A Decision-Making Tool for Home Health Care Nurses' Planning

Transcription

1 A Decision-Maing Tool for Home Healh Care Nurses' Planning Rm Ben Bachouch Universié de Lon, LIESP, INSA-Lon URAII, INSAT, Tunis Alain Guine Universié de Lon, LIESP, INSA-Lon Sonia Hari-Gabou URAII, INSAT, Tunis This aricle deals wih problems encounered be rouing nurses hrough home healh care services. I is difficul o assign paiens o differen care worers b aing ino accoun heir availabili and heir sills. If paiens need several cares during a wee, he ma be reaed b he same emploee. We show ha his problem is equivalen o a rouing problem wih some specific consrains. We propose an ineger linear program for deciding (1) which human resource should be used and (2) when o execue he service during he planning horizon in order o saisf he care plan for each paien served b he home healh care providers. Ke words: scheduling, home healh care, mahemaical modeling, mixed linear program, resource planning Coprigh BEM ISSN prin ISSN online Acnowledgmens This wor was suppored b he Naional School of Social Securi of Sain Eienne (France) in a PhD wor suding home healh care operaional problems. I is par of an OSAD (Organisaion des Soins A Domicile) proec ha is sponsored b he Rhones-Alpes region. Suppl Chain Forum An Inernaional Journal Inroducion Man indusries have discovered he benefis of improving efficienc b woring on he rouing decisions involved in heir aciviies. Beer rouing and scheduling allow hese decision maers o achieve savings in heir coss and o expand heir service capabiliies. Home healh care (HHC) services are a growing service indusr ha mus face scheduling and rouing problems. HHC developmen is acceleraed b several facors such as he pressures of governmen o reduce he cos of healh care, he difficulies of adaping healh care ssems o mee he growing needs of an aging populaion, new illnesses and cures, and a severe shorage of nursing saff. Home healh care services provide complex and coordinaed medical and paramedical care o paiens a heir homes. The include nursing, herap aciviies, medical and social services, house cleaning, and so on. There is an increasing need o develop innovaive approaches o improve he efficienc of HHC organizaions. The pariculari of HHC organizaions is ha he paien is a componen of he healh care suppl chain. Therefore, we have o ae ino accoun addiional consrains such as he ime window o provide care o paiens, he necessi o snchronize all resources (i.e., humans and maerials) involved in he care deliver process and he necessi o ae ino accoun care worers sills for each care deliver. In his aricle, we are ineresed in he rouing problem of care worers in HHC. In he firs par, we propose a review of he exising lieraure concerning saff planning and resource allocaion. In he second par, we describe he rouing problem. In he hird par, we presen he proposed approach for scheduling care worer planning. In he fourh par, we discuss and analse he obained resuls. Finall, we sugges some prospecs for fuure research. Lieraure review This secion surves various soluion echniques ha are available in HHC. There have been few aricles relaed o HHC rouing problems in he lieraure. Cheng Suppl Chain Forum An Inernaional Journal Vol N

2 and Rich (1998) consider wo pes of nurses: par ime and full ime. The global problem is formulaed as a vehicle rouing problem wih ime windows (VRPTW). Two formulaion approaches using mixed-ineger linear programming are described: one using ripleindexed variables and he oher using double-indexed variables. The implemened heurisics are a wo-phase algorihm: he firs sage builds several roues simulaneousl and he second sage aemps o mae improvemens on hese ours. Chahed e al. (2009) deal wih he planning of operaions relaed o chemoherap a home. The considered problem is resriced o he analsis of he sages of producion and deliver of anicancer drugs. An exac mehod based on linear programming wih he obecive of minimizing he oal ravel ime for he nurse is proposed. Berels and Fahle (2006) presen anoher opimizaion and planning ool. Here, nurses have differen sills and he obecive is no onl o minimize he oal cos bu also o provide a weighed sum of he oal ravelled disance plus a sum of penalies associaed o he violaion of ime windows or paien preferences. The heurisic developed b he auhors is divided in wo pars: (1) o build a se of paiens o assign o each nurse and (2) o find an opimal sequencing for each se of paiens. The approach is based on a combinaion of linear programming, consrain programming, and meaheurisics. Eveborn e al. (2006) describe a decision suppor ssem called Laps Care o aid he planners b using a se-pariioning model. The ssem consiss of a number of componens including informaion daa bases, maps, opimizaion rouines, and repor possibiliies. A repeaed maching approach is used for finding a soluion. The visi plan proposed is evaluaed according o wo performance crieria: he efficienc of he plan and is quali (coninui of care). Borsani e al. (2006) develop anoher linear ineger model. The auhors are ineresed in he problem of deciding which human resources should be used and when o execue he service during he planning horizon in order o saisf he care plan for each paien. The weel plans generaed b he proposed models are compared wih he real ones according o a se of performance indicaors: care coninui, ousourced visis, preferenial das, and geographic coherence. Begur e al. (1997) sud he scheduling and rouing of nurses in Alabama and develop a spaial decision suppor ssem for HHC providers. This ssem aes ino accoun roue consrucion, nurse availabili, and paien needs wih heir availabili. I develops for each nurse a lis of paiens o visi raned in an order ha maximizes heir producivi. Home healh care (HHC) services are a growing service indusr ha mus face scheduling and rouing issues. Thomson (2006) invesigaes how mehods from operaional research can be applied o he HHC field and emphasizes he rouing problem, which is formulaed as a VRPTW. The aim is o minimize he ravelled disance and maximize he number of visis. To solve he problem, an inserion heurisic is used. The soluions found via he inserion heurisic are used as iniial soluions for a abu search. Chiba e al. (2005) develop a decision suppor ssem for HHC using a muli-agen ssem. The decision is performed auonomousl b negoiaions among agens so ha i is sufficien for cusomers and helpers o confirm schedules seled b he agens. The can confirm he schedules using PDAs, which can be easil handled even b older individuals. Consequenl, i is expeced ha he proposed decision suppor ssem reduces he oal cos of an HHC service. De Angelis (1998) sudies he problem of allocaing resources (nurses, docors, social assisance, ec.). To solve his problem, De Angelis formulaes a sochasic linear programming model in order o maximize he oal number of paien deliveries. Bold and Howell (1980) presen a case sud of mehods o allocae a given amoun of home help resources o a number of geographical areas wihin a coun social services deparmen. The approach described could also be applied o oher healh or social services resources for which an equiable disribuion beween areas or beween differen cusomer groups is required. Blais e al. (2003) underoo anoher disricing sud for he Côe-des-Neiges local communi healh clinic in Monreal. The errior models he area where a paricular clinic is responsible for he logisics of HHC visis. The area mus be pariioned ino several (six) disrics b suiabl grouping erriorial basic unis. Five disincive crieria mus be saisfied: indivisibili of basic unis, respec for borough boundaries, connecivi, personnel mobili, and worload equilibrium. The problem is solved b means of a abu search echnique. Because of he recen developmen of HHC organizaions, he number of exising aricles abou HHC problems is quie modes. The main issues acled are he disricing problem and he human resources planning problem or more precisel he nurse planning problem. Oher sudies (Landr & Philippe, 2004; Beaulieu e al., 2001) focused on new managemen ideas in order o beer undersand he role and impac of logisics in healh care, o conain healh care coss, and o adap he healh care ssem o he changing demographics. The presen examples of how o beer inegrae logisics aciviies hrough a unique combinaion of reengineering and Suppl Chain Forum An Inernaional Journal Vol N

3 acivi-based cosing. Delivering care in HHC is no an eas as because of he large number of acors ha paricipae in he process, he varie of clinical and organizaional decisions, and he difficul of snchronizing human and maerial resources a he acical and operaional levels. Our ineres is on he operaional level where ime consrains have o be considered in a differen wa because some paiens require simulaneous or sequenial inervenions involving muliple resources. Moreover, planning in HHC is made difficul for several pracical reasons: he service involves paiens whose clinical and social condiions ma change quicl, he large number of procedures and proocols o be followed reduce he flexibili of providers' organizaion, paiens ma be spread in a wide area, he snchronizaion of resources is relevan o provide he service in an effecive and efficien wa, and so on. In his conex, he developmen of a shor-erm planning suppor ool for HHC providers is quie ineresing. In HHC, he visi plans for each care worer are esablished b he nurse coordinaor. In his wor, we aim o provide a decision suppor ool o esablish a feasible planning for care worers aing ino accoun all he consrains concerning coninui of care, paien availabili, and so on. Our purpose is o faciliae he nurse coordinaor wor nowing ha here is no reail offering for rouing problems in HHC. Mos of French HHC uses dedicaed sofware ha offer differen applicaions for managing he paien care plan and medical records bu do no offer planning ools. We propose an exac mehod o solve he rouing problem in HHC. We aim o incorporae he proposed approach o he French HHC informaion ssem. Thus, French HHC will have onl o inerface heir exising sofware b adding our ool for roue planning. Table 1 illusraes he consrains sudied in he papers discussed previousl. In French HHC, we observe ha here are man consrains o ae ino accoun in nurse planning. In addiion, scheduling he care worer roue is difficul because of he need o snchronize human and maerial resources. I is imporan o ae ino accoun all he sudied consrains in order o provide an efficien planning ool. In Table 1, Bold and Howell (1980) and Blais e al. (2003) do no appear because he auhors did no menion he consrains considered in esablishing he nurse planning. We propose an ineger linear program o minimize he ravelled disance, aing ino accoun he nurses' sills, paien availabili, lunch breas for nurses, shared visis (i.e., visis requiring more han one care worer), and nurses' ime window. On he one hand, he proposed approach aes ino accoun all he consrains considered in he previous wors. We inegrae all he consrains sudied in Cheng and Rich (1998), Begur e al. (1997), De Angelis (1998), Thomson (2006), and Chiba e al. (2005) in order o mae an efficien planning ool. Eveborn e al. (2006) use a se-pariioning model and Borsani e al. (2006) use a mahemaical model bu our mahemaical formulaion is oall differen from he one presened in Borsani e al. (2006). The nex secion focuses on he nurse rouing problem. Problem descripion All paiens in HHC service have o be reaed according o heir care plans, which include, among oher facors, he number, pe, and sequence of visis ha he paien should receive. To provide his Table 1 Consrains in HHC planning Suppl Chain Forum An Inernaional Journal Vol N

4 service, an HHC srucure has o coordinae is resources, especiall he human ones. In mos cases, he HHC srucure provides a dail visi plan for all is care worers, poining ou which paiens each operaor has o assis, wha ind of visi he or she has o realize, and possibl when, specifing he hour. Unforunael, care worer planning is done b hand and here is no decision suppor ool o esablish planning. Nurse coordinaors assign he care o care worers considering sills, woring hours, and he paien needs. The mos imporan quali obecive for HHC is coninui of care : he assigned care worer o a paien is considered as he paien reference operaor during he whole duraion of he care plan. The nurse coordinaor defines he das of visi for each paien aing ino accoun personal preferences. Afer esablishing he care worer planning, he nurse coordinaor mus manage all he unpredicable evens ha ma occur during he wee. Planners could also as he famil o execue some simple care aciviies for he paien. These aciviies are called ousourced visis and in order o eep a high level of paien saisfacion, planners have o avoid hese pes of visis. Assumpions and noaions For given wee, a lis of paiens needing several cares is nown and he care worer plans mus be calculaed for paien care deliver a home. The crierion o opimize is he weel ravelled disance minimizaion. A care can also require more han one care worer. Care worers (nurses, phsical herapiss, care assisans, ec.) are available o rea paiens under erms of woring hours or geographical allocaions. Some cares have o be assigned o he same care worer in order o ensure coninui of care. Noaions Le us consider a se C = { 1,..., n} of care worers, Si he sill of he care worer i. Each care worer has a lis of cares o deliver per da according o his or her sill and woring hours. Dur_max represens he maximal duraion of a woring da for a care worer. We allow ha each care worer wors eigh hours per da and has he righ o ae a lunch brea. This brea ma be modeled as a preassigned care of one hour. We noe B = { b1,..., bn} he se of breas of one hour o be assigned o care worers. There is a se P = { 0,...,m} of paiens o be reaed a home. We inroduce a dumm paien denoed b 0, which represens he HHC office. We allow ha each care worer mus leave and reurn o he office a he end of he care our for informaion and feedbac. Each care is characerized b a duraion of reamen pi, he number of care worers nc needed o perform he care for he paien, and a ime window [ e, l] during which he care mus begin. Le dis, denoe he disance (in minues) beween wo consecuives visis and. In order o allocae a geographical area o care worers, we define he daa Dis_max o delimi he disance separaing wo sequenial visis. There is a se of das D = { 1,.., d} represening he planning horizon. To ensure he coninui of roues, we define he se Q = { 0,..., n + m} o ae ino accoun breas (m breas) and visis (n visis) in he assignmen of care worers. Indexes Paiens:,, h = 1,, m wih m number of paiens Care worers: i = 1,, n wih n number of care worers Da: = 1,, d wih d number of woring das in a wee General assumpions - The care plan has a finie horizon of one wee. - Onl one reference operaor can be assigned o one paien. - Onl one visi b da mus be done for each paien. - Travel imes are no included in he visi duraion. - Care worer sills are expressed as Si assuming he following values: i is equal o 1 if operaor i has he sill o rea he paien ; 0 oherwise. - Each paien has a ime window of availabili. - Visis have differen duraions. - A visi can require more han one care worer. These visis are called shared visis and we figure ha care worers arrive a he same ime o he paien home. Decision variables - The variable i models a visi o paien before he paien assigned o he operaor i during he da, and i assumes he following values: i is equal o 1 if he visi is carried ou b he care worer i o paien before paien during he da ; 0 oherwise. - The variable ai indicaes he arrival ime of he care worer i o he paien on he da. Obecive funcion The obecive funcion (1) minimizes he oal ravelled disance b he care worers. Min i C P P\ D i dis (1) Model consrains - Care worers can visi paiens onl when he are available according o he ime window. The ime window indicaes he earlies and laes dae of a visi beginning o he paien (consrains (2) and (3)). D, i C : D, i C : (2) (3) - All visis mus be planned and performed b he needed number of care worers nc. Consrains (4) and (5) consider he case of shared visis when more han one care worer mus perform he visi o rea he paien a home. P, P, D : D : (4) (5) - In he case of shared visis, he care worers have o be a he paien home a he same ime. Consrain (6) calculaes he arrival ime o he paien home for he care worers who perform he shared visi. i C P\ i C P\ s i, D, nc 2 : P a e ai ai l = i nc = i nc i = P a s (6) Suppl Chain Forum An Inernaional Journal Vol N

5 - The care worer sills mus saisf he paien needs (consrain (7)). The daa Si indicae if he care worer i has he sills o perform he visi and i assumes he value 1 if he care worer can perform he visi ; 0 oherwise. 1 (7) - Consrain (8) ensures ha he arrival ime of he care worer i o he paien mus be calculaed aing ino accoun he reamen duraion and he arrival ime o he preceding visied paien. P,, D : (8) : ai ai + p + dis + ( i 1) HV - In order o assign each care worer o an area, we define a maximal disance Dis_max separaing wo successive visis and (HV is a noaion o model an infinie value) in consrains (9). D,, i C, P, P : (9) ai ai p dis _ max + (1 i) HV - Each care worer has one lunch brea per da (consrains (10) and (11)). We define he se B of breas. The number of breas is equal o he care worer number. We assume ha breas are ficiious cares of one hour wih a ime window in order o resric he beginning and ending dae of each brea. (10) (11) - To avoid overime for care worers, we limi heir woring das o a maximal duraion Dur_max (consrain (12)). Afer each visi, he model calculaes he our lengh performed, which mus no exceed dur_max including he HHC office reurn. D, P : ai + p + dis0 dur _ max (12) - Consrain (13) ensures he coninui of care worer roues: when a care worer visis a paien home, he or she has o finish his visi before beginning anoher one. D, P, h Q : i C D : i C P\ i i = i si D : i = 1 B P D : i = 1 B P Q\ h i C Q\ h ih i (13) - Consrain (14) expresses he coninui of care: cares mus be performed b he same care worer during he wee. D, P : i C i i = P\ i C h P\ i (14) - Consrains (15) and (16) impose ha each care worer exis from he HHC office onl once and comes bac o i a he end of his or her woring da. (15) (16) - Consrains (17) and (18) denoe ha i and ai are respecivel binar and non negaive variables. (17) (18) Technical improvemens In order o improve he processing ime, some cus can be added according o he ime windows. Two sequenial cares canno have wo overlapping ime windows. The earlies dae for beginning he care adding he reamen duraion and he disance ravelled mus no exceed he laes beginning dae of he nex visi (consrain 19). Analsis of resuls ih ( + 1) P,, D : i i D : i0 = 1 P D : i0 = 1 P C, P, D : ai (19) The ineger linear program has been esed on random insances of he indicaed problem. The scheduling model was solved wih wo inds of sofware: LINGO of LINDO Ssems (2003) and ILOG OPL-CPLEX STUDIO of ILOG. We aim o compare he obained resuls of he wo inds of sofware. Duraion of care belongs o he inerval [15mn, 60mn] and he lengh of he ime window for paien availabili is one hour. The compuing processing ime was limied o wo hours. I is well nown ha CPLEX is usuall faser in providing resuls han LINGO. However in previous research (Trilling, 2007; Ben { 0,1} P, D, : : e + p + dis l + ( i 1) HV 0 Bachouch, 2007), LINGO provided beer resuls han CPLEX. Thus, we use he wo inds of sofware o solve he proposed model. Table 2 presens he obained resuls wih he model described in he aricle for differen problem sizes. In a second par, we compare he resuls obained wih anoher model in which we do no ae ino accoun cu consrains and care worer sills. Based on randoml generaed cases, we inended o sud he applicabili of he proposed approach and we invesigaed i on wo planning horizons: dail planning and weel planning. We manipulaed he model for differen problem sizes and in all cases he proposed approach provides a feasible nurse planning. CPLEX does no give a soluion for all insances because of memor usage, ha is, he compuer did no have enough memor o solve he linear ineger model. Even hough LINGO provides a feasible soluion, i is no opimal. However, in care worer planning a feasible soluion is sufficien. In his approach, we show ha a simple ineger linear program is able o produce good soluions. Table 1 summarizes all he consrains considered. Our approach is similar o Borsani e al. (2006) bu we added wo imporan consrains: nurse's lunch breas and shared visis. The proposed linear ineger model aes ino accoun he same consrains, bu we use fewer variables and daa han in Borsani e al. (2006) and our model solves differen problems sizes: from 3 o 7 nurses and 7 paiens o 20 paiens. The larges insance in Cheng and Rich (1998) involved 4 nurses and 10 paiens, which was solved wih an ineger linear program solver. Thus, he proposed approach is simple and useful o esablish dail and weel planning. In he case of planning 7 nurses and 20 paiens, a feasible soluion is found afer 34 seconds wih LINGO bu we inerrup he resoluion o reach he opimal soluion. For dail and weel planning, he soluion is opimal or a leas Suppl Chain Forum An Inernaional Journal Vol N

6 Table 2 Compuaional experimens feasible and good soluion. This is no he case wih CPLEX and i is is maor drawbac. Table 3 Compuaional experimens feasible in all cases wih LINGO. CPLEX did no provide feasible soluions because of compuer performances. For weel planning, LINGO appears o be faser and more efficien han CPLEX. When we inerrup he resoluion wih LINGO, we can have he nurseplanning informaion pu ino an Excel file, whereas wih CPLEX, we can ge soluion resuls onl if he opimal soluion is found. Table 3 illusraes he comparison beween he resuls obained wih he wo differen model versions. The model1 is issued from a previous version in which we do no ae ino accoun he qualificaion of nurses and he cu consrains. The model2 is he model described in he hird secion of his paper. Thus, he model1 is equivalen o model2 wihou consrains (7) and (19). The cu consrains reduce he number of infeasible soluions. The qualificaions consrains also reduce he compuaion imes. In fac, when we ae ino accoun nurses' sills, we mach each nurse o a se of paiens, which reduces he soluion number. The combinaion of qualificaion consrains and cu consrains reduces he compuaion ime. The aim of he sofware comparison is o idenif which is adequae for scheduling care worer planning. In our experimens, i appears ha LINGO is more efficien and provides feasible soluions in all cases. Wih LINGO, we can inerrup he resoluion a an ime having a Conclusion The French HHC service is increasing rapidl in size and he need for decision suppor ools o improve he planning and quali of service is imporan. In his aricle, we considered he problem of assigning paiens o nurses in HHC services. The nurse shor-erm planning process for HHC providers requires he respec of a large number of consrains and obecives in erms of he efficienc and quali of care. We sudied previous wors ha have sudied rouing problems and resource allocaion in he HHC area. We noed ha he amoun of exising research in HHC is limied and he nurse rouing problem is among he mos sudied issues. The proposed approach focuses on care worer rouing problems and we have included a larger varie of consrains han hose of previous conribuions. Our conribuion is in inegraing all he consrains ino a model ha could be calculaed b a solver and adding o he informaion suppor sofware of French HHC. To our nowledge, French HHC providers do no have an planning ools in heir informaion ssems and he nurse coordinaors esablish he dail planning b hand. In his conex, we proposed a simple model ha involves all he consrains needed in care worer planning such as paien availabili, nurses' sills, shared visis, and so on. The proposed ineger linear program provides a nurse planning for differen sizes of applicaion insances. Furhermore, we have compared wo inds of sofware: LINGO of LINDO Ssems and CPLEX of ILOG. I is well nown ha CPLEX is faser han LINGO bu in few cases, LINGO could be faser and more efficien han CPLEX. In our experimens, LINGO appears o be faser han CPLEX and provided good soluions. Besides, our aim was o provide a planning, no necessaril he opimal one, because a feasible one is ofen sufficien. For his Suppl Chain Forum An Inernaional Journal Vol N

7 reason, we sugges inerruping he solver afer wo hours when he opimal soluion is no found; however, we alwas found a feasible nurse planning. The model proposed can be exended b aing ino accoun addiional consrains or b modifing he obecive funcion such as balancing worloads beween care worers. For his sud, we used randoml generaed cases; however, his analsis will be validaed laer wih real daa. We based our approach on mahemaical programming because i is an efficien mehod ha does no require sofware developmen o implemen our model and because LINGO and CPLEX wors wih Excel shees. References Beaulieu, M., Landr, S., & Friel, T. (2001). Poins of care logisics. Suppl Chain Forum: an Inernaional Journal, vol 2(1), Begur, S. V., Miller, D. M., & Weaver, J. R. (1997). An inegraed spaial decision suppor ssem for scheduling and rouing home healh care nurses. Insiue of Operaions Research and he Managemen Science, 27(4), Ben Bachouch, R. (2007). Planificaion des lis dans un éablissemen hospialier. Maser's hesis. Lon: INSA. Berels, S., & Fahle, T. (2006). A hbrid seup for a hbrid scenario: Combining heurisics for he home healh care problem. Compuers and Operaions Research, 33, Blais, M., Lapierre, S. D., & Lapore, G. (2003). Solving a home care disricing problem in an urban seing. Journal of he Operaional Research Socie, 54, Conference on Service Ssems and Service Managemen), Troes, France, pp Chahed, S., Marcon, E., Sahin, E., Feille, D., & Daller, Y. (2009). Exploring new operaional research opporuniies wihin he home care conex: The chemoherap a home. Healh Care Managemen, 12, Cheng, E., & Rich, J. L. (1998). A home care rouing and scheduling problem. Technical Repor TR Houson, TX: Deparmen of Compuaional and Applied Mahemaics, Rice Universi. Chiba, M., Iabashi, G., Tahashi, K., & Kao, Y. (2005). A suppor ssem for home care service based on muli-agen ssem. Inernaional Conference on Informaion Communicaion and Signal Processing, Bango, Thailand, pp De Angelis, V. (1998). Planning home assisance for AIDS paiens in he Ci of Rome, Ial. Insiue of Operaions Research and he Managemen Science, 28, Eveborn, P., Flisberg, P., & Ronnqvis, M. (2006). LAPS CARE-An operaional ssem for saff planning of home care. European Journal of Operaional Research, 171, Landr, S., & Philippe, R. (2004). How logisiics can service healhcare. Suppl Chain Forum: an Inernaional Journal, 5(2), LINDO Ssems. (2003). LINGO 8.0 user's manual. Chicago: Auhor. Trilling, L. (2007). Aide à la décision pour le dimensionnemen e le piloage de ressources humaines muualisées en milieu hospialier. PhD hesis. Lon: INSA. Abou he auhors Rm Ben Bachouch is a PhD candidae in indusrial engineering in he LIESP Laboraor (Laboraor of Compuer Science for he Enerprise and he Producion Ssems) in INSA (Naional Insiue of Applied Science) in Lon, France. Her research ineress include logisics, suppl chain managemen, and operaional research. Alain Guine is a universi professor in he indusrial engineering deparmen of INSA. He received a PhD in 1983 and a enure (habiliaion o lead research aciviies) in He eaches operaion research, saffing and scheduling, and business process engineering. His research aciviies are based on hospial managemen problems such as operaing heaer conrol, hospial regrouping managemen, emergenc newor reengineering, home care resource coordinaion, hospial suppl chain, and so on. His scienific invesigaions include human and maerial resources sizing, planning, and scheduling; producion newor reengineering; logisics; and so on. Sonia Hari-Gabou is a professor a he Tunisian Insiue of Applied Sciences and Technolog (INSAT). She received her BS degree in elecrical engineering from he Naional Engineering School of Monasir in Tunisia. She go her MS and PhD degrees in indusrial compuing and auomaic from he Universi of Sciences and Technologies of Lille (USTL) in France. She received her qualificaion o direc research degree from he Naional Engineering School of Tunis (ENIT). She is he associae responsible a he URAII Research Uni in auomaic and indusrial compuing of he Insiue of Applied Sciences and Technolog in Tunis. Her research ineress include design, configuraion and conrol of manufacuring ssems, opimizaion, and decision maing. Bold, D., & Howell, N. (1980). The geographical allocaion of communi care resources: A case sud. Journal of he Operaional Research Socie, 31, Borsani, V., Maa, A., Beschi, G., & Sommaruga, F. (2006). A home care scheduling model for human resources. Proceedings of ICSSSM06 (Inernaional Suppl Chain Forum An Inernaional Journal Vol N