A location comparison of three health care centers in Sfax-city

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1 Iteratioal Joural of Egieerig Research ad Developmet e-issn: , p-issn: , Volume 11, Issue 02 (February 2015), PP A locatio compariso of three health care ceters i Sfax-city JLASSI Jihee* ISGI de Sfax Route Mharza, Km 1.5-B.P Sfax., Tuisia Abstract:- The problem of health facilities locatio is explored uder a mathematical optimizatio approach. Several models are developed for the locatio of a geeralized health facility system i a maer that the selected criteria are optimized. From the literature we use i our paper the criteria efficiecy ad availability of the service. The optimal locatios satisfyig two obectives, oe that miimizes health care ceters-patiet distace ad aother that captures as may patiets as possible withi a pre-specified time or distace. The results idicate that the existig locatios provide ear-optimal geographic access to health care ceter. Keywords:- Locatio, efficiecy, availability, patiet satisfactio, health care ceters. I. INTRODUCTION The aim of facility locatio is to determie spatial positio of differet types of facilities i order to provide good customer service ad to attai a competitive advatage. Locatio problems are cocered with the locatio of (physical or o physical) resources i some give space. A vast literature has developed out of the broadly based iterest i meetig this challege. Operatios research practitioers have developed a umber of mathematical programmig models to represet a wide rage of locatio problems. Several differet obective fuctios have bee formulated to make such models ameable to umerous applicatios. The study of locatio theory formally bega i 1929 whe Alfred Weber cosidered how to positio a sigle warehouse so as to miimize the total distace betwee it ad several customers. Locatio theory gaied reewed iterest i 1964 with a publicatio by Hakimi, who sought to locate switchig ceters i a commuicatios etwork ad police statios i a highway system. I fact, may models have bee made to help decisio makig i this locatio area. Love et al (1988), Fracis et al (1992), Mirchadai et al (1990), Daski (1995), Drezer et al (2002), Nickel et al (2005), Church et al (2009), Farahai ad Hekmatfar (2009), Jais Grabis et al (2012) ad Domiik Kress et al (2012). The obective of this paper is to develop a facility locatio model accoutig for wide rage of factors affectig decisio-makig to compare locatio of three health care ceters i Sfax city Tuisia. Locatig hospitals is a process that must take ito cosideratio may differet stakeholders: patiets who eed ready access to the facility, doctors who wat attractive ad easy-to-reach workplaces, taxpayers who wat value for their moey ad politicias who wat to demostrate their ability to deliver a quality product. There are a sigificat umber of studies cocerig the locatio of health care facilities. Rosethal et al (2005) modeled customer ad physicias locatios o a zip code level ad modeled accessibility as the umber of physicias per capita ad the average distace betwee patiets ad physicias for rural ad urba areas. Usig more detail, Love ad Lidquist (1995) assessed customer ad hospital locatios at the cesus block group level for the State of Illiois. Griffi et al (2008) ivestigate a variatio of the maximal coverig locatio problem whereby the locatio ad services offered at each locatio are determied. Oliveira ad Beva (2006) cosider two locatioallocatio models for the redistributio of hospital capacity. The first model equalizes capacity utilizatio across facilities give each facility s predicted utilizatio. The secod model miimizes a weighted distace betwee the facilities ad geographic regios while cosiderig how patiet flows ad demad chage i respose to the supply offered by hospitals. Stummer et al (2004) determie the locatio ad size of medical departmets. The remaider of the paper is orgaized as follows. Sectio 2 discusses healthcare factors ifluecig facility locatio. Sectio 3 develops the model for determiig optimal solutio. Sectio 4 reports ad discusses the results, ad Sectio 5 cotais some cocludig remarks ad directios for future research. II. FACTORS INFLUENCING FACILITY LOCATION Traditioal facility locatio models optimize facility locatio cost or some kid of coverage criterio. Typical factors ifluecig facility locatio are customer demad, facility locatio costs ad distace betwee facilities ad customers (Owe & Daski, 1998). However, additioal factors are ofte cosidered i practice. Number of criteria that are relevat i the evaluatio of health care facilities ad their locatio will be the 79

2 A locatio compariso of three health care ceters i Sfax-city quality of services (a somewhat ebulous cocept that eeds to be quatified ad measured by a appropriate proxy), the accessibility of services, ad possibly the fairess of the services. The quality of medical services could be expressed i terms of expected or worst case waitig times for a specific service, the expected success rates of ecessary procedures, or others. The accessibility of services is probably easier to measure i terms of distace to a potetial patiet s home, or the expected coverage of the populatio at large withi a give amout of time. Fairess, aother soft cocept, could be expressed as the variace of quality ad availability of medical services i differet regios (Burkey et al, 2012). The two mai criteria cosidered i this work are: The quality of medical service ad the service availability. III. MODEL FORMULATION As a measure of quality of medical service, we will use the average distace (or time) betwee ay potetial patiet ad his closest hospital. A importat compoet of locatio modelig is distace. Most locatio models attempt to miimize distace, average distace (p-media), or maximum distace (p-ceter) (Curret et al, 2002; Daski, 1995; Love et al, 1988). Our model is the p-media formulatio. This formulatio is formulated by Hakimi i the mid-sixties (Hakimi, 1964), has established the foudatio for a myriad of locatio problems i the public ad private sector. The basic problem is to fid P locatios (i our case p health care ceters) that miimize the average distace (or travel time) i a etwork. Oly the odes of the etwork eed to be cosidered as locatio cadidates, sice there is always at least oe optimal solutio that cosists of locatig the facilities o the etwork odes. The p-media model ivolves the locatio of p facilities o the etwork so that total weighted distace is miimized. It is assumed that each demad is served by their closest facility. Give that Hakimi (1965) proved that there is always at least oe optimal solutio to a p-media problem that cosists etirely of odes of a etwork, virtually all solutio methods have bee based o the search for the best solutio comprised etirely of odes. Cosider the followig otatio: i: idex of customer locatios (potetial patiets) : idex of potetial facility locatios d i shortest distace from ode i to ode, (distace betwee a customer i ad a facility ) a i : demad at ode i, (customers at poit i) y = 1 if a facility is sited at site ad demad at assigs to it as well (y assume a value of oe, if a facility is located at site ) 0 otherwise, x i = 1 if demad at i assigs to facility at (xi express the proportio of customer i s demad that is satisfied from facility ) 0 otherwise, p the umber of facilities that are to be located. Usig the otatio defied by ReVelle ad Swai (1970), ad actualized by (Mariaov et al, 2011) (Burkey et al, 2012), formulated the p-media problem as a Iteger Liear Problem(ILP): Mi Z St 1 for each i 1,2,, 2 1 Y 1 Y i i ad i i i i 1 1 i p Y for each i 1,2,, ad 1,2,, where i 4 0 for each i 1,2,, ad 1,2,, 5 0 or 1 for each 1,2,,

3 A locatio compariso of three health care ceters i Sfax-city The obective seeks to miimize the total weighted distace of all demad assigmets. Costraits of type 2 esure that each demad must assig exactly oce. The fourth type of costrait maitais that a demad caot assig to a ode uless that ode has bee selected for a facility. Sice the obective miimizes the distaces of assigmets, costraits of type 2 ad 4 i cocert with the obective esure that at optimality, each demad assigs to their closest located facility. The third costrait fixes the umber of located facilities to be equal to p. Note that i solvig this model, it is oly ecessary to require the Y variables to be zero-oe. I the cotext of this study, the problem locates a give umber of p health care ceters, so as to miimize the average patiet-hospital distace. The service availability may be measured as the proportio of the populatio that is located withi a prespecified distace D from their earest facility (Burkey et al, 2012). All authors use travel time rather tha distace, as distace is ust a proxy for time. We decided to use 30 miutes i this study as a goal. (Bosaac, 1976) (Carr, 2009) (Frezza,1999) This factor is preseted by aother model i locatio theory. The Maximal Coverig Locatio Problem. A well-kow type of locatio problems, which has bee studied sice the very begiig of locatio sciece, is the coverig locatio problem (CLP). It seeks a solutio to cover a set of demads while oe or more obectives are to be optimized. There are two distict categories of CLPs i the literature as maximal coverig locatio problem (MCLP), ad set coverig locatio problem (SCLP). Regardless of type of the problem, a populatio is covered if it ca be reached withi a pre-defied time/distace by oe or more facilities. While a SCLP calls for coverig all the demad odes with the least possible umber of facilities, MCLP is associated with coverig the maximum possible demad with a kow umber of facilities. MCLP was first itroduced by Church ad ReVelle (1974) o etworks. Sice the, umerous applicatios ad theoretical extesios to the classical model of MCLP have bee preseted. I order to formulate the problem, defie the set Ni= {: di <D} as the set of all departmets hospitals that ware o farther away from patiet i tha the service level distace D. Furthermore, we will use the biary variables Y defied earlier. I additio, we eed coverage variables i, which assume a value of oe, if all patiets at site i are withi distace D of ay of the hospitals. We ca the formulate the maximal coverig locatio problem as: S: The distace (or time) stadard withi which coverage is expected, N i : { di S} = the odes that are withi a distace of S to ode i, i : A biary variable which equals oe if ode i is covered by oe or more facilities statioed withi S ad zero otherwise. Max Z Y 1 1 i 1 a i 1 St i 1,2,, 2 Y i i i 1,2,, 4 Y i p 1or 0 1,2,, 5 IV. EVALUATION OF HEALTH CARE CENTERS LOCATIONS IN SFA For the purpose of evaluatig actual situatios o the criteria delieated i the previous sectio, we have chose three health care ceters that are comparable i size, populatio ad desity. These ceters are: Agareb, Mahres ad El Hecha. Table 1 presets the basic iformatio (Sfax 2010). 81

4 A locatio compariso of three health care ceters i Sfax-city TABLE1. DESCRIPTIVE STATISTICS Regios populatio Lad area Pop/Km 2 Agareb ,07 51,77 Mahres ,65 71,46 El Hecha ,32 84,56 I this case we take three samples each represets 50 patiets. Tables 2, 3 ad 4 idicate that there is a very strog correlatio betwee distace ad time. TABLE2. ACTUAL RESULTS Ceters Mea distace Mea time Pop Pop<30mi %<30mi Agareb (A) 7, Mahres (M) 8, El Hecha (E) 8,4 15, TABLE3. OPTIMIZATION RESULTS (P-MEDIAN) Ceters Mea distace Mea time Pop Pop<30mi %<30miu A 6,16 13, M 7,1 14, E 7,15 14, Overall mea TABLE4. OPTIMIZATION RESULTS (MA COVER STATE) Ceters Mea distace Mea time Pop Pop<30mi %<30mi A 8,6 16, M 9,2 17, E 9,3 17, Overall mea Tables 2, 3 ad 4 clearly show that actual solutio ad that of the p-media problem are quite similar. I both tables 5 ad 6 x% more quality of medical service meas x% less time. TABLE5. IMPACT OF USING P-MEDIAN SOLUTIONS Ceters Quality of medical service Service availability A 7,62% more 10% more M 5,33% more 6% more B 6,1% more 4% more Average 6,35% 6,67% more Table 5 idicates that o average, the p-media solutio is able to improve the actual situatio of the quality of medical service ad the service availability by about 6%. TABLE 6.IMPACT OF USING OPTIMAL MA COVER SOLUTIONS Ceters Quality of medical service Service availability A 1,2 less 14% more M 2,3% less 10% more B 1,34 less 8% more Average 1,63 less 10,67% more Table 6 presets The max cover solutio which sigificat decreases of 1,6% i quality of medical service ad some icrease of service availability. 82

5 A locatio compariso of three health care ceters i Sfax-city V. CONCLUSION The locatio decisio describes, give a set of alteratives, the problem of where to locate a orgaizatio s facility (Melo et al, 2009). The optimal locatios, studied i this paper, satisfyig two obectives, oe that miimizes health care ceter -patiet distace ad aother that captures as may patiets as possible withi a pre-specified time or distace. The purpose of this study was to provide us with a theoretical optimum that ca be used as a bechmark to evaluate the existig locatios o. Remarkably, we foud that the existig health care ceters locatios i these regios are very efficiet relative to the optimized set of locatios. Similarly, the existig locatios provide a good level of service availability. Aother aveue for future research could be to add other criteria i the model ad to add other health care ceters of the regio. REFERENCES A. Weber, Uber de Stadort der Idustrie (Alfred Weber's Theory of the Locatio of Idustries), Uiversity of Chicago, [1]. S.L. Hakimi, Optimum locatios of switchig ceters ad the absolute ceters ad medias of a graph, Operatios Research 12 (1964) [2]. Love, R., Morris, J., & Wesolowsky, G. O. (1988). Facility locatio: Models ad methods. [3]. Amsterdam, The Netherlads: North-Hollad. [4]. Fracis, R. L., McGiis, L. F., & White, J. A. (1992). Facility layout ad locatio: A aalytical approach (2d ed.). Eglewood Cliffs, NJ, US: Pretice-Hall. [5]. Mirchadai, P. B., & Fracis, R. L. (Eds.). (1990). Discrete locatio theory. New York, US: Wiley- Itersciece-Itersciece. [6]. Daski, M. S. (1995). Network ad discrete locatio: Models, algorithms ad applicatios. New York, US: Joh Wiley ad Sos. [7]. Drezer, Z., & Hamacher, H. W. (Eds.). (2002). Facility locatio: Applicatios ad theory. Berli, Germay: Spriger-Verlag. [8]. Nickel, S., & Puerto, J. (2005). Locatio theory: A uified approach. Berli, Germay: Spriger Verlag. [9]. Church, R. L., & Murray, A. T. (2009). Busiess site sectio, locatio aalysis ad GIS. New York: Wiley. [10]. Farahai, R. Z., & Hekmatfar, M. (Eds.). (2009). Facility locatio: Cocepts, models, algorithms ad case studies. Heidelberg, Germay: Physica Verlag. [11]. Jais Grabis., Charu Chadra., Jais Kampars. (2012). Use of distributed data sources i facility locatio. Computers & Idustrial Egieerig 63 (2012) [12]. Domiik Kress., Erwi Pesch. (2012). Sequetial competitive locatio o etworks. Europea Joural of Operatioal Research 217 (2012) [13]. Rosethal M, Zaslavsky A, Newhouse J. The geographic distributio of physicias revisited. Health Services Research 2005;40(6 Part 1):1931e52. [14]. Love D, Lidquist P. The Geographical accessibility of hospitals to the aged: a GIS aalysis withi Illiois. Health Services Research 1995;29:629e51. [15]. Griffi, P., Scherrer, C., Swa, J., Optimizatio of commuity health ceter locatios ad service offerigs with statistical eed estimatio. IIE Trasactios 40 (9), [16]. Oliveira, M., Beva, G., Modellig the redistributio of hospital supply to achieve equity takig accout of patiet s behavior. Health Care Maagemet Sciece 9 (1), [17]. Stummer, C., Doerer, K., Focke, A., Heideberger, K., Determiig locatio ad size of medical departmets i a hospital etwork. Health Care Maagemet Sciece 7 (1), [18]. Owe, S. H., & Daski, M. S. (1998). Strategic facility locatio: A review. Europea Joural of Operatioal Research, 111(3), [19]. M.L. Burkey, J. Bhadury, H.A. Eiselt. (2012). A locatio-based compariso of health care services i four U.S. states with efficiecy ad equity. Socio-Ecoomic Plaig Scieces 46 (2012) 157e163. [20]. Bosaac EM, Parkiso RC, Hall DS. Geographic access to hospital care: a 30-miute travel time stadard. Medical Care 1976;14/7:616e24. [21]. Carr BG, Braas CC, Metlay JP, Sulliva AF, Camargo Jr CA. Access to emergecy care i the Uited States. Aals of Emergecy Medicie 2009;54(2):261e9 [22]. Frezza EE, Mezghebe H. Is 30 miutes the golde period to perform emergecy room thoratomy (ERT) i peetratig chest iuries? Joural of Cardiovascular Surgery (Torio) 1999;40(1):147e51. 83

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