions we e loca ed di e en ly compa ed o he exis ing design. The column To al a el ime o ambulances o pa ien s ep esen s he e i ciency o he sys em measu ed as he o al a el ime o ambulances o all po en ial pa ien s. The wo kload o ambulances exp essed as he Numbe o people pe ambulance is summa ised in he las h ee columns. The a e age wo kload is iden ical in all designs because all solu ions p ese e he numbe o exis ing s a ions. Since ou goal was o p opose an e en dis ibu ion o ambulances wo kload, he mos impo an indica o was he ange be ween he minimum and maximum wo kload. The g ea es ange can be obse ed in he case o he cu en deploymen o s a ions. The mos e en dis ibu ion o wo kload was achie ed by he combined Lop -Decomp heu is ic. These ac s a e as well demons a ed in Fig. 2. Me hod o s a ion loca ion Numbe o cen es Numbe o di e en ly loca ed s a ions To al a el ime o ambulances o pa ien s [million pe son* minu es] Numbe o people pe ambulance [in housands] min a g max cu en 209 0 14.06 1.3 19.8 70.9 Lop 233 104 11.86 5.3 41.8 Decomp 186 102 13.52 4.4 40.6 Lop -Decomp 186 101 13.43 5.8 33.6 Sou ce: own Tab. 1: E alua ion o he deploymen s o s a ions ij ij ij ij ij EM_3_2015.indd 35EM_3_2015.indd 35 25.8.2015 10:51:1625.8.2015 10:51:16 36 2015, XVIII, 3 Ekonomika a managemen Howe e , he uni o m dis ibu ion o wo kload may be achie ed a he expense o long a el imes o ambulances o some illages. The e o e we in es iga e he impac o he uni o m wo kload on he anspo a ion accessibili y o municipali ies. Table 2 gi es how many people a e accessible wi hin a gi en ime limi . All alues abou he popula ion a e gi en in % o he o al popula ion o he Slo ak Republic. The column Ex eme con ains he maximum a el ime and he popula ion o he illage wi h he longes a el ime. As i can be seen, he bes accessibili y was achie ed by he Lop heu is ic. The limi a ion o he applicabili y o he p esen ed app oach consis s in he ac ha we do no conside cos s o edeploymen o s a ions. To achie e a mo e ai design, he model changes subs an ially he cu en deploymen o EMS s a ions (see he hi d column in Table 1). To implemen p oposed solu ions would hus equi e o es uc u e he exis ing in as uc u e conside ably wha migh be oo cos ly. I his issue is o impo ance, i can be p ac ical o educe he numbe o eloca ed s a ions, o o es ima e he cos o closing and opening a s a ion a si e i and equi e o al in es men cos s o be in an alloca ed budge . To inco po a e such cons ain s in he ma hema ical model, wo new a iables ui and i mus be supplemen ed, which indica e he numbe o closed and open s a ions a si e i, espec i ely. They a e de i ned by cons ain s (16) – (18), whe e si is he cu en numbe o s a ions a si e i. iii ysu  o i  I (16) iii sy  o i  I (17)  0 Z u ii, o i  I (18) Le n be he uppe bound o he accep able numbe o eloca ed s a ions. Then he cons ain ha limi s he numbe o changes can be in he o m:    Ii inu (19) This cons ain migh be eplaced by ano he cons ain s equi ing ha he econs uc ion o Fig. 2: Numbe o people assigned o one ambulance Sou ce: own EM_3_2015.indd 36EM_3_2015.indd 36 25.8.2015 10:51:1625.8.2015 10:51:16 37 3, XVIII, 2015 Business Adminis a ion and Managemen he sys em will no exceed he o al budge q. Le symbols i c and i o deno e he cos o closing and opening a s a ion a si e i, espec i ely. Then he co esponding cons ain is  q u Ii i o ii c i   (20) The p esen ed solu ion me hods would be able o cope wi h such ex ension o he model (1) – (7). Ano he way how o imp o e he loca ion model is o eplace he capaci y cons ain s (4) by an i egula i y measu e [19] applied o ambulances’ wo kload. Conclusion In he pape , he p oblem o EMS s a ions loca ion is o mula ed as a capaci a ed p-median p oblem. A new decomposi ion me hod is p oposed. The compa ison o he new Lop -Decomp me hod wi h p e iously de eloped heu is ics Lop and Decomp is p esen ed wi h ega d o ambulances wo kload and anspo a ion accessibili y. The bes esul s in e ms o he dis ibu ion o wo kload we e achie ed by he Lop -Decomp me hod, and in e ms o he accessibili y by he Lop me hod. Howe e , hese esul s a e jus he es ima ions o he eal sys em pe o mance because a de e minis ic ma hema ical p og amming model igno es he s ochas ic cha ac e o he modelled sys em. The bes way how o es ima e pe o mance cha ac e is ics be o e he implemen a ion o he solu ion in he eal en i onmen is o use a compu e simula ion model. Such a model o he EMS sys em was buil wi hin he cu en esea ch [15], ne e heless, we do no ha e ealis ic da a needed o calib a e he model. In he u u e we will endea ou o ob ain da a om esponsible au ho i ies and o e i y he conclusions by means o a compu e simula ion. 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