Maximising the Coverage of Emergency Medical Services with Time-Dependent Demand Restrictions: a Case Study in Shanghai

Home , Huajing, Luwan District, Xuhui District, Yangpu District, Zhongshan Hospital

Maximising the coverage of emergency medical services with time-dependent demand restrictions: a case study in Shanghai

Ming Kun Li and Jia Wei Zhang School of Management, Shanghai University, Shanghai, People’s Republic of China

ABSTRACT

In many Asian cities, periodic changes in the demand for emergency medical services are concerned, but few existing studies have discussed the time-dependent factor in delivering these services. This study proposes a formula for locating emergency medical services, in which factors of varying demand, time-dependence, cost and facility capacity are considered. A real case is investigated in order to understand the impact of time-dependence on decision making. The case study suggests different solutions depending on whether the design is service-oriented or cost-oriented. The analysis also indicates that the limitations on demand complicate the making of decisions to optimise service locations, e.g. more service stations are required. By creating a design for allocating service sites based on demand nodes in a real case, this study provides a framework for analysing the location problem when demand changes.

KEYWORDS Emergency medical services; integer programming; location; time-dependent restrictions CONTACT Ming Kun Li [email protected] Received 8 July 2016

1. Introduction staff workloads can be easily detected, as indicated below in the summary of emergency medical services in Shanghai The Shanghai society faces a variety of challenges from 2001 to 2014. As a result, the response time for due to rapid urbanisation. At the end of 2014, the elderly ambulance services in urban cities is getting longer (Qi and population in Shanghai was 28.8% of the total population Jing, 2017). (Shanghai Civil Affairs Bureau, 2015). The growing Along with the increasing demand for medical services, proportion of elderly residents, together with the booming other problems have emerged during the implementation of a number of migrants is placing growing pressure on the more effective service, such as limited resources and changes city’s emergency medical services. A significant growth in in demand. This paper observed that the time-dependent

Table 1. Summary of emergency medical services in Shanghai. (source: www.sn120.sh.cn)

Year Distance travelled (km) Number of vehicle-times Number of patients 2001 3,684,900 157,400 146,600 2002 4,757,000 192,200 179,800 2003 5,540,600 223,200 207,500 2004 6,237,800 254,000 234,200 2005 6,898,700 297,400 268,300 2006 7,573,300 327,200 290,100 2007 8,251,600 359,000 322,800 2008 9,052,700 396,800 361,900 2009 9,632,700 430,200 396,100 2010 11,330,100 498,700 455,800 2011 - 535,900 487,800 2012 12,016,600 594,500 541,000 2013 12,648,300 628,500 571,900 2014 12,367,700 642,000 584,000

aspect of the demand problem is mainly being caused by the dynamic setting of ambulance locations (Gendreau et mobility of citizens. al., 2001; Rajagopalan et al., 2008; Zarandi et al., 2013) To put it simple, a large portion of the population is was considered. Another direction for applying current now choosing to live in the growing suburbs and commute coverage models to real problems is to consider capacitated downtown to work. Thus, the movement of the population facilities (Chung et al., 1983; Current and Storbeck, 1988; has substantially changed the demand for emergency Murray and Gerrard, 1997). Applications of the extended services in different regions of the city at different times. capacitated covering models to real-world problems are Where one medical station might have once been sufficient provided by authors (Yin and Mu, 2012). for communities in a designated region, the fluctuating In recent years, the time-dependent aspect in coverage overall demand for ambulances from a shifting population problems has attracted growing attention. One of the often leads to long response times by medical services. features is that the speed of the ambulance is affected by These shifting population patterns also influence unfavourable traffic conditions during rush hours, and the planning procedures for emergency facility locations. therefore the radius of prompt cover can vary at different So, optimising facility locations for emergency medical times (see arguments on vehicle routing problems in Hill services has become a priority for local government. and Benton, 1992; Malandraki and Daskin, 1992; Ichoua et This study is driven by the time-dependent nature of al., 2003). the demand for emergency medical services. Shackled by This led to the problems of ambulance location and limited budgets and finite land resources, planners have relocation in relation to time-dependent service (Budge et al., to consider many factors such as the city layout, costs, the 2010; Schmid and Doerner, 2010). In medical emergency limited number of candidate sites and the mobility of the logistics, the time window was also an important factor when population, in order to optimise the use of facilities while optimising the number and locations of supply nodes to achieving a satisfactory service level. Consequently, the demand nodes (see a case study by Tuzkaya et al., 2014). allocation problem for emergency medical sites needs to be Some other researchers (Griffin et al., 2008) argued investigated from a variety of different angles to ensure the that the cost of health services and the locations of health optimum allocation of facilities for each demand node. In centres are subject to fluctuations in needs, while some this research, a real case in Shanghai is discussed. recent surveys (Basçar et al., 2012; Farahani et al., 2012) highlighted the fact that the time-dependence aspect of emergency service station location problems were under- 2. Literature review developed areas of academic research. On the one hand, rapid urbanisation in Asia and an The importance of ambulance services in any urban ageing population have resulted in a growing need for society has been explored extensively in the literature. more ambulances and health care services overall, (Loo Many problems are considered such as the location of and Lam, 2012), while is the residential shifts of people has ambulance stations, and the relocation and dispatching of exacerbated the delivery of the services. On the other hand, ambulances. however, we can see from the literature that few studies These problems are connected to each other, but have discussed models and applications for covering solving the facility location problem is the basis for making problems of delivering medical services with time- all the other related decisions (Aringhieri et al., 2017). dependent demand restrictions. Minimising the cost of covering all the demand nodes Therefore, on the basis of some real cases in Asian (Toregas et al., 1971) and covering the largest possible level cities, a formula addressing two time-dependent demand of demand (Church and ReVelle, 1974) are some recognised constraints was considered in this research. A better plan objectives of previous research. Similar objectives have for the location of medical stations was attempted with appeared in studies on determining the locations of fire reference to changing demands during different time stations (Indriasari et al., 2010) and emergency warning periods. sirens (Current and O’Kelly, 1992). Early research work, however, has some major drawbacks, e.g. the assumption of un-capacitated facilities and the 3. Model formulations static condition of demand, largely negate the application of current coverage models. More background on the planning process is introduced To remedy this situation, more attention must be to provide the mathematical formulation. In reality, a new paid to improve the models to reflect real-world problems. plan for facilities is often made from the existing service Hence, some researchers (Hogan and ReVelle 1986; locations and some new potential candidates. The budget Gendreau et al., 1997) considered the Double Standard restricts the number of locations in this plan, and also Model to ensure multiple coverage of each demand node, imposes an upper limit on the capacity of medical emergency while other researchers (Daskin 1983; Batta et al., 1989) services at each site. extended the studies on investigating the availability of In order to facilitate the service process and control the ambulances at different time periods. More recently, the costs, one demand node is assigned to at most one service

010 HKIE Transactions | Volume 26, Number 1, pp.9–19

In order to facilitate the service process and control the costs, one demand node is assigned to at most one service site. The demands of a node correspond to the population, while the demand varies periodically over time. More specifically, it is also affected by work time and leisure time. Authorities will always attempt to improve service levels, and therefore, in this research, maximising the coverage of emergency services within a limited budget, and time-dependent restriction were the major objectives.

The problem is formulated as follows:

Parameters: N the set of existing and candidate emergency service sites, N 0 the set of existing emergency service sites at the beginning of the plan, i.e. 0 0 0 = jN ∈ N |{ x j = 1 } , where x j denotes the initial status of site j, M the set of demand nodes, ⎧ ,1 if the distance from i to j is not greater than the upper limit of services aij = ⎨ , ⎩ ,0 otherwise

f j the cost of setting up emergency service at site j or removing the service from j, ∑ a ij h i ij ≤ Cz x jj ∈∀ Nj , (3) v the cost of maintaining emergency services at site j, ∈Mi j ∑ a ij h i ij ≤ Cz x jj ∈∀ Nj , (3) ∈Mi a h ' ≤ Cz x ∈∀ Nj , (4) ∑ i ijij jj TC the upper limit of costs for a setting h ' ≤ Cz upx emergency services∈∀ Nj ∈, Mi at candidate sites (4)and ∑ i ijij jj ∈Mi 0 removing emergency services from existing facilities, ≤ ∑ f j (0 x − jj ) + ∑ fx x jj ≤ TC , (5) 0 ∈Nj 0 j ∈ / NN 0 ≤ ∑ f j (0 x − jj ) + ∑ fx x jj ≤ TC , (5) hi the population of a demand node∈Nj 0 i in working j ∈ / NN 0 hours, a h ≤ Cz x ∈∀ Nj , (3) ∑ ij i ij jj ∈Mi x j ∈{0,1} ∈∀ Nj , (6) h' the population of a demandx ∈ {0,1}node i in non-working hours,∈∀ Nj , (6) i j a h ' ≤ Cz x ∈∀ Nj , (4) ∑ i ijij zjj ∈{0,1} ∀ Mi , ∈∈ Nj . (7) C the capacity of emergency services at site j. ∈Mi ij j z ∈{0,1} ∀ 0 Mi , ∈∈ Nj . (7) ij ≤ ∑ f j (0 x − jj ) + ∑ fx x jj ≤ TC , (5) In order to facilitate the service process0 and control the0 costs, one demand site. The demandsVariables: of a node correspond to the population, The objective∈Nj of this modelThe objective j is∈ to/ NN maximise of this the model coverage is to maximise the coverage of emergency services, i.e. In order to facilitate the servicenode process is assigned and tocontrol at most the one costs, service one sdemandite. The demands of a node correspond to the In orderwhile to facilitatethe demand the servicevaries periodicallyprocess and controlover time. theThe costs,More objective one demand of this model is to maximise the coverage of emergency' services, i.e. ⎧ ,1 if emergence services are positioned at sitex j j∈ {0,1} α i zh ij + ( ∈∀ −Nj α, )1 i zh ij , while minimising(6) the total cost of providing the node is assignednode to isat assignedmost one to service at most site one. The service demandspopulation, site. ofThe a nodedemandswhile correspond the of demand a nodeof to emergency correspondthevaries periodically services,' to the i.e. over ∑∑ time. More ∑∑specifically, it is, specifically, itx isj =also affected by work time and leisure , ∈∈Mi Nj ∈∈Mi Nj ⎨ α i zh ij + ( −α)1 i zh ij , while minimising the total cost of providing the population, whilepopulation, the demand while varies the demand ,0 periodically varies over alsoperiodically time.affected otherwiseMore over∑∑by specifically, worktime. timeMore∑∑ it andspecifically, is leisure time. it is Authorities will always attempt to time. Authorities will⎩ always attempt to improve ∈∈serviceMi Nj while∈∈Mi Nj minimisingz ∈{0,1} the total costservices, of providing i.e. the v ∀ x services,+ Mi , f ∈∈ i.e.Nj x 0 . − )( + fx x (7). also affected In order by towork facilitate time theand serviceleisureimprove processtime. service Authorit and levels,controlies will andthe therefore,alwayscosts, one attempt ij indemand this to research, maximising the coveragejj ∑∑ j of jj ∑ jj also affected levels,by work andIn time order therefore, and to facilitateleisure in this time. the research, serviceAuthorit processmaximisingies will and always controlthe attempt the costs, to one demand0 ∈Nj ∈Nj 0 j ∈ / NN 0 node is assigned to at⎧ most,1 if one demand service s nodeite. The i is demands services,serviced of i.e. bya node site v correspond x j jj + ∑∑ f j to x the− jj )( + ∑ fx x jj . improve Inservice order levels,to facilitate and therefore, the serviceemergency in processthis research, services and control maximising within the a costs,limited the onecoverage budget, 0demand andof time-dependent0 . restriction were the improve servicenodecoverage levels, is assigned ofand emergency ztherefore, to= at most servicesin onethis service research, within site a maximising.limited The demands budget, the of coverage a node∈Nj correspond of . ∈ Nj to the j ∈ / NN population, whileij the⎨ demand varies periodically over time. More specifically, it is emergency servicesnodeemergencypopulation,and time-dependent is within assigned serviceswhile a limited to the at restrictionwithin⎩ most demandbudget,,0 onea limited were andvariesservice time-dependentthe budget, majorperiodically smajorite. otherwise objectives.The and objectives. demands time-dependent over restriction time. of a Morenodewere restriction correspondthespecifically, The were objectiveto it the is of this model is to maximise the coverage of emergency services, i.e. also affected by work time and leisure time. Authorit ies will alwaysThe serviceattempt tolevel Theis measured service level by is ameasured weighted by a weighted summation of the population, e.g., α is population,major objectives. while the demand varies periodically over time. More specifically, it is ' major objectives.also affected by work time and leisure time. AuthoritThe serviceies will levelsummation always is measured attempt of the byα population, toazh weighted + the weighte.g.summation ( − α)1 isfor zh the the,of weightwhile thepopulation population, minimisingfor the of demande.g., the α total nodesis cost during of providing working thehours. In order to improve service levels, and therefore,The in problemthis research, is formulated maximising as follows: the coverage ∑∑ ofi ij ∑∑ i ij alsoimproveThe problemaffected service isby formulated levels,work timeand as therefore,follows:and leisure in thistime. research, Authorit maximisingies will always the coverageattempt∈∈Mi Nj toof ∈∈Mi Nj emergency services within a limited budget, and time-dependentthe weight forpopulation restrictionthe population of were demand ofthe demand nodesanalyse during nodes theworking during impact workinghours. of theIn hours. orderobjective In orderfunction to on solutions, w as a weight to the The problem isTheimproveemergency formulated problem service services asisThe formulatedfollows: levels, integer within and asa therefore,programminglimitedfollows: budget, in this and formulationresearch, time-dependent maximising is as restriction follows:. the coverage were theof 0 analyse the impactto analyse of thetheservices, impactobjective i.e. of thefunctionsecond v objective x jj + parton∑∑ function solutions,of f j the x −objective on jj )( wsolutions,+ as∑ was a fx weight introduced.x jj . to the major objectives. ' 0 0 0 emergencymajorParameters: objectives. services within a limited budget, and time-dependent restriction as a weight were to the the second∈Nj part∈ Nj of the objective, j ∈ was/ NN Max(∑∑α i zh ij + ∑∑ ( secondα h i z partij ))1 −− of w the( objective v x jj + was∑∑ introduced. f j x − jj )( + ∑ fx x jj ) major objectives. Parameters: 0 0 N the set of existing∈∈Mi Nj and candidate∈∈Mi Nj emergency introduced.∈Nj ∈Nj Constraint j (1)∈ /ensuresNN that each demand node is serviced by at most one emergency Parameters: Parameters:The problem is formulated as follows: N the set of existing and candidate emergency service sites, The problemservice is formulated sites, as follows: Constraint (1) ensuresConstraint thatThe each service (1) demand ensures levelservice nodeis thatmeasured issite. eachserviced Constraint bydemand a by weighted at (2) nodemost states summation oneis that emergency a demand of the population, node i cannot e.g., be α serviced is by a site j, The 0 problem the set of isSubject existingformulated andto: as candidate follows: emergency 0 the set service of existing sites, emergency service sites at the beginning of the plan, i.e. N the set of N existing andthe setcandidate of existing emergency emergency serviceN service sites, sites service at the site. Constraintserviced by (2)the at states mostweight thatone for aemergency demandwhenthe population the node servicenode i cannotofis site. demandnot Constraintbecovered serviced nodes by duringbythe a servicesite working j, of jhours. or the In emergency order to service is not 0 0 0 0 0 N the set of N existing the set emergency of existing service emergency sites atservice the= beginning jN sites∈ N at |{ x the of= 1 } beginningthe, where plan,(2) states xi.e.of denotesthe thatanalyse plan, a thedemand i.e. initialthe impact node status i cannot ofof stheite bejobjective, serviced function by a site on solutions, w as a weight to the Parameters:beginning zij of≤ the1 plan, i.e. whenj the ∈∀ nodeMi , is notj covered by the servicepositioned(1) of jat or j. the emergency service is not 0 In order to ∑facilitate0 the service process0 and control the costs, one demand 0 Parameters:0 ∈Nj 0 j, when thesecond node ispart not of covered the objective by the was service introduced. of j or the = jN ∈ N |{ x == 1 } , jN where∈ N |{ x jx= 1 denotes} , where the x initialj denotes status the of initial sitepositioned j ,status of satite j. j, Parameters:nodeNj is theassigned setwhere ofto at existing mostj denotes one serviceand thecandidate site initial. The demands status emergencyM of theof a nodesite set service correspondjof, demand s iteto thes, node emergencys, service is not positioned at j. population,N the whileset of the existing demand varies and candidateperiodically over emergency time. More servicespecifically, site it s,is Constraints (3) and (4) ensure that the assignment of demands i to j cannot exceed the M 0 thethe setset ofof demandexisting node emergencys, service⎧ ,1 sitesif the at distancethe beginning from i to of j isthe not plan, greater i.e. th an the upper limit of services M the set ofalsoMN demand0 affected the set thenode by of setwork s,existing of time≤ demand and iand n { leisureaz nodes,candidate ,m x time.} Authorit emergencyies will alwaysservice attempt site s,to Constraints, Constraint (3) and (1) (4)ensures ensure(2) that that each the demand assignment node of is serviced by at most one emergency N the set of ijexisting emergencyij j serviceaij = ⎨ sites Constraintsat the ∀ beginning (3) Mi ,and ∈∈ of (4) Nj the ensure plan, that i.e. the assignmentcapacity of of j .demands Constraint i, to (5) j cannotgives the exceed budget the limitations on setting up new emergency ⎧ ,1 if theimprove distance0 ⎧ service,1 fromifif the thelevels, idistance distance0to andj is therefore, not from from greater ini to ithis 0 tothj isresearch,anj notis the not greater upper maximising ⎩greater,0 limitthan thentheofthe coverageservices upper the limitof demands of services i to otherwise j cannot exceed the capacity of j. Constraint (5) aN 0= =the jN ∈set N of |{ x 0jexisting= 1 } , where emergency x 0j denotes service the sites initial capacityat status the beginning ofof s jite. Constraint j, of the service(5) ,plan, gives i.e.site. the Constraintbudgetservice limitations sites(2) states and onremoving that setting a demand upthe new service node emergency fromi cannot some be existing serviced sites. by a site j, aij = ⎨ emergencyij =⎨ jN services∈ N |{ x within= 1 a} limited, where budget, x and denotes time-dependent the initial restriction status were of the s, ite j, 0 ,0 upper limit0j of services,0j otherwise gives the budget limitations on setting up new emergency5 ⎩ ,0 major objectives.⎩ , whereotherwise x denotesf j thethe initialcostservice of status setting sitesof upsite and emergency j, removing whenservice the servicethe at nodesite from j oris removingnotsome covered existing the byservice sites. the servicefrom j, of j or the emergency service is not M = the jN ∈set N of |{ x demandj = 1 } , where nodes, x j denotes the initial status of site j, M the setotherwise of demand nodes, service sitespositioned and removing at j. the service from some existing f the cost off jsetting the costup emergency of setting upservice emergency at site servicej or removing at site jthe or serviceremoving from the j ,service from j, Constraints (6) and (7) are the integrality constraints. j TheM problem ⎧the,1 set isif formulated theof demanddistance as follows: fromnode s,i to j is notv jgreater the costthan ofthe maintaining upper limitsites. of emergency services services at site j, faj = ⎧ ,1 theif the cost distance of setting from up i to emergency j is not greater service than atthe site upper j limit of services , ij ⎨ Constraints (6) and (7) are, the integrality constraints. v the cost ofva jijmaintaining = ⎧the⎩⎨ ,1 ,0 costif the of emergency distancemaintaining from services emergency i to j isat not siteotherwise greaterservices j, th anat stheite upperj, limit of services j ⎧ ,0 or removing the service fromTC otherwisej, the upper limit of costs for settingConstraints, up emergency (3) and services (4) ensure at candid that theate assignment sites and of demands i to j cannot exceed the aij = ⎨⎩ , In the above mixed integer and linear programming formulation, Constraints TCParameters:f the ,0 costupper of limit setting of upcosts emergency for setting serviceotherwise up emergency at site j or services removing at thecandid Constraintsserviceate s fromites (6) and j, and (7) are the integrality constraints. TC the upperv jlimitj ⎩ of thecosts cost for of setting maintaining up emergency emergencyremoving services services emergency at candid at site servicesateIn the sites above fromand mixed existingcapacity integer facilities of jand. Constraint, (3)linear and programming (4) (5) are gives introduc the formulation, budgeted in limitationsconsideration Constraints on ofse ttingthe time-dependent up new emergency feature of demand. Nf j the the set costof existing of setting and candidate up emergency emergency service service sites, at site j or removing the service from j, removing emergencyremovingf 0 the services cost jemergency, of fromsetting existingservices up emergency facilitiesfrom existing hservice, the facilities atpopulation site(3) j, orand removing of (4) a demandare introducthe servicenodeed servicei in infrom workingconsideration sitesj, andhours, removing of the time-dependent the service from feature some existingof demand. sites. vNjj the the set cost of existing of maintaining emergency service emergency sites at ithe services beginning at ofs itethe j,plan, i.e. In the above mixed integerConstraint and (3)linear refers programming to the population which could benefit from the emergency TCv j0 the costthe0 upperof maintaining limit0 of costsemergency for setting services up emergencyat site j, h the populationhi = the of jN ∈ N apopulation |{ demandx j = 1 } , where node of ax jidemand denotesin working the node initial hours, istatus in working of site j, Constrainthours, (3) refers to the populationmedical which servicescould benefit during businessfrom the hours. emergency i TCv j the the costupper of limitmaintaining of costs emergency for settingh' i servicesup theemergency population at site jservices, of a demand atformulation, candid nodeate i sin itesConstraints non-working and (3) hours, and (4) are introduced in j services at candidate sites and removingmedical services during businessConstraints hours. (6) and (7) are the integrality constraints. TChM' thethe set populationupperof demand limit node of s,of a costs demand for nodesetting i in up non-working emergency serviceshours, considerationat candidate sites of theand time-dependent feature of demand. h'i the populationTCremovingi the of aupper emergencydemand limit node ofservices costs i in non-working for from setting existingC up hours, the emergencyfacilities capacity , servicesof emergency at candid servicesate sites at s iteand j . TCremoving ⎧ ,1 theif theupper emergencyemergency distance limit from ofservicesiservices to costsj is not greaterfromfor from setting th existing anexisting the upperj up facilities, emergencylimitfacilities of services , services at candidate sites and Constraint (4) considers the number of citizens which could be serviced during leisure aij = ⎨ , Constraint (3) refers to the population which could benefit removingCh ⎩ the,0 the population capacity emergency of of emergency services a demandotherwise from servicesnode existing i in at working s facilitiesite j. hours,, In the above mixed integer and linear programming formulation, Constraints C j the capacityremovinghi j of emergency theemergency population services services of at as fromitedemand j. existingVariables: node facilities i in workingConstraint, (4)from considers the emergencythe number ofmedical citizenstime. Theseservices which two could during constraints, be servicedbusiness together during with leisure the objective function, achieve the goal of hf i thethe cost population of setting up emergencyof a demand service node at site ji orin removing working the hours,service from j, h j the populationhours, of a demand node i in working timehours,. These two constraints,(3) and together (4) are with introducmaximising the objectiveed in the consideration overallfunction, service achieve of thelevel thetime-dependent under goal budgetof restrictions. feature of demand. Variables: Variables:hi'i thethe population population of of a a demand demand node node i iin in working ⎧non-working,1 if emergence hours, hours, services hours. are positioned at site j v j the the cost population of maintaining ofemergency a demand services node at site i jin,= non-working hours, , h'i x j ⎨ maximising the overallConstraint serviceConstraint level(4) considers (3)under refers budget theto restrictions.the number population of citizens which could benefit from the emergency ⎧ ,1 if emergenceh'h'i ⎧the,1 servicespopulationtheif emergence population are positionedof servicesa ofdemand a demand atare site node positioned jnode i in inon-working⎩ in at,0 non-working site j hours, otherwise TCChx'ij = the the upper capacity limit of costs of emergency for setting up emergencyservices servicesat site at j .candid , ate sites and medical services during business hours. x j = ⎨ Cj ⎨the capacityhours, of emergency services, at site j. which could be serviced Notingduring leisurethat a simple time. Theseset coverage two problem is a classic NP-complete problem (Gary ⎩ ,0 removingj ⎩ ,0 emergencyotherwise services from existingotherwise facilities, ⎧ ,1 if demand node i is serviced by site j Variables:C j the capacity of emergency services at site j. Noting that a constraints,simple set togethercoverage with problem the objective is a classic function, NP-complete achieve the problem (Gary C the capacity of emergency serviceszij = at site j. . and Johnson, 1979). In the literature, various algorithms and heuristics have been Variables:hi j the population of a demand node i in working hours, ⎨ ⎧ ,1 if demand⎧ node,1 if i demandis serviced node by isite is serviced j by site⎩ j,0 otherwise Constraint (4) considers the number of citizens which could be serviced during leisure Variables:z = ⎧ ,1 if emergence services are. positioned at. site andj Johnson, goal1979). of maximisingIn the literature, the overall various service algorithms level underand heuristics budget have been zij = ⎨ Variables:hij'i the⎨ population of a demand node i in non-working hours, , x j = ⎨⎧ ,1 ,0 if emergence servicesotherwise are positioned at site j 6 ⎩ ,0 x = ⎩ ,0 otherwise otherwise , restrictions.time . These two constraints, together with the objective function, achieve the goal of C j the⎧⎩⎨ capacity,1 if emergence of emergency services services at are site positioned j. at site j ,0 if emergence servicesotherwise are positioned at site j,, maximising the overall service level under budget restrictions.6 x j = ⎨⎩ The integer programming formulationNoting is that as follows:.a simple set coverage problem is a classic Variables:⎧ ,1 ,0 otherwise.if demand node iotherwise is serviced by site j ⎩ . NP-complete' problem (Gary and0 Johnson, 1979). In the Thezij = ⎧integer⎨⎧,1 ,1 if emergenceif programming demand services node are positioned formulationi is serviced at site j byMaxis siteas( follows:. j α zh + ( α h z ))1 −− w ( v x + f x − )( + fx x ) , The integer programming formulation is as follows:. , ∑∑. i ij ∑∑ i ij jj ∑∑ j jj ∑ jj xzj ==⎨ ,0 otherwise ij ⎧⎩⎨ ,1 ifif demand demand node node ii isis servicesserviced' by sitesite ∈∈ jMi , Nj ∈∈Mi0 Nj literature, Notingvarious∈Nj that algorithms a simple0 andset coverageheuristics problem have0 been is a classic NP-complete problem (Gary Maxz =⎩(⎩,0 ,0 α zh +otherwise' otherwise ( α h z ))1 −− w ( v .0 x + f x − )( + fx x ) , ∈Nj j ∈ / NN Max(∑∑α i zh ijij +⎨∑∑ ( i αij h i∑∑ z ij ))1 −− w ( v i x jj ij+ ∑∑ f j x −jj jj )( ∑∑ + ∑ j fx x jj )jj , ∑ jj ⎧ ,1 ,0 if demandotherwise. node i is servicedotherwise by site j 0 0 0 discussed (Farahani0and Johnson, et al., 1979). 2012), In but the optimal literature, solutions various can algorithms and heuristics have been ∈∈Mi Nj ⎩∈∈Mi Nj ∈∈Mi Nj ∈Nj . Subject∈Nj ∈Nj to: ∈Nj j ∈ / NN j ∈ / NN zij = ⎨ The ⎩integer,0 programmingotherwise formulation is as follows:. hardly be ensured. Some researchers (Sorensen and Church, Subject to: 6 Subject to: The integer programming formulation' is aszij follows:.≤1 0 ∈∀ Mi , (1) Max( α zh + ( α h z ))1 ∑−− w ( v x + f x − 2010))( + exhibited fx x ) , good results by using the ILOG CPLEX TheThe integer integerinteger∑∑ programming programmingi ij formulation∑∑ formulation is as follows:.i' ij is∈Nj as follows:.jj ∑∑ j 0 jj ∑ jj Maxzij( ∈∈≤Mi1 Nj α i zh ij + ∈∈Mi∈∀ Mi Nj ( , α h i z ij∈∀ ))1 −− Mi w ,( ∈Nj v x jj +(1) 0 f j x − mixed-integer(1)jj )( + 0 fx x jj )programme, solver on solving real cases of zij ≤1 ∑ ∑∑ ∑∑' ' 0 ∑∑ ∈Nj 0 j ∈∑/ NN ∑ Max( α zh + ( α h z ))1 −− w ( v x + f x − )( + fx 0x ) , 0 ∈Nj Max∈Nj ∑∑( ∈∈Mi Nj i αij i∑∑zh ij + ∈∈Mii Nj ( ij α h i z ijjj ))1 −− ∑∑ w ( j ∈Nj v x jj jj +∑∈Nj f jj j x − jj )( + j ∈ / NN fx x jj ) , ∑∑ ∑∑ 0 ∑∑ 0 ∑ ∈∈Mi Nj ∈∈Mi Nj ∈Nj ∈ijNj ≤ i n { az ij ,m j x ∈ j/} NN 0 specific ∀ set0 Mi coverage, ∈∈ Nj , problems. Hence,(2) the commercial Subject∈∈Mi to: Nj ∈∈Mi Nj ∈Nj ∈Nj j ∈ / NN Subject≤ to: i n to: { az ,m x } ∀ Mi , ∈∈ Nj , mathematical(2) solver in experiments was attempted, and it ij ≤ i n { az ij ,m x j ij} ij j ∀ Mi , ∈∈ Nj , (2) 5 Subjectzzij≤1≤ 1to: ∈∀ Mi , ∈∀ Mi , (1) returned(1) satisfactory and feasible solutions to the problem ∑ ijz ≤1 ∈∀ Mi , (1) ∑∈Nj Nj ij , (1) 5 5 ∈Nj z ≤1 ∈∀ Mi , instances(1) of a real case (see details in Section 3). ∑ ij ∈ijNj ≤ a ij i nh { i az ijij ,m x ≤j } Cz x jj ∀ Mi , ∈∈ Nj , ∈∀ Nj , (2) (3) ∑ij ≤ i n { az ij ,m x j } ∀ Mi , ∈∈ Nj ,, (2) (2) ∈Mi a ij h i ij ≤ Cz x jj ∈∀ Nj , (3) ∑ij ≤ a h i n { az ≤ij Cz ,m x x j } ∀ ∈∀ Mi Nj ,, ∈∈ Nj , 5 (2)(3) ∑∈Mi a ijij h ii ijij ≤ Cz x jj jj ∈∀ Nj , (3) ∑ij ≤ a ij h i ' nij { az ≤ij Cz ,m x x j } jj ∀ ∈∀ Mi Nj , ∈∈ Nj , (2)(3) 5 ∑∈Mi a h ≤ Cz x ∈∀ Nj ,, (3) (4) ∑∈Mi i' ijij jj 4. Application 5 ∈Mi a h ≤ Cz x ∈∀ Nj , (4) 'i' ijij jj 5 ∑ a h ' ≤ Cz x ∈∀ Nj , (4) 5 ∑∈Mi a h i ijij ijij ≤ Cz x jj jj ∈∀ Nj , (4) ∑ a h i ijij ≤ 0 Cz x jj ∈∀ Nj ,, (4) (4) ∑∈Mi ≤ i f j (0 x − jj ) + fx x jj ≤ TC , (5) ∈Mi ∑ 0 ∑ In this section, a real case in Shanghai, a city of ≤ 0 f (0 x − ) + 0 fx x ≤ TC , (5) ∑∈Nj j 0 jj j ∈∑/ NN jj ≤ 0 f (0 x 0 − ) + 0 fx x ≤ TC , China,(5) is discussed. As mentioned previously, the growing ≤ ∑∈Nj f j j (0 x − jj jj ) + j ∈∑/ NN fx x jj jj ≤ TC , (5) ≤ ∑0 f (0 x − ) + ∑ fx 0 x ≤ TC ,, (5) (5) ∑∈Nj 0 j jj j ∈∑/ NN 0 jj ∈Nj 0 j ∈ / NN 0 population and an expanding boundary of the city is placing x j ∈∈{0,1}Nj j ∈ / NN ∈∀ Nj , (6) x ∈{0,1} ∈∀ Nj ,, (6) (6) x j ∈{0,1} ∈∀ Nj , growing(6) pressure on the city government to satisfy the x jj ∈{0,1} ∈∀ Nj , (6) x j ∈{0,1} ∈∀ Nj , changing(6) needs for emergency medical services. zij ∈{0,1} ∀ Mi , ∈∈ Nj .. (7) (7) zij ∈{0,1} ∀ Mi , ∈∈ Nj . (7) zij ∈{0,1} ∀ Mi , ∈∈ Nj . (7) zij ∈{0,1} ∀ Mi , ∈∈ Nj . (7) ij The objective of this model is to maximise the coverage of emergency services, i.e. 011 The objective of this model is to maximise the coverage of emergency services, i.e. ' HKIE Transactions | Volume 26, Number 1, pp.9–19 The objectiveα i zh ij + of this ( model−α)1 iiszh ij to, whilemaximise minimising the coverage the total of emergency cost of providing services, i.e.the The∑∑ objectiveα zh + of∑∑ this ( model−α)1 'iszh to, whilemaximise minimising the coverage the total of emergency cost of providing services, i.e.the ∈∈Mi Nj i ij ∈∈Mi Nj i'' ij ∑∑α zh + ∑∑ ( −α)1 ' zh , while minimising the total cost of providing the ∑∑∈∈Mi Nj α ii zh ijij + ∑∑∈∈Mi Nj ( −α)1 ii zh ijij , while minimising the total cost of providing the ∑∑α i zh ij + ∑∑ ( −α)1 i zh ij ,0 while minimising the total cost of providing the services,∑∑∈∈Mi Nj i.e. ∑∑∈∈Mi v x Nj + f x − )( + fx x . ∈∈Mi Nj ∈∈Mi Nj jj ∑∑ j 0 jj ∑ jj services, i.e. ∈ v x + 0 f x − )( + fx 0 x . Nj jj ∑∑ ∈Nj j 0 jj j ∈∑/ NN jj services, i.e. v x + 0 f x 0 − )( + fx 0 x . services, i.e. ∈Nj v x jj jj + ∑∑ ∈Nj f j j x − jj jj )( + j ∈∑/ NN fx x jj jj . services, i.e. v x + ∑∑ 0 f x − )( + ∑ fx 0 x . ∈ jj 0 j jj 0 jj ∈Nj ∑∑ ∈Nj j ∈∑// NN ∈Nj ∈Nj 0 j ∈ / NN 0 The service level is measured by a weighted summation of the population, e.g., α is The service level is measured by a weighted summation of the population, e.g., α is theThe weightservice forlevel the is populationmeasured by of a demandweighted nodes summation during of working the population, hours. Ine.g., order α tois Thethe weightservice forlevel the is populationmeasured by of a demandweighted nodes summation during of working the population, hours. Ine.g., order α tois theanalyse weight the forimpact the populationof the objective of demand function nodes on during solutions, working w as hours. a weight In order to the to theanalyse weight the forimpact the populationof the objective of demand function nodes on during solutions, working w ashours. a weight In order to theto analysesecond partthe ofimpact the objective of the wasobjective introduced. function on solutions, w as a weight to the analysesecond partthe ofimpact the objective of the wasobjective introduced. function on solutions, w as a weight to the second part of the objective was introduced. second part of the objective was introduced. Constraint (1) ensures that each demand node is serviced by at most one emergency Constraint (1) ensures that each demand node is serviced by at most one emergency Constraintservice site. (1) Constraint ensures that(2) stateseach demandthat a demand node is node serviced i cannot by at be most serviced one emergencyby a site j, Constraintservice site. (1) Constraint ensures that(2) stateseach demandthat a demand node is node serviced i cannot by at be most serviced one emergencyby a site j, whenservice the site. node Constraint is not covered(2) states by that the a servicedemand ofnode j or i cannotthe emergency be serviced service by a issite not j, servicewhen the site. node Constraint is not covered(2) states by that the a servicedemand ofnode j or i cannotthe emergency be serviced service by a issite not j, whenpositioned the nodeat j. is not covered by the service of j or the emergency service is not whenpositioned the nodeat j. is not covered by the service of j or the emergency service is not positioned at j. positioned at j. Constraints (3) and (4) ensure that the assignment of demands i to j cannot exceed the Constraints (3) and (4) ensure that the assignment of demands i to j cannot exceed the Constraintscapacity of j(3). Constraint and (4) ensure (5) gives that the the budget assignment limitations of demands on setting i to jup cannot new emergencyexceed the Constraintscapacity of j(3). Constraint and (4) ensure (5) gives that thethe budgetassignment limitations of demands on setting i to jup cannot new emergencyexceed the capacityservice sites of j .and Constraint removing (5) the gives service the budgetfrom some limitations existing on sites. setting up new emergency capacityservice sites of j .and Constraint removing (5) the gives service the budgetfrom some limitations existing on sites. setting up new emergency service sites and removing the service from some existing sites. service sites and removing the service from some existing sites. Constraints (6) and (7) are the integrality constraints. Constraints (6) and (7) are the integrality constraints. Constraints (6) and (7) are the integrality constraints. Constraints (6) and (7) are the integrality constraints. In the above mixed integer and linear programming formulation, Constraints In the above mixed integer and linear programming formulation, Constraints (3) and (4)In theare aboveintroduc mixeded in integer consideration and linear of theprogramming time-dependent formulation, feature ofConstraints demand. (3) and (4)In theare aboveintroduc mixeded in integer consideration and linear of theprogramming time-dependent formulation, feature Constraintsof demand. Constraint(3) and (4) (3)are introducrefers toed the in considerationpopulation which of the could time-dependent benefit from feature the ofemergency demand. (3)Constraint and (4) (3)are introducrefers toed the in considerationpopulation which of the could time-dependent benefit from feature the ofemergency demand. Constraintmedical services (3) refers during to business the population hours. which could benefit from the emergency Constraintmedical services (3) refers during to business the population hours. which could benefit from the emergency medical services during business hours. medical services during business hours. Constraint (4) considers the number of citizens which could be serviced during leisure Constraint (4) considers the number of citizens which could be serviced during leisure Constrainttime. These (4) two considers constraints, the number together of with citizens the objectivewhich could function, be serviced achieve during the goalleisure of Constrainttime. These (4) two considers constraints, the number together of with citizens the objectivewhich could function, be serviced achieve during the goalleisure of timemaximising. These thetwo overall constraints, service together level under with budgetthe objective restrictions. function, achieve the goal of timemaximising. These thetwo overall constraints, service together level under with budgetthe objective restrictions. function, achieve the goal of maximising the overall service level under budget restrictions. maximising the overall service level under budget restrictions. Noting that a simple set coverage problem is a classic NP-complete problem (Gary Noting that a simple set coverage problem is a classic NP-complete problem (Gary Notingand Johnson, that a simple1979). setIn thecoverage literature, problem various is aalgorithms classic NP -completeand heuristics problem have (Garybeen Notingand Johnson, that a simple1979). setIn thecoverage literature, problem various is a algorithmsclassic NP -completeand heuristics problem have (Gary been and Johnson, 1979). In the literature, various algorithms and heuristics have been and Johnson, 1979). In the literature, various algorithms and heuristics have been6 6 6 6

In order to facilitate the service process and control the costs, one demand node is assigned to at most one service site. The demands of a node correspond to the population, while the demand varies periodically over time. More specifically, it is also affected by work time and leisure time. Authorities will always attempt to improve service levels, and therefore, in this research, maximising the coverage of M K LI AND J W ZHANG emergency services within a limited budget, and time-dependent restriction were the major objectives.

The problem is formulated as follows:

f j the cost of setting up emergency service at site j or removing the service from j,

v j the cost of maintaining emergency services at site j, TC the upper limit of costs for setting up emergency services at candidate sites and removing emergency services from existing facilities,

hi the population of a demand node i in working hours,

h'i the population of a demand node i in non-working hours,

Figure 1. The change of population inFigure sub-districts. 1. The changeC j of the population capacity ofin emergencysub-districts services. at site j.

Variables:

⎧ ,1 if emergence services are positioned at site j x j = ⎨ , The city government attempted to establish more ⎩ ,0 give a net inflow otherwiseof the population during working hours. It ambulance stations to improve the service, in particular, is clear from the figure that the population stays relatively ⎧ ,1 if demand node i is serviced by site j in the central region of the city, because it accommodateszij = ⎨ steady in a few sub-districts which is denoted. by bars. more than one-third of the population, and provides a ⎩ ,0 Noting thatotherwise the working hours defined in this study majority of joba few opportunities. sub-districts Existing which is facilities denoted includeby bars. 33 include business hours, i.e. from 9:00am to 5:00pm, and

emergency medical sites, which are distributed across eightThe integerasome few programming sub-districtstransit time formulation betweenwhich is thedenoted is workplaceas follows:. by bars. and living place. districts of thisNoting central that region the working of Shanghai.a hoursfew sub-districts defined ina few thiswhich sub-districtsstudy is Itdenoted include is common which by business bars. inis denoted Shanghai hours, by' i.e. that bars. from an employee needs to0 spend Max (∑∑α i zh ij + ∑∑ ( α h i z ij ))1 −− w ( v x jj + ∑∑ f j x − jj )( + ∑ fx x jj ) , 9:00am to 5:00pm, and some transit time between the workplace and living place. It is 0 0 In order to reflect a real problem, great effort was ∈∈MiNotingaround Nj thattwo∈∈ theMior Nj threeworking hours hours on definedcommutation∈Nj in this∈Nj eachstudy day. include In business j ∈ / NN hours, i.e. from common in Shanghai thatNoting an employee that the workingneeds to hoursspend definedaround intwo this or studythree includehours on business hours, i.e. from put into investigating the census, i.e. the demographicNotingSubject that to:9:00am otherthe working words, to 5:00pm, hourshe/she anddefined spends some inapproximate transit this study time between includeone-third businessthe of workplace his/ hours, and i.e. livingfrom place. It is zha h yearbooks≤ Cz x andcommutation reports released a each h ∈∀ byday.≤Nj Cz the, In9:00amx city other medical towords, 5:00pm, services he/she9:00am and spends some to∈∀ (3)5:00pm,Nj commonher transitapproximate, time and time inon Shanghaisome workbetween one transit inthird thateachthe oftime workplacean his/herweek. employeebetween(3) Hence, and the needs living workplacewithout to place. spend loss and It aroundisof living twoplace. or Ithreet is hours on ∑ ij i ij jj ∑ ij i ij jj z ≤1 ∈∀ Mi , (1) ∈Mi authority. Parameter ∈valuesMi in this casecommon study inare Shanghai givencommon∑ on that ij in ancommutation Shanghai employee that needs each an1 employeeday.to spend In other aroundneeds words, totwo spend he/she or three around spends hours two approximate on or three hours one third on of his/her time on I)work with in periodic each week. change Hence,s in without demands ∈lossNj of II) generality,generality, without periodicα = waschangewas set. set.s in demands ' the basis of the investigation.' commutation each day. In other words, he/she3 spends approximate one third of his/her zha h ≤ Cz x a h ∈∀ ≤Nj Cz , x commutation∈∀ (4)Nj ,each day. In other words, he/she(4) spends approximate one third of his/her1 ∑ i ijij jj ∑ i ijij jj time on work in each week. Hence, without loss of generality, α = was set. When deciding the value of N , anotherij ≤ common i n { az ij ,m x When jpractice} deciding that ambulances the ∀ value Mi are, of ∈∈ Nj , another common(2) 3 ∈Mi ∈Mi time on work in timeeach onweek. work Hence, in each without week. lossHence, of generality, without loss α of= generality,1 was set. α = 1 was set. 4.1. Data inputoften stationedFigure in hospitals 2. Results or ofmedical locations centres of emergency in Chinesepractice medical citiesthat ambulances was sites noted. when areHence,w =often0. 1. stationed3 in hospitals3 ∑ a ij h i∑ij a ≤≤ij Cz h i x ijjj f ≤ (0 Cz x 0x −jj ) + fx x ∈∀ ≤≤Nj TC, ∈∀ , f Nj (0 x ,0 − ) + fx x (3)≤ TC , (3)(5) When deciding the value(5) of N , another common practice that ambulances5 are ∈Mi ∈Mi ∑ j jj after∑ investigatingjj ∑ j all possible jj locations∑When decidingjj to set theup orvaluenew medical emergencyof N , centresanother medical incommon Chinese sites practice incities thatwas ambulances noted. Hence, are ∈Nj 0 j ∈ / NN 0 ∈Nj 0 j ∈ / NN 0 Whenoften deciding stationed the in value hospitals of N , oranother medical common centres practice in Chinese that ambulances cities was arenoted. Hence, The eightcentral districts Shanghai, in the centralthere regionwere 146of Shanghai candidates (Appendixafter investigating 1). In allother possible words, locations to set up new zha h ' a ≤ Cz h ' x ≤ Cz x ∈∀ Nj , ∈∀ Nj , often stationed inoften(4) hospitals stationed(4)after or medical ininvestigating hospitals centres or all medicalin possible Chinese centres locationscities in was Chinese to noted.set upcities Hence, new was emergency noted. Hence, medical sites in ∑ i∑ijij i ijij jj consistjj of 76 sub-districts, and these sub-districts are emergency medical sites in central Shanghai, there ∈ ∈Mi x ∈{0,1} 0 x ∈{0,1}∈∀ Nj , after investigatingafter all investigating possible∈∀ (6)Nj central, locations allShanghai, possible to set there locationsup new were emergency(6)to 146set upcandidates newmedical emergency sites(Appendix in medical 1). sitesIn otherin words, Mi j regarded as demandN = 1{ ,..., nodesj 33}, andin this N study.= 1{ ,... 33Noting,34,..., 179that} .the were 146 candidates (Appendix 1). In other words, 0 0 central Shanghai,central there Shanghai, were 146 there candidates were 146(Appendix candidates 1). (AppendixIn other words,1). In other words, 0 ≤ ∑ f ≤ j (0 x ∑− f j (0 jj x ) Chinese+− ∑jj ) + fx governmentx ∑jj The≤ TC fx valuesx ,jj ≤conductsTC of ,parameters the population were determined census every(5) by referring(5)N = to1{ the,..., 3312th}, and five-year N = 1{ plan,...33 on,34 ,...,179}.. 0 z ∈ 0{0,1} 0 0 z ∈{0,1} 0 . 0 (7) . (7) ∈Nj ij ∈Nj 10 j years,∈ / NN and j ∈ / NN thereforeij the ∀ most Mi completed, N∈∈ =Nj 1{ ,..., data33} , forandN the =N ∀ 1{ =,...,1{ Mi 33,...}33,, and,34∈∈ ,...,Nj N179=}1{ .,... 33,34,...,179}. the development of Shanghai emergency medical servicesThe values (Shanghai of parameters Municipal were determined by population is updated only till 2011. The demographic The values of parameters were determined by referring to the 12th five-year plan on x ∈{0,1}x ∈ {0,1} Commission ∈∀ Nj ,of ∈∀ HealthNj , andThe Familyvalues Planning,of parametersThe(6) values 2013).(6) were thereferring of In parameters determineddevelopmentthis plan,to the thewere 12thby standardof referring determined five-yearShanghai for to the theplanbyemergency 12threferring on the five-year development medicalto the plan 12th services on five-yearof (Shanghai plan on Municipal j j yearbook 2011 in Shanghai districts (Statistics Department, Shanghai emergency medical services (Shanghai Municipal The objective of thiscovering modelThe radiusis toobjective maximise of each thesiteof thethis isdevelopment 5 coverage modelkilometers, theis ofto and development emergencyShanghaimaximise thusCommission the emergencyvalue theofservices, Shanghaicoverageof of a Health medicalwasi.e. emergencyofdetermined. and emergency services Family medical Planning,(Shanghai services, services 2013). Municipal i.e. (ShanghaiIn this plan, Municipal the standard for the 2011a-2011h) was referred, and data were input to Commission of Healthij and Family Planning, 2013). In this ' Commission of 'HealthCommission and Family of Health Planning, and Family 2013). Planning, In this plan, 2013). the Instandard this plan, for thethe standard for the zij ∈{0,1}zij ∈ {0,1} ∀ Mi , ∀ , while∈∈ Mi Nj ,. minimising∈∈ Nj . the (7)total, while cost(7)covering minimisingof providing radius theof theeach total site cost is 5 kilometers,of providing and thusthe the value of was determined. ∑∑α ithezh ij +parameters∑∑By ( − referringofα)1 ∑∑i .zh ijThe toα thevaluesi zh populationij + of∑∑ parameter in ( the−α central)1 i zh wereij region andplan, the the standard standard of forthe theambulance covering radius of each site is aij ∈∈Mi Nj ∈∈Mi Nj ∈∈Mi Nj covering∈∈Mi Nj radius of each site is 5 kilometers, and thus the value of was determined. estimated by referring to the report on the occupationalcovering radiusfive ofkilometers, each site isand 5 kilometers,thus the value and thusof aij thewas value determined. of aij was determined. service, the capacity of a service site should coverBy areferring population to the of populationno more thanin the central region and the standard of the ambulance composition of the employed0 population in Shanghai0 By referring to the population in the central region and the services, i.e. v x jj + ∑∑ services, f j x − i.e.jj )( + By∑ v referring fx x jj x +jj . ∑∑ to f theBy j x populationreferring− jj )( + to in ∑the the population fx centralx jj . region in the and central the standard region and of16 the the ambulancestandard of the ambulance The objectiveThe objective of this ofmodel this modelis250,000, to maximise 0is i.e.,to maximise C the= 25 coveragewas the set 0 coverage forof eachemergency0 of j. emergencyAccording services,service, toservices, the0i.e.the criteria capacity i.e. for of setting a service up site should cover a population of no more than districts∈Nj (Statistics∈Nj Department,j 2009). j ∈ Nj / AccordingNN ∈Nj to these standard j ∈ / NN of the ambulance service, the capacity of a service service, the capacityservice, of thea service capacity site of should a service cover site a shouldpopulation cover of ano population more than of no more than ' , while' , whileminimising minimising the total the costtotal of cost providing 250,000,ofsite providingshould thei.e., cover Cthe =a 25populationwas set forof noeach more j. Accordingthan 250,000, to the criteria for setting up ∑∑α∑∑ i zh ij +α∑∑i zh ijvalues+ ( ∑∑− αof)1 ( i emergencyzh −andijα)1 i ,zh ija figure medical for sitesthe populationin Shanghai change (Statistics in Department, 2003),j the cost for ∈∈Mi Nj ∈∈Mi Nj ∈∈Mi Nj ∈∈Mi Nj 250,000, i.e., C250,000,= 25 was i.e., set Cfor= each25 was j. Accordingset for each to j.the According criteria forto thesetting criteria up for setting up The servicesub-districts level is measured buildingis outlinedThe a bynewto service demonstratea siteweighted is level between the summationis measuredmajor one million feature of jby andthe of a weighted1.5population, million,i.e. j summation while e.g., was theα set operational isoffor the each population, j .cost According e.g., to the α criteria is for 0 0 emergency medical sites in Shanghai (Statistics Department, 2003), the cost for services,services, i.e. i.e. v the x periodic+ v x f +change x − f in x )( demand.+− )( + fx x . fx x . setting up emergency medical0 sites in Shanghai (Statistics the weight forjj ∑∑ thejj population j is ∑∑ one j thequarter.jj ofweight ∑ demandjj Hence, for∑jj emergency withoutthenodes populationjj duringloss medical ofemergency working generality,of sites demand in buildinghours.medical Shanghailet nodes f Inasites new= order10during(Statistics siteinfor Shanghai to is working between ∈Department,Nj , (Statistics andonehours. million 2003), InDepartment, andorder the 1.5 costto million, 2003),for while the thecost operational for cost ∈Nj ∈Nj As∈ Nj shown0 ∈ Nj in0 Figure 1, j ∈ a /netNN 0 outflow j ∈ / NN 0 of the population Department,j 2003), the cost for building a new site is analyse the impact of the analyseobjective the function impactbuilding onof a thenewsolutions, objectivesitebuilding is betweenw a functionnewas aone site weight millionis on between solutions,to and the one1.5 million,million w as andwhile a 1.5weight the million, operational to whilethe costthe operational cost 0 in working hours is represented by crosses, while triangles is one quarter. Hence, without loss of generality, let f = 10 for , and 0 between one million and 1.5 million, while the operational j ∈ Nj f = 100 for ∈ / NNj , and let v = 25 for each ∈ Nj . In the 12th five-year 0 0 second part of the objectivej secondwas introduced. part of isthe one objective quarter.j was isHence, one introduced. quarter.without Hence, loss of without generality, loss letof generality,f j = 10 for let ∈f Nj =,10 and for ∈ Nj , and The serviceThe service level is level measured is measured by a weighted by a weighted summation summation of the population,of the population, e.g., α e.g., is α is j 0 plan (Shanghai Municipal Commission of Health andf j = Family100 for Planning, ∈ / NNj 2013),, and thelet v j = 25 for each ∈ Nj . In the 12th five-year the weightthe weight for the for population the population of demand of demand nodes nodesduring duringworking for working hours.0 ,hours. Inand order let In toorder 0 tofor each . In the 12th five-year Constraint012 (1) ensures that Constrainteach demand (1) nodeensuresf j = 100is servicedthat each∈f j by= demand/100 NNj at mostfor node one∈ visemergency/j NNj =serviced25, and let by v atj = most∈25Nj for one each emergency ∈ Nj . In the 12th five-year analyseanalyse the impact the impact of the ofobjectiveauthority the objective wouldfunction establishfunction on solutions, or on reconstruct solutions, w fiveas a wor weight asless plana emergency weight to(Shanghai the to medical theMunicipal facilities Commission in of Health and Family Planning, 2013), the service site. Constraintthe (2)central statesservice region that site. of a Shanghai. demandConstraintHKIE Thus,node Transactions (2) the i statescannot budget | thatVolume be limit aserviced 26,demand TC Number is 500. by 1,node pp.9–19 a s itei cannot j, be serviced by a site j, secondsecond part of partthe objectiveof the objective was introduced. was introduced. plan (Shanghai planMunicipal (Shanghai authorityCommission Municipal would of CommissionHealthestablish and or Familyreconstructof Health Planning, andfive Familyor 2013), less Planning,emergency the 2013), medical the facilities in when the node is not coveredwhen by the the node serviceauthority is not of wouldcoveredj or the establish byemergency the or service reconstruct service of j five isor notorthe less emergency emergency service medical isfacilities not in authority wouldthe central establish region or ofreconstruct Shanghai. five Thus, or theless budget emergency limit TCmedical is 500. facilities in positioned at j. 4.2. Resultspositioned and Discussions at j.the central regionthe of central Shanghai. region Thus, of Shanghai.the budget Thus, limit theTC budgetis 500. limit TC is 500. ConstraintConstraint (1) ensures (1) ensures that each that demand each demand node is node serviced is serviced by at mostby at one most emergency one emergency 4.2. Results and Discussions serviceservice site. Constraint site. Constraint (2) states (2) thatstates a demandthat a demand node i nodecannot i cannotbe serviced be serviced by a s iteby ja, site j, Constraints (3) and (4) ensureConstraintsIn thatorder the to assignment analyse(3)4.2. and Resultsthis (4) problem ofensure anddemands4.2. Discussions thatmore Results thei comprehensively,to assignment j and cannot Discussions exceed of four demands the instances i to with j cannot exceed the when thewhen node the isnode not iscovered not differentcovered by the settings byservice the wereservice of j tested,or of the j i.e.oremergency thew = emergency1.0 , αservice= 1 service withis notIn Constraintsorder is not to analyse (1) -this (7), problem more comprehensively, four instances with capacity of j. Constraint (5)capacity gives the of budget j. Constraint limitations (5) gives on se thetting budget up3 new limitations emergency on setting up new emergency positionedpositioned at j. at j. In order to analyseIn order this problemto analyse more this comprehensively, problem more comprehensively, four instances with four instances with service sites and removing theservice service sites from and some removing existing the sites.service fromdifferent some settings existing were sites. tested, i.e. w = 1.0 , α = 1 with Constraints (1) - (7), 1 3 w = 1.0 , α = 0 with differentConstraints settings (1) different- were(2) and tested,settings (4) i.e.- were(7), w =wtested,=1.0 1,,αα i.e.==1 w with=with1.0 ,Constraintsα = 1 with (1) Constraints- (7), (1) - (7), 33 3 ConstraintsConstraints (3) and (3) (4) and ensure (4) ensurethat the that assignment the assignment of demands of demands i to j cannot i to j cannotexceedw = 1.0 exceed ,theα = 0 the with Constraints (1) - (2) and (4) - (7), w = 1 , α = 1 with Constraints (6) and (7)Constraints are theConstraints integrality (1) - (7), and(6) constraints. andw = (7)1,α are= the0 withintegrality Constraints constraints. (1) - (2) and (4) - (7). 3 capacitycapacity of j. Constraint of j. Constraint (5) gives (5) the gives budget the budget limitationsw limitations= 1.0 on, α se=tting on0 w sewithup=tting new 1.0 Constraints, αup emergency= new0 withemergency (1) Constraints- (2) and (4)(1) - (7),(2) andw = 1(4), α -= (7),1 withw = 1 , α = 1 with 3 3 serviceservice sites and sites removing and removing the service the service from some from existing some existing sites. sites. Constraints (1) - (7), and w = 1,α = 0 with Constraints (1) - (2) and (4) - (7). In the above mixed integer More specifically, Inand the linearConstraints above the programming mixedsetting (1) -integerConstraints (7),w = and formulation,1.0 and impliesw (1)= linear1 ,-α (7),that= Constraints programmingand 0the with designw = Constraints1, α in = Instanceformulation,0 with(1) I- Constraints (2) and Constraints (4) -(1) (7). - (2) and (4) - (7).

(3) and (4) are introducanded II isin(3) service-oriented, consideration and (4) are introduc ofbut the changes time-dependented inin considerationdemand would feature notof theofbe More considered demand.time-dependent specifically, in Instance the feature setting ofw demand.= 1.0 implies that the design in Instance I ConstraintsConstraints (6) and (6) (7) and are (7)the are integrality the integrality constraints. constraints. More specifically, the setting w = 1.0 implies that the design in Instance I Constraint (3) refers to theConstraint population (3) whichrefers couldto the benefit population from Moreand which IIthespecifically, is service-oriented,emergency could the benefit setting but from wchanges=8 the1.0 impliesin emergency demand that would the design not be in considered Instance I in Instance

medical services during businessmedical hours. services and during II is service-oriented, businessand IIhours. is service-oriented, but changes in demand but changes would in not demand be considered would not in be Instance considered in Instance In the aboveIn the abovemixed mixedinteger integer and linear and programminglinear programming formulation, formulation, Constraints Constraints 8 8 8 (3) and(3) (4) and are (4) introduc are introduced in considerationed in consideration of the oftime-dependent the time-dependent feature feature of demand. of demand. Constraint (4) considers theConstraint number of (4)citizens considers which the could number be serviced of citizens during which leisure could be serviced during leisure ConstraintConstraint (3) refers (3) refersto the topopulation the population which whichcould couldbenefit benefit from thefrom emergency the emergency time. These two constraints,time together. These with two the constraints, objective togetherfunction, with achieve the objectivethe goal offunction, achieve the goal of medicalmedical services services during duringbusiness business hours. hours. maximising the overall servicemaximising level under the budget overall restrictions. service level under budget restrictions.

ConstraintConstraint (4) considers (4) considers the number the number of citizens of citizens which whichcould becould serviced be serviced during duringleisure leisure Noting that a simple set coverageNoting thatproblem a simple is a classicset coverage NP-complete problem problem is a classic (Gary NP -complete problem (Gary time. Thesetime. Thesetwo constraints, two constraints, together together with the with objective the objective function, function, achieve achieve the goal the of goal of and Johnson, 1979). In theand literature, Johnson, various 1979). algorithms In the literature, and heuristics various havealgorithms been and heuristics have been maximisingmaximising the overall the overall service service level under level budgetunder budget restrictions. restrictions. 6 6 NotingNoting that a thatsimple a simpleset coverage set coverage problem problem is a classic is a classicNP-complete NP-complete problem problem (Gary (Gary and Johnson,and Johnson, 1979). 1979).In the Inliterature, the literature, various various algorithms algorithms and heuristics and heuristics have beenhave been

6 6

aa fewfew sub-districtssub-districts whichwhich isis denoteddenoted byby bars.bars. a fewfew sub-districtssub-districts whichwhich isis denoteddenoted byby bars.bars. a few sub-districts which is denoted by bars. a fewfew sub-districtssub-districts whichwhich isis denoteddenoted byby bars.bars. NotingNoting thatthata few thethe sub-districts workingworking hourshours which defineddefined is denoted inin thisthis by studystudy bars. includeinclude businessbusiness hours,hours, i.e.i.e. fromfrom

a few sub-districts whicha ais fewfew denoted sub-districtssub-districts by bars. whichwhich isis denoteddenoted9:00am9:00am byby bars.bars. toto 5:00pm,5:00pm, andand somesome transittransit timetime betweenbetween thethe workplaceworkplace andand livingliving place.place. IItt isis a few sub-districtsNoting that which the isworking denoted hours by bars. defined in this study include business hours,Noting i.e. that from the working hours defined in this study include business hours, i.e. from Noting that the working hours defined in this study include business hours, i.e. from commoncommon inNotingin ShanghaiShanghai that the thatthat working anan employeeemployee hours needsneedsdefined toto in spendspend this aroundstudyaround include twotwo oror business threethree hourshours hours, onon i.e. from 9:00am to 5:00pm, and some transit timetime between the workplace and living9:00am place. to 5:00pm, Itt isis and some transit time between the workplace and living place. It is 9:00am to 5:00pm, and someNoting transit thattimetime the between working the Noting Notinghoursworkplace defined thatthat and thethe in livingworkingworking this studyplace. hourshours includeItt isisdefineddefined commutationcommutation business inin thisthis9:00am hours, studystudy eacheach to i.e. includeday.includeday. 5:00pm, from InIn otherbusinessother business and words, words,some hours,hours, transit he/shehe/she i.e.i.e. time spendsfromspendsfrom between approximateapproximate the workplace oneone thirdthird and ofof living his/herhis/her place. It is Noting thatcommon the working in Shanghai hours definedthat an inemployee this study needs include to spend business around hours, twotwo i.e. oror commonfromthreethree hourshours in Shanghaionon that an employee needs to spend around two or three hours on common in Shanghai that an9:00am employee to 5:00pm, needs to and spend some9:00am9:00am around transit toto 5:00pm,twotwo5:00pm, time oror between threethree andand somehourssomehours the workplace transit transitonon timetime and betweenbetweencommon living thetheplace. in workplaceworkplace Shanghai It is and andthat livingliving an employee place.place. IItt needsisis to spend around two or three hours on 9:00am tocommutation 5:00pm, and someeach day. transit In timeother between words, he/she the workplace spends approximate and livingtimetimea few onplace.on one workworksub-districts commutationthird It inisin of eacheach his/her whichweek.week. each Hence,isHence, day. denoted In withoutwithout other by bars.words, lossloss ofof he/she generality,generality, spends αα approximate== 11 waswas set.set.one third of his/her commutation each day. In othercommon words, in he/she Shanghai spends that commoncommonapproximate an employee inin ShanghaiShanghai one needs third tothat thatof spend his/her anan employeeemployee around two needsneeds orcommutation threetoto spendspend hours aroundaround each on day. twotwo In oror other threethree words, hourshours he/sheonon spends approximate33 one third of his/her common in Shanghai that an employee needs to spend around two or three hours1 on timetimecommutation onon workwork inin each eacheach day. week.week.a few Incommutationcommutation otherHence, Hence,sub-districts words, withoutwithout eacheach he/shewhich lossloss day.day. spends isofof InIn denoted generality,generality, otherother approximate words,words,by bars. α =he/she he/she oneWhenWhentime was wasthirdspendsspends decidingon deciding set.set. of work approximate approximatehis/her in thethe each valuevalue week. oneone ofof NthirdNthird Hence,,, anotheranother ofof his/herhis/her without commoncommon loss practice practiceof generality, thatthat ambulancesambulances α = 1 was areare set. time on work in eachcommutation week. Hence, each withoutday. In otherloss of words, generality, he/she αspends= 1 approximate was set. one thirdNoting of his/her3 timethat onthe work working in each hours week. defined Hence, in thiswithout study loss include of generality, business αhours,= 1 3i.e. was from set. time on work in each week. Hence, without loss of generality, α = 3 was set. 3 When deciding thetimetime value onon ofworkworkN ,, inanotherinanother 3 eacheach week. week.commoncommon Hence,Hence, practicepracticeoftenoften withoutwithout thatthatstationedstationed1 loss lossambulancesambulances ofof in ingenerality,generality, hospitalshospitals areare αorαor = =medicalmedical11 waswas centrescentres set.set. inin ChineseChinese citiescities waswas noted.noted. Hence,Hence, time on work in each week. Hence, without loss of generality,1 9:00amα = to was5:00pm, set. When and deciding some transit the33 valuetime betweenof N , another the workplace common andpractice living that place. ambulances It is are When decidingtime on the work value in eachof N week.,, anotheranother Hence, commoncommonNoting without thatpracticepractice loss the of workingthatthat generality, ambulancesambulances hours α defined =areare afterafter wasin this investigating investigatingset. study 3 include When allall possiblebusinesspossible deciding locationshours,locations the value i.e. to to fromof setsetN ,up upanother newnew emergencycommonemergency practice medicalmedical that sitessites ambulances inin are often stationed in hospitals or medical centres in Chinese3 citiescommon wasoften noted.in Shanghai stationed Hence, that in hospitalsan employee or medicalneeds to centres spend aroundin Chinese two citiesor three was hours noted. on Hence, 9:00am to 5:00pm, WhenWhen deciding decidingand some thethe transit valuevalue time ofofNN between,, anotheranotheroften the commoncommon stationed workplace practicepractice in and hospitals living thatthat ambulancesambulances place.or medical It is areare centres in Chinese cities was noted. Hence, often stationed in hospitals Whenafter or medical decidinginvestigating When centres the deciding value all in possible ofChinese theN ,value another locations cities of Ncommon was, anotherto noted.set practice up common Hence,new that emergency practice centralambulancescentral that Shanghai,Shanghai,medical ambulances are sites therethere inare werewere 146146 candidatescandidates (Appendix(Appendix 1).1). InIn otherother words,words, common in Shanghai that an employee commutationneeds toafter spend investigatingeach around day. twoIn otherall or possiblethree words, hours he/shelocations on spends to set approximate up new emergency one third ofmedical his/her sites in after investigating all possibleoften locations stationed to inset hospitals up newoftenoften oremergency stationed stationedmedical centresinmedicalin hospitalshospitals in sites Chinese oror in medicalmedical cities00 centrescentres wasafter noted. inininvestigating ChineseChinese Hence, citiescities all possiblewaswas noted.noted. locations Hence,Hence, to set up new emergency medical sites in often stationedcentral in Shanghai,hospitals orthere medical were centres 146 incandidates Chinese cities(Appendix was noted. 1).== InHence, centralother,, andand words,Shanghai, NN == 1{ 1{ ,...,... 3333there,,3434,..., ,...,were179179} }.. 146 candidates (Appendix 1). In other words, commutationafterafter investigatinginvestigating each day. all allIn otherpossiblepossible words, locationslocationsNN he/shetime 1{ 1{ onto,..., to,...,spendscentral workset33set33} } upup approximate in Shanghai,new neweach emergency emergencyweek. onethere Hence, third medicalmedicalwere withoutof his/her146 sitessites loss candidates inin of generality, (Appendix α = 1 1). was In set. other words, central Shanghai,after there investigating wereafter 146investigating all candidatespossible all locations (Appendixpossible to locations set1). up In new toother set emergency upwords, new emergencymedical sites medical in sites in a few sub-districts which is denoted3 by bars. N 00 = 1{ ,...,,...,33},, andand N = centralcentral1{ ,...,...33,, 34 Shanghai,Shanghai,,...,,...,179}.. therethere werewere 146146 candidatescandidates0 (Appendix(Appendix 1).1). InIn otherother words,words, 00 central Shanghai, theretime onwere work 146 in eachcandidates week. Hence, (Appendix withoutTheThe values1).values loss In ofN of0of generality,other parameters=parameters1{ ,...,words,33 },α andwerewere = 1 N determineddetermined =was1{ ,... set.33 , 34 byby ,..., referringreferring179}. toto thethe 12th12th five-yearfive-year planplan onon N = 1{ ,...,,...,33},, andandcentral N = Shanghai,1{ ,...,...33,,34,..., ,...,there179} .. were 146 candidates (Appendix 1). In other words,N When= 1{ ,...,deciding33}, and the valueN3 = 1{ of,...N33,, 34another,...,179 common}. practice that ambulances are 0 00 thethe developmentdevelopment ofof ShanghaiShanghai emergencyemergencyNoting thatmedicalmedical the working servicesservices hours (Shanghai(Shanghai defined MunicipalMunicipal in this study include business hours, i.e. from 0 TheN values= 1{ ,..., of33 parameters}, and N = wereNN1{ ,...== 33determined1{ 1{ ,,...,34,...,,...,3333}179},, andand }by. referringNN == 1{ 1{ ,...,... 3333to, ,3434the,...,,..., often12th179179 } }five-yearstationed.. The values planin hospitalsof on parameters or medical were determinedcentres in Chineseby referring cities to wasthe 12thnoted. five-year Hence, plan on The values of parametersN = 1{ ,..., were33} ,determined and N = 1{ by,... 33referring, 34 ,..., 179 to When }the. 12th deciding five-year the valueplan onof NCommissionCommission, anotherThe common of ofvalues HealthHealth practice of andandparameters FamilyFamilythat ambulances Planning,werePlanning,9:00am determined are to 2013).2013). 5:00pm, InbyIn this thisreferringand plan,plan,some theto thetransit the standardstandard 12th time five-year betweenforfor thethe theplan workplace on and living place. It is thethe developmentdevelopment ofof ShanghaiShanghai emergencyemergency medicalmedical servicesservices after(Shanghai(Shanghai investigatingthe developmentMunicipalMunicipal all possible of Shanghai locations emergency to set up newmedical emergency services medical (Shanghai sites Municipalin thethe developmentdevelopment ofof ShanghaiShanghaiThe emergencyvaluesemergency of parameters medicalmedicaloften The The services wereservicesstationed valuesvalues determined (Shanghai (Shanghai ofofin parametersparametershospitals by MunicipalreferringMunicipal or werewere medical determinedtodetermined the centres 12th thefive-yearby byin referringreferringChinesedevelopment plan totocities on thethe of 12thwas12th Shanghai noted.five-yearfive-yearcommon Hence,emergency planplan in ononShanghai medical that anservices employee (Shanghai needs toMunicipal spend around two or three hours on The valuesCommission of parameters of Healthwere determined and Family by Planning, referring 2013).to the In12th this five-year coveringplan,coveringcentral the plan radiusstandardradiusCommissionShanghai, on ofof foreacheach thethere of sitesite Health isiswere 55 kilometers,kilometers, and 146 Family candidates andand Planning, thusthus thethe(Appendix 2013). valuevalue ofofIn this1).aaijij waswas plan,In determined.determined.other the standardwords, for the Commission of Health and Familythe development Planning, 2013).of afterShanghai Inthethe investigatingthis developmentdevelopment plan,emergency the allstandard ofof possiblemedical ShanghaiShanghai for locations theservices emergencyemergency to(Shanghai setCommission medicalupmedical new Municipal emergencyservicesservices of Health (Shanghai(Shanghai medical and commutationFamily sitesMunicipalMunicipal Planning,in each 2013). day. In In other this words,plan, the he/she standard spends for approximate the one third of his/her the development of Shanghai emergency medical services (Shanghai 0Municipal covering radius of eachcentral siteCommissionCommission isis 55Shanghai, kilometers,kilometers, ofof HealthHealththere andand thusthus wereandand thethe FamilyFamily 146 valuevalue candidatesPlanning,Planning, ofof aijijwascovering 2013). 2013). determined.(Appendix In Inradius thisthis 1).plan,ofplan, eachIn thethe siteother standardstandard is 5words, kilometers, forfor thethe and thus the value of a was determined. CommissionCommission of Health and of HealthFamily and Planning, Family 2013). Planning, In this 2013). plan, In the this standardByBy plan, N referringreferring =the forcovering1{ ,...,standard the toto33 thethe}, and radius population populationfor theN of= each1{ ,... inin33 thesitethe,34 central centralis,..., 5179 kilometers, }regionregion. andand and thethe thus standardstandard the value ofof thethe of ambulanceambulancea ijwas determined. 1 covering radius of each site isis 55 kilometers,kilometers, andand thusthus thethe valuevalue ofof aijijwas determined. time on work in each week. Hence, withoutij loss of generality, α = was set. 0 3 By referring to the populationcoveringcovering in the radiusradius central ofof region eacheach sitesite and isis the 55 kilometers, kilometers,standardservice,service, ofthethe and andthe capacitycapacity thusthusambulance thethe of ofvaluevalue a a serviceservice ofof aa waswassitesite determined.determined.shouldshould covercover aa populationpopulation ofof nono moremore thanthan covering radius of eachN site= is1{ ,..., 5 33kilometers,}, and N and= 1{ thus,...33 the,34 ,...,value179The }of. values aijBywas referringof determined. parameters to the werepopulation ijijdetermined in the by central referring region to andthe 12ththe standard five-year of plan the ambulanceon By referring to thecovering population radius in ofthe each central site regionis 5 kilometers, and the standard and thus of the the value ambulance of aij was determined.By referring to the population in the Whencentral deciding region and the thevalue standard of N , anotherof the ambulance common practice that ambulances are By referring to the populationservice,service, in the thethe central capacitycapacity region ofof and aa serviceservice the standard sitesite a should should fewof the sub-districts ambulancecovercover aa populationpopulation which 250,000,250,000,the is denoteddevelopment ofof i.e.,i.e., nono moreCmorebyC bars.== 2525thanofthan waswas Shanghai setset forfor emergency eacheach jj.. AccordingAccording medical totoservices thethe criteriacriteria (Shanghai forfor settingsetting Municipal upup TheByBy values referringreferring of parameters toto thethe populationpopulation were determined inin thethe centralcentral by referring regionservice,region jandjand tothe thethe capacity standard12thstandard five-year of of ofa thetheservice planambulanceambulance onsite should cover a population of no more than service,service, thethe capacitycapacity ofof aa serviceserviceBy referring sitesite shouldshould to the populationcovercover aa populationpopulation in the central ofof nono region moremore and thanthan the standard service,of the ambulance the capacity of a serviceoften stationed site should in hospitals cover a orpopulation medical centresof no more in Chinese than cities was noted. Hence, By referring250,000, to the populationi.e., C = 25in thewas central set forfor region eacheach andjj.. AccordingAccording the standard toto ofthethe the Commissioncriteriacriteria ambulance forfor settingsetting of Health upup and Family Planning, 2013). In this plan, the standard for the service, the capacityjj theof service,service,adevelopment service thethe site capacitycapacity ofshould Shanghai ofofcover aa serviceservice emergencya populationemergencyemergency sitesite should shouldmedical of250,000, medicalmedical no covercover moreservices i.e.,a asites sites thanpopulationpopulation C (Shanghai injin= ShanghaiShanghai25 wasofof afterno noMunicipalset (Statisticsmore(Statisticsmore forinvestigating eachthanthan Department, Department,j. According all possible 2003),2003),to locationsthe thecriteriathe costcost to for setforfor setting up new up emergency medical sites in 250,000, i.e., Cservice,= 25was the set capacity forfor eacheach of jja.. AccordingAccordingservice site to toshould thethe criteriacriteria coverNoting forfora populationthat settingsetting the workingupup of no hoursmore250,000, definedthan ini.e., this C studyj = 25 includewas set business for each hours, j. According i.e. from to the criteria for setting up C jj = 25 Commission of Health and Family Planning,covering 2013). radius In thisof each plan, site the is standard 5 kilometers, for the and thus the value of a was determined. emergency medical sites 250,000,250,000,in Shanghai i.e.,i.e.,9:00am (StatisticsCC == 25 25to waswas5:00pm, Department, setset forforandbuildingbuilding eacheachsome 2003), j j .transit .a a According Accordingnewnew the timesite sitecost is isbetween tobetweentoforbetween thethe criteriathecriteria oneone workplace millionmillion forcentralfor settingsetting andand Shanghai, 1.5 1.5living upup million, million, place. there whilewhile It iswere thethe operationaloperationalij146 candidates costcost (Appendix 1). In other words, 250,000, i.e., C j = 25 was set for each jj. According to the criteriaemergency for setting medical up sites in Shanghai (Statistics Department, 2003), the cost for 250,000, i.e., C j = 25 was set for each j. According to the criteria for settinga few up sub-districts which is denoted by bars. emergency medical sites in Shanghai (Statistics Department, 2003), the cost for emergency medical sites in Shanghai0 (Statistics Department, 2003),00 the cost for building a new site is betweencovering one radius million ofcommon each and site 1.5 in ismillion,Shanghai 5 kilometers, whileisis that Byoneone anthereferringand quarter. quarter. employeeoperational thus tothe Hence, Hence,the valueneeds costpopulation ofwithout withoutto spendaij was in loss loss around thedetermined. centralofof twogenerality,generality, regionor three andlet lethours theff standardon==1010 forfor of the∈∈ Nj Nj ambulance,, andand emergencyemergency medicalmedical sitessites inin ShanghaiShanghai (Statistics(Statistics building Department,Department, a new site is 2003),2003), between N thethe one= costcost1{ ,...,million 33forfor} , andand 1.5N j =jmillion,1{ ,...33 ,34while,...,179 the} operational. cost building a new site is betweenemergency one million medical and 1.5 sites million, in Shanghai while thecommutation (Statisticsoperational eachDepartment, cost day. In other2003),building words, the ahe/shecost new for sitespends is between approximate one million one third and of 1.5 his/her million, while the operational cost emergency medical sites in Shanghaicost (Statistics is one quarter.Department, Hence, 2003), without service,the losscost theoffor generality,capacity 00 of a servicedependent site shoulddemands cover of ambulancea population services. of no more It is thanworth 0 isis oneone quarter.quarter. Hence,Hence,By without withoutbuildingreferringbuilding loss loss aato newnew the ofof site populationsitegenerality,generality, isis betweenbetween in let letthe one one centralff jj millionmillion= 10 region forfor andandNoting 1.5and1.5∈ Nj million, thatmillion,the,, standardandtheand whileworkingwhile of thethe the hours operationaloperational ambulance defined costcost in this study include business hours, i.e. from building a new site is between one million and 1.50 0million, while the isoperational one quarter. cost00 Hence, withoutThe values loss ofof parametersgenerality, were let determinedf j = 10 for by referring∈ Nj 0 , and to the 12th five-year plan on building a new site is between one million and 1.5 million, while the operationalff ==100100 is for for costone ∈∈quarter.//NNj NNj ,, Hence, andand mentioningletlet without vv ==2525 loss the forfor results ofeacheach generality, in∈ ∈IINj Nj and.. InInlet III thethe thatf j 12th12th= the10 five-yearfive-yearsolutionsfor ∈ Nj are, and isis oneone quarter.quarter. Hence,Hence, withoutwithout lossloss ofof generality,generality, letlet ff jj = 10time forforfor on work∈ Nj ,in, and andeach week.jj Hence, 9:00amfor without to 5:00pm, loss, of and generality, somejj transit α = time1 wasbetween set. the workplace and living place. It is service, the capacity of a service site 250,000,should cover i.e., aC populationj0 = 25 was ofset nofor themore each development thanj00. According of toShanghai the criteria emergency for setting medical up services (Shanghai Municipal 00 isis oneone quarter.quarter. Hence,Hence, withoutwithout lossloss ofof generality,generality, letlet ff ==1010exactly forfor the∈∈ same,, and3and with existing emergency service sites in is one quarter. Hence, without loss of generality, let f j = 10 0for ∈ Nj , andj j 0 Nj Nj is one quarter.ff jj = 100 a Hence,few forfor sub-districts without∈ // NNj losswhich,, andandand of is letlet letgenerality,denoted v jj = 25by letbars.forforfor eacheachf j = 10 ∈forNj .. InIn∈ theNj the common, 12th12thand five-yearfive-year in for Shanghai that0 ,an and employee let needs for to spendeach around. twoIn theor three12th hoursfive-year on 00 250,000, i.e., C = 25 was set for eachplanplan j .(Shanghai (ShanghaiAccordingf j = 100 MunicipalMunicipal to the criteria ∈ CommissionCommission/ NNj for Commissionsetting ofof Health Healthupv j = of 25andand Health FamilyFamily and Planning,Planning,Family∈ Nj Planning, 2013),2013), thethe2013). In this plan, the standard for the j When decidingemergency the valuef j =of 100medicalN , anotherfor sites∈ common in/ NNj Shanghai., That practiceand islet to(Statistics that say,v j =ambulances the25 existingDepartment,for each arefacilities ∈2003),Nj in. Inthe thethe central cost12th region forfive-year ff jj = 100 forfor ∈ //NNj ,, andand letlet v jj = 25 forfor eacheach ∈ Nj .. InIn thethe 12th12th five-yearfive-year commutation each day. In other words, he/she spends approximate one third of his/her 0 plan (Shanghai Municipal00 Commissionauthorityauthority wouldwould of Health establishestablish and or or reconstructreconstruct fivefive oror lessless emergencyemergency medicalmedical facilitiesfacilities inin planf =(Shanghai100 for0 Municipal f,fCommission jjand==100100 let forforv often =of∈25∈ Health stationed for//NNj NNj each ,and, andand in Family hospitalsletlet vbuildingv. jjPlanning,In== 2525orthe medical forafor12th new 2013),eacheach five-yearsite centres isthe∈∈ between Nj Nj .in. In InChinese of the theone Shanghai 12th covering12thmillion cities five-yearfive-year can wasand radius meet 1.5noted. ofmillion, the each Hence, requirements site while is 5 the kilometers, operationalfor such and services cost thus the value of a was determined. f = 100 forj Noting∈ / NNj that, andthe∈ workingletemergency/ NNj v = hours25 medicalfor defined jeach sites in ∈this inNj .study ShanghaiIn the include∈ Nj 12th (Statistics businessfive-yearplan Department, (Shanghaihours, i.e. from Municipal2003), the Commission cost for of Health and Family Planning, 2013), the ij plan (Shanghai Municipalj authorityCommission would of establishHealth and orjFamily reconstructFamily Planning, Planning,after five investigating or2013), 2013), less emergencythe the authority allthethe possible centralcentral medical wouldplantime regionlocationsregion facilities on(Shanghaiestablish workofof Shanghai.Shanghai.to in setor Municipaleach up Thus,week.newThus,if the emergency Commissionthe theHence,population budgetbudget without limitmedicallimit wouldof lossTCHealthTC is sitesisofnot 500.500. generality, and varyin Family periodically, α Planning,= 1 wasor 2013),if set. the the building a new site is between one million and 1.5authority million, would while establish the operational or reconstruct cost five or less emergency medical3 0 facilities in authority would establish orplan reconstruct 9:00am(Shanghai tofive 5:00pm, Municipal or less and planplanemergency reconstruct Commissionsome (Shanghai(Shanghai transit medical five timeMunicipalofMunicipal orHealth between facilitiesless emergency andCommissionCommission thein Family workplace is medicalonePlanning, ofof authority HealthandHealthquarter. facilities living 2013), andand wouldHence, place. in Family Family thethe establish Iwithoutt is Planning,Planning, orlossBy reconstruct referring2013),2013),of generality, thethe tofive the or populationlet less f emergencyj = 10 in thefor centralmedical∈ Nj region, facilitiesand and thein standard of the ambulance plan (Shanghaithethe centralcentral Municipal regionregion Commissionofof Shanghai.Shanghai. Thus,Thus,of Health thethecentral budget budgetand Family Shanghai,limitlimit TC Planning, isis 500.there500. a 2013), fewwere sub-districtsthe the146 central candidates region which of is (AppendixShanghai. authoritiesdenoted by Thus, 1).havebars. In the to considerotherbudget words,limit budget TC constraints.is 500. They could commona few sub-districts in Shanghai which thatcentral an is employeedenotedregion of by needsShanghai. bars. to spend Thus, around the budget two or limit three When TC hours isdeciding on the value0 of N , another common practice that ambulances are thethe centralcentral regionregion ofof Shanghai.Shanghai.authority Thus,Thus, the thewould budgetbudget establish limitlimitis one authority authorityTC or isisquarter.reconstruct 500.500. wouldwould Hence, fiveestablishestablish orwithout less oror emergency reconstructreconstructloss4.2.4.2. of ResultsResultsgenerality, medicalfivefivethe or orand andcentral lesslessfacilities DiscussionsletDiscussions emergency emergencyregion in of Shanghai. for medicalmedicaleven removeservice, facilitiesfacilitiesThus,, and onethe the sitein incapacitybudget from limit theseof aTC existingservice is 500. sitessite shouldin the setting cover a population of no more than authority would establish or reconstruct five or less0 emergency medical facilities in f j = 100 ∈ Nj commutation each day.thethe500. Incentralcentral other region regionwords,N = ofof he/she 1{ Shanghai.Shanghai.,...,33 spends}, and Thus,Thus, approximateN =thefthe1{ = ,...budgetbudget10033 often, 34onefor limit,...,limit stationed third179 ∈TCTC} of. isis / his/her NNj 500.500.in ,hospitals and let orv medical= 25 for centres each in∈ ChineseNj . In thecities 12th was five-year noted. Hence, the central4.2. regionthe Results central of Shanghai. andregion Discussions of Thus, Shanghai. the budget Thus, limitthe budget TC is 500.limit TC is 500.Notingj that the working hoursof IV, defined i.e.j the in cross this asstudy shown include in Figure business 3. hours, i.e. from Noting that the working hours defined in this study include business4.2. Results hours, and i.e. Discussions from 250,000, i.e., C j = 25 was set for each j. According to the criteria for setting up 0 after investigating all possible locations to set up new emergency medical sites in 4.2. Results and Discussions time on work in eachf = week.100 for Hence, ∈The without /valuesNNj , lossand of ofparameterslet generality, v = 259:00am were forαInIn4.2. =determined ordereachorderto 1Results 5:00pm, wastoto ∈ analyseanalyse andset.Nj byand. InreferringDiscussions some thisthisthe problemproblem12thtransit toNext, thefive-year time more12th morethe between results five-year comprehensively,comprehensively, fromthe plan workplace the onprospect fourfour and instancesinstancesof living a covering place. withwith levelI t is 9:00am to 5:00pm,j and4.2. some Results transit and timeDiscussions between thej workplaceplan (Shanghai and3 living Municipal place. ICommissiont is of Health and Family Planning, 2013), the 4.2. Results and Discussions4.2.4.2. ResultsResults andand DiscussionsDiscussions central Shanghai, therewere wereexplored,emergency 146 i.e. candidatesmedical sites (Appendix in Shanghai 1). In(Statistics other words,Department, 2003), the cost for 4.2. Results and DiscussionscommonInIn orderorder intoto Shanghaianalyseanalyse thisthis that problemproblem an employeethe moremore development comprehensively,comprehensively,needs to spendof differentdifferentShanghaiauthority aroundcommon fourfour settings settings instancesinstances twoemergencywould in orShanghai Inthreewereestablishwere withwithorder medical hours tested, tested,that to or analyseanon reconstruct i.e. servicesi.e.employee wwthis== (Shanghaiproblem fiveneeds1.0 1.0 ,,αα or= = to less1more1 spendMunicipal emergencywithwith comprehensively, around ConstraintsConstraints twomedical or three(1)(1) fourfacilities - - hours instances(7),(7), in on with InIn orderorder toto analyseanalyse thisthis problemproblem When moremore decidingcomprehensively,comprehensively,plan (Shanghai the value Municipal fourfourof N instancesinstances, another Commission commonwithwith practiceof Health that0 and ambulances InFamily order Planning,to are analyse building2013),this problem the a new more site33 iscomprehensively, between' one million four andinstances 1.5 million, with while the operational cost Commission of Health theandcommutation centralFamilyN region =Planning,1{ ,...,each of33 day.Shanghai.} ,2013). and In otherN In =Thus, this 1{ words,,...α plan,33thei zh ,34 ijbudgethe/she +,...,the179 standard spendslimit} ( . − TCα approximatefor)1 isi zh the500.ij one third of his/her differentoftencommutation settings stationed were eachinauthority hospitalstested, day. In wouldIni.e. otherorInIn order medicalorderorderw establish words,= to toanalyseto1.0 ,,centresanalyseanalyse αhe/she or= thisreconstruct1 inspendsthisthis problem withwithChinese problemproblem approximateConstraintsConstraints fivemore cities moremoreor comprehensively, lesswas comprehensively,comprehensively,one(1) (1)emergency noted. third-- (7),(7), ofHence, his/her medical four∑∑four facilities instancesinstances in ∑∑withwith 1 In order to analyse this problem more comprehensively,3 fourdifferent instances settings with were∈∈Mi tested, Nj i.e. ∈∈Miw = Nj 1.0 , α =1 with Constraints (1) - (7), 0 different settings were tested,In order i.e. to analysew = 1.0 this,,α =problem1 withwith more ConstraintsConstraints comprehensively, (1)(1) -- a(7),(7), fewfour sub-districts wwinstances == 1.0 1.0 ,,αdifferentα with= =which0 0 withwith settingsis denoted ConstraintsConstraints were by bars.tested, (1)(1)is one- - i.e.(2) (2)quarter. wandand= (4)(4)1.0 Hence,, α-- =(7),(7), without 3 wwwith==11 ,,loss1αConstraintsα == 1of1 generality, withwith (1). - (7),let f = 10 for ∈ Nj , and after investigatingthe all central fourpossible instancesregion locationscovering of Shanghai. with to radius differentset Thus,up of eachnew thesettings emergencysitebudgettime is onwere5The limit kilometers, work values medical tested,1TC in is each of500. andi.e. sitesparameters week. thus in Hence,the valuewere without determinedof aij losswas of determined.by generality, referring3 toα hthe=+ 12th ( was −3five-year3α set. )1 h' plan on j time on work in each3 week. Hence, without loss1 of generality, α = 11 was set. i ∑∑ 3 i different settings were differentdifferenttested, i.e. settingssettings w =1 werewere1.0 , α =tested,tested, with i.e.i.e. 4.2. Constraintsww ==Results1.0 1.0 ,,αα and ==1(1)3 Discussions - withwith(7), ConstraintsConstraints (1)(1) -- (7),(7), ∈Mi ∈Mi different settingsw = central1.0 ,,wereα = Shanghai,0tested, withwith i.e.Constraints Constraintsthere w = were1.0 ,(1)(1)α 146 = -- (2)(2)candidates with withandand Constraints Constraints(4)(4)3 (Appendix-- (7),(7),ConstraintsConstraints (1) w-(1) (7),= 11).-the ,w, α (1) (7),(1) =In=development - - (7),1.0 (7),other,3α3 andwithwithand= words, 0 w w =withof=1 1 ,,Shanghaiαα Constraints== 00 with withemergency ConstraintsConstraints(1) - (2)medical (1)and(1) -- (2) (2)(4)services andand- (7), (4)(4) (Shanghai -- (7).w(7).= 1 , α =Municipal1 with By referring3 1 to Notingthe population that the inwworking =theWhen 1.0 central,3 αdecidinghours= region0 defined with the and value Constraintsin the this ofstandard Nstudy, another (1) includeof the- common(2) ambulance business and practice0(4) hours, - (7), that i.e. ambulanceswfrom= 1 , α = 1are3 with w = 1.0 ,,α = 0 withwith ConstraintsConstraints (1)(1) - - (2)(2)When andand deciding (4)(4) -- the(7),(7), value w = of1 ,,Nα ,= another withwith common practiceCommission that ambulances of Health are and TheFamilyf j = results100 Planning, for of the∈ 2013).covering/ NNj In, andthislevel letplan, for v jfourthe= 25 standard instances, for each3 for the∈ Nj . In the 12th five-year 0 4.2. Results and Discussions3 11 Constraintsw = N1.0 ,=α (1)1{ =,..., - 0(7),33 }with ,and and ConstraintswwwNwith====1,,1{ α 1.0 1.0 Constraints,...,,α=α33 ,0(1)=34=service, with,..., 0with0- 179 withwith(1)(2) ConstraintsConstraints } the- .and (2)ConstraintsConstraints capacity and(4)9:00am (4) (1)(1)- - (7),- of- (7),to(2)(1)(2)(1) often a5:00pm, andandw1service-- = (2) (2) stationed(4)Constraints1(4)In, α -and-andorder site (7).(7).= some1 (4) (4) shouldinto (1)withwithanalysehospitals --transit (7),-(7), cover(7), time wthisandwi.e. or==a 11I,betweenproblempopulationmedicalw, ,II,αα= =1III=,α and themorecentres= with withofIV,workplace0 comprehensively,no with are in more 100%, ChineseConstraints and than 100%, living cities (1) four91.99%place. was - (2)instances noted. Iandt andis (4) 98.61%,Hence, with- (7). w = 1.0 , α = 0 oftenwith Constraintsstationed in (1)hospitals - (2) orand medical (4) - centres(7), w in= 1Chinese, α = cities Constraints More Morewith was specifically,specifically, 3noted. (1) - (7),Hence, thethe and The settingsetting w results= 1 w,wα= =3of3= 1.0 the1.0 0 implies implies withcovering Constraints thatthat level thethe designdesignfor (1) four - (2) inin instances, andInstanceInstance (4) - I(7). I i.e. I, II, III and IV, are 100%, Constraints (1) - (7), and w = 1,,α = 0 with with ConstraintsConstraints (1)(1) -- (2)(2) andand (4)(4) -- (7).(7). after3 investigatingcovering radius all of possible each site locations planis 5 kilometers,(Shanghai to set up Municipaland new thus emergency the Commission value ofmedical a ijofwas Healthsites determined. in and Family Planning, 2013), the after investigating all possible 250,000,locations i.e.,to setCcommon up= 25newwas in emergency Shanghaiset for each thatmedical anj. Accordingemployee sites inrespectively. needsto the to criteria spend That isaroundfor to setting1say, two all upordemands three hours are covered on by the ConstraintsThe values (1) -of (7), parameters and ConstraintsConstraintswConstraints=In 1were, αorder= determined(1)(1) (1) 0to -- with- (7),analyse(7), (7), and andConstraints by this wwreferring= =problem1j1,, α α(1)andand= = to-different (2)0 II0moreIIthe iswith withis withand 12thservice-oriented,service-oriented, comprehensively, Constraints (4)ConstraintsConstraintssettings five-year - (7). were (1) plan(1)(1) - but but -- tested, (2)fouron(2) changeschanges 100%,andand instances i.e. (4)(4)authority inin 91.99% -- wdemand(7).demand(7). =with 1.0 wouldand , wouldαwould 98.61%,= establish notnot with beberespectively. considered orconsideredConstraints reconstruct That inin Instance Instance(1)five is -to or (7),say, less all emergency demands aremedical covered facilities by in Constraints (1) - (7),central More More and specifically,specifically,wShanghai,= 1,α = 0 therethethe with settingsetting were Constraints w146= 1.0 candidates (1) implies implies - (2)commutation and thatthat(Appendix (4) thethe -central (7).designdesign each 1). Shanghai,ininday. InstanceInstanceIn In other Moreother thereII specifically,words,words, were37 he/she service 146 the spends sitessettingcandidates inapproximate Instancew = (Appendix31.0 I implies andone thirdby 1).that33 of sitesInthe his/her designotherin Instance words,in Instance II. I More More specifically,specifically, thethe settingsettingthe development w = 1.0 implies implies of (2)Shanghai thatthat and thethe(4) emergency-designdesign (7). inin InstanceInstance medical II services (ShanghaiBy referring1 More Municipal to thespecifically, population the 37the theservice incentral setting the centralsites region w in= regionInstance of1.0 Shanghai. implies and I andthe that Thus, standardby the 33 the designsites budgetof inthe in Instance ambulance Instancelimit TC II. Iis The 500. authorit ies reduce and II is service-oriented,different but changes settings ininemergency demanddemandwere tested, wouldwould medical i.e. notnot bebesitesw =consideredconsidered in01.0 ,Shanghaiαand= IIinin isInstanceInstance withservice-oriented,(Statistics Constraints Department,The authoritiesbut(1) changes - (7),2003), reduce in demandthe the cost number would for ofnot locations be considered in Instances 8 in8 Instance Commission0 of Health and MoreFamily More More specifically, Planning, specifically,specifically, 2013). the timethethe setting setting Insettingon this work wN = plan,ww in==1.0 =andservice, each, implies1{ theα,...,1.0 1.0 II = 33standard implies impliesweek.3is }0 service-oriented,the,that andwith Hence,capacity thatthe thatfor N Constraints =thethe without1{ ,...designofthedesign33 abutnumber ,34service loss inin,...,(1)changes Instance Instance179 of -of generality,site}(2) .locations in should anddemandII (4) αincover would=Instances- 1(7), a notwaspopulationw be= IIIset.1 considered,and α = IV,of1 nobut with inmore at Instance the than cost of service level, i.e. and II is service-oriented, but More changes specifically,N Moreinin= demanddemand1{ ,..., specifically, the33} settingwould,would and N notnotthew= = bebesetting1{ ,... consideredconsidered1.0 33 building implies, 34w,...,= 179 thatinina1.0 } newInstanceInstance implies. the site design thatis between inthe Instance design one inmillionI Instance and I1.5 million,III and whileIV, but the at operationalthe cost of costservice3 level, i.e. 91.99%3 and and II is service-oriented,andand butII.design IIII changesIn isis contrast,service-oriented,inservice-oriented, Instance in demand the I andsetting would butbutII is changeschanges w service-oriented,not= 1be suggests inconsideredin demanddemand250,000, that but wouldwouldin the Instancechangesi.e., notfactornot 8 8 C bebe = consideredconsideredof25 91.99%wascosts 4.2. set1will andin inResultsfor InstanceInstance be 98.61%.each more and j . ItDiscussionsAccording is interesting to the to criterianote that for the setting covering up8 level of IV is greater and II is service-oriented,covering radius but changes ofw each= in1.0 site ,demandα is= 5 0kilometers, wouldwith notConstraints andbe considered thus the(1) valueConstraintsWhen- The in(2) Instance ofvalues decidingand aij (1)was (4) of - theparameters (7),determined.- (7),value and j w of =wereN 198.61%., ,αanother determined= It common withis interesting byConstraints referringpractice 0to that (1)tonote the- ambulances (2) that12th and the five-year(4) covering -are (7). plan level on 8 The values of parametersin demand were is determinedwould one quarter.not bybe referringconsideredHence,8 8 withoutto the in 12thInstance loss five-year of II.generality, In plan w =onthan 1 letα that=f 30 =of10 III, for even ∈withNj fewer, and service sites. More detailed results of the allocation weighted in the design. Instance III and IV, and Instance IV will not j consider the often stationedthe development in hospitals ofor 8 medicalShanghaiof IVcentres emergency is greater in Chinese thanmedical8 8 thatcities ofservices wasIII, evennoted. (Shanghai with Hence, fewer Municipal service Bythe referring development to theConstraints population ofcontrast, Shanghai (1) in the- the(7), emergencysetting central and w region= 1medical ,suggestsα and= 0 the services withthat standard theConstraintsemergency (Shanghaifactor of8 the of (1)ambulance costs medical Municipal- (2) and sites of (4) facilities -in (7). Shanghai to demand (Statistics nodes areDepartment, presented as2003), follows. the cost for daytime restriction on demand, i.e. Constraint (3). sites. More detailedIn order results to analyse of the thisallocation problem of morefacilities comprehensively, to four instances with Commission of Health and Family Planning, 2013).after investigating In 0thisCommission plan, More allthe possibleofstandard specifically, Health locationsfor and the theFamily setting to setPlanning, upw =new 1.0 2013). emergency implies In thisthat medical plan,the design the sites standard in inInstance for theI service, the capacity ofwill a beservice more f jsiteweighted= 100 should for in cover the∈ design. a/ NNj population, Instanceandbuilding let of vIII jno =aand new25more IV,for site than each is between ∈ Nj one. In millionthe 12th and five-year 1.5 million, while the operational cost central andShanghai, II is service-oriented, there were 146 but demand changescandidatesdifferent nodes in demand (Appendix aresettings presented would were1). not as Intested,follows.be consideredother i.e. words, w in= Instance1.0 , α = 1 with Constraints (1) - (7), and Instance More specifically, IV will not the consider setting the wcovering daytime= 1.0 implies radiusrestriction thatof each onthe sitedesign is 5 in kilometers, Instance I andTable thus 2. Thethe value allocation of a ofij was facilities determined. to demand0 nodes. covering radius of each site isA ll5 kilometers,instances are and tested thus theby IBMvalue ILOGof aij wasCPLEX determined. 12.4 running on a desktop 3 250,000, i.e., C j = 25 was set forplan each (Shanghai j. According Municipal to the Commission criteriais one forquarter. ofsetting Health Hence, up and withoutFamilyThe detailed Planning,loss of allocation generality, 2013), patternthe let forf j =the10 four for instances∈ Nj , and and IIdemand, is service-oriented, i.e. Constraint but (3). changes 0 = in demand, and would N = not1{ ,... be33 considered,34,...,179} in. Dem Instanceand computer withauthority a 3 GHz would processor.N establish1{ ,..., ABy 33or limit referring}reconstruct of one to thehourfive population isor setless ongiven emergency ineach the in computation.Tablecentral medical 2 regionwas facilitiescompared, and the instandard and thus of morethe ambulance properties8 1 By referring to the populationAll instances in the central are tested region by and IBM the ILOG standard CPLEX of the 12.4ambulance w = 1.0 , α = 0 with Constraints (1) - (2) and (4) - (7), w = 1 , α = with emergency medical sitesCPLEX in Shanghaireturned an (Statistics optimal orDepartment, a satisfactory f2003), solution= 100 the for to cost Instance∈ for/ for NNj II0 inthisFac, and64.5ility realistic letseconds. v problem1 = 25It2 for could 3each be4 explored.∈5 Nj . 6In the7 12th8 five-year9 10 11 12 13 14 315 service, the capacityrunning of a service onthe a desktop centralsite should regioncomputerThe cover of values Shanghai. with a service,population ofa 3parameters Thus,GHz j the oftheprocessor.capacity no budgetwere more determinedof limit thana service TC is by500. site referring should8 j to cover the 12th a population five-year planof no on more than building a new site is returnedbetween satisfactoryone million solutionsand 1.5 million, to Instance while I, theIII andoperational IV in 3,600 cost seconds.InstanceUnderConstraints The the solution same (1) -settings (7), and to w =and1, αother= 0parameters, with Constraints the (1) - (2) and (4) - (7). A limit of one hour is setthe on eachdevelopment computation. of Shanghai CPLEX emergency medical services (Shanghai Municipal 250,000,plan i.e., (Shanghai C j = 025 Municipalwas set forⅠCommission each j.27 According of16 Health 3 to and 8the Family24criteria 4 Planning,for33 setting2 2013), 7up 25 the 1 18 19 5 15 250,000, i.e., C j =gap25 wasis 1.6%, set for 0%, each 8.9% j. Accordingand 4.7%, respectively.to the criteria More for settingdetailed up allocationresults are of presented facilities to demand nodes in I and III is quite is one quarter. Hence,returned without an 4.2. lossoptimal Results of generality,or anda satisfactoryCommission Discussions let f solutionj of= 10Health for to andInstance∈ FamilyNj , and Planning, 2013). In this plan, the standard for the and demonstrated below. authority would establishdifferent orⅡ reconstruct to the More24result five 11 specifically,of orII24 lessand 29 IV,emergency the 33respectively. setting8 medical 22w This=11 facilities1.0 result 2 implies 4 in that 3 the28 design 5 in19 Instance 18 I emergency medicalII sites in 64.5 in Shanghaiseconds. (StatisticsIt returned Department, satisfactoryemergency 2003),solutions medical the tocostsites forin Shanghai (Statistics Department, 2003), the cost for 0 covering radius theof eachcentral site region is 5 kilometers, of Shanghai.impliesⅢand and that Thus, II thus isthe service-oriented, the11theallocation budgetvalue4 of patternlimit8 a23ij TCbutwas of is changes 7servicedetermined. 500.16 sitesin15 demand to24 demand 33 would 22 not18 be considered6 1 18 in Instance2 f j = 100 for ∈ /InstancesNNj , and I,let III v andj = 25IVIn orderforin 3,600each to analyseseconds.∈buildingNj .this InThe problem thea solutionnew 12th site more five-yeargap is between comprehensively, one million four and instances 1.5 million, with while the operational cost building a new site is between First, one the million results and of 1.5selected million, emergency while the medical operational stations costnodes were Ⅳ depictedneeds to beon11 rearrangedthe2 24 when11 attempting4 a6 satisfactory1 33 5 18 17 25 2 6 is 1.6%, 0%, 8.9% and 4.7%,By referring respectively. to the More population detailed in the central region and the standard of the ambulance 0 0 1 8 plan (Shanghai Municipalfollowing Commission figures.different of settingsHealth andwere Family istested, one 4.2.Planning, quarter.i.e. Results w =2013),Hence, and1.0 , αDiscussions the=without covering with loss level,Constraints of butgenerality,16 with17 (1) periodic 18-let (7), 19 f changes j =2010 for21in demand.22∈ Nj 23 , 24and 25 26 27 28 29 30 is one quarter. Hence,results without are presented loss of and generality, demonstratedservice, letthe below.capacityf j = 10 forof a service∈ Nj , andsite3 should cover a population of no more than authority would establish or reconstruct five or less emergency medical facilities in Ⅰ 12 1 14 20 25 18 29 24 13 103 20 6 5 32 124 First, the results of selected emergency medical 0 0 1 the central region of Shanghai. Thus,w = the1.0 budget, α = limit0250,000, withInsert TC is ConstraintsFigurei.e., f500.j = C100 2j =and for25(1) 3 wasIn here- ∈ order set(2) / forNNj andto ,analyse eachand(4) jlet-.Ⅱ thisAccording(7), v j problem=w25= 1 for,toα more the=each criteriacomprehensively, with∈ Nj for. In setting the 12th four up five-yearinstances with f j = 100 for ∈ stations/ NNj , andwere let depicted v j = 25 on forthe followingeach ∈ figures.Nj . In the 12th five-year 12 17 320 5 19 28 18 19 20 18 20 14 31 13 27 5. Concluding remarks different settings were tested,Ⅲ i.e. 28w = 191.0 , α = 120 with24 Constraints17 5 (1)4 - (7), 17 31 13 32 31 WhenConstraints deciding the (1) emergencyvalues- (7), and of plan wmedical,= the1(Shanghai,α difference =sites0 withMunicipalin ShanghaiinConstraints Commission (Statistics (1) - (2) ofandDepartment, Health (4) - (7). and 2003),Family3 the Planning, cost for 2013), the 4.2.plan Results (Shanghai and Discussions Municipal Commission When deciding of Health the values and Family of w , Planning,the difference 2013), in theresults Ⅳ with different results with different practicalbuilding focuses aauthority new sitewere wouldis attemptedbetween establish one million or reconstruct and 1.5 fivemillion,27 or 19less while 12emergency the12 operational 7 medical20 cost29 facilities 17 17 in 29 18 6 14 13 31 authority would establish or reconstruct five or less emergency medical facilities in In this research, the location problem for emergency practito explore.cal focuses In fact, were Moreit attempted is impliedspecifically, to fromtheexplore. centralthe w setting =In region fact,1.0 , thatαw it of= theis Shanghai.0 implied1.0 with implies Constraintsfrom Thus, that wthethe= designbudget (1)1.0 31 that- inlimit32 (2) Instance 33TCand is34(4) 500.I 35- (7),36 w =371 , α38 = 391 with40 41 42 43 44 45 the centralIn order region to ofanalyse Shanghai. this problemThus, the more budget comprehensively,is limitone TCquarter. is 500. Hence, four instances without with loss medical of generality, services letwith ftime-dependent= 10 for ∈ demandNj 0 , and restrictions 3 thegovernment governmentand concerns II is service-oriented, concernsmore with themore but service changes with level, in demandthe i.e. wouldservice not Ⅰ belevel, considered 124 i.e.124 inj Instance31 28 17 30 30 15 17 31 13 22 14 19 28 ' Constraints (1) - (7), andwas winvestigated.= 1,α = 0 Multiple with Constraints factors in(1) the - (2) decision and (4) making - (7). α zh + ( −α)1 zh 1 , but not the cost. Ⅱ 12 14 32 7 6 12 6 30 4 14 13 3 17 25 1 different settings were∑∑ tested,i iji.e. ∑∑w = 1.0 , α =i ij, but with not4.2. the ConstraintsResults cost. and0 (1)Discussions - (7), process were considered, i.e. periodic changes in demand, 4.2. Results and Discussions∈∈Mi Nj ∈∈Mi Nj f =3100 for ∈ / NNj , and let v = 25 for each ∈ Nj . In the8 12th five-year j j Ⅲ 31 14 27 28 25 13 20 6 19 32 27 1 In contrast, the authority has to accept a More more specifically, costs andthe settingthe capacity w = of1.0 the implies facilities. that the Time-dependent design in Instance I w = 1.0 , α = 0 with Constraints (1) - (2) and (4) - (7), w In= 1 order, α = to1 analyse with this problemⅣ more28 comprehensively,31 32 3 28 four7 instances5 33 with22 20 28 24 14 19 13 In order to analyse this problem moreplan comprehensively, (Shanghai andMunicipal IIfour is service-oriented,instances Commission3 withdemand ofbut Health changesrestrictions and in Familydemand into the Planning,would formula not were2013), be considered introduced, the in andInstance Ineconomical contrast, thesolution authority for locations has to accept when a this more weight economical is large, solution for locations when authority would establish or reconstructmaximising five or less the 48emergency coverage 46 147 ofmedical 49emergency 50 facilities 51 services 52in 53 while54 55 56 57 58 59 60 Constraintsdifferent (1)settings - (7), andwerethisi.e. w weighttested,= 1., αTherefore, is =i.e.large,0 w with i.e.= it Constraintsis1.0 w ,indicated=α1=. Therefore,1 (1) differentfromwith - (2) iFiguresConstraintst andis settingsin (4)dicated 2 - and(7). (1)were from 3 - tested,Figures(7), i.e.2 and w 3= that1.0 ,theα = with Constraints (1) - (7), the central3 region of Shanghai. Thus, theminimising budgetⅠ limit the 6TCtotal is32 500.cost 312 of providing4 103 118the services6 27 were33 172 8 118 29 23 21 11 authoritythat the authoritywould set would up 37 set and up 33 37 locations and 33 locationsfor emergency for medical services when aimed.Ⅱ 2 31 32 33 27 6 1 127 22 5 25 23 16 7 30 w = 1.0 More, α = specifically,0 withemergencyw = Constraints 1.0 the, while setting medical it (1) onlyw =services- needs(2)1.0 impliesand 33 when and(4) that 32w- = sites(7),the1.0 design ,when, wwhileα ==1 the,in 0αit Instancebudgetonly=with1 Constraints withis I more important (1) - (2)when and (4) - (7), w = 1 , α = with 4.2. Results and Discussions 3 TheⅢ formula30 is12 used 14 to16 study 7 a 30real 11 problem 3 25 in 30 12 29 2 3 29 and II is service-oriented,needsw = but1. 33 Furthermore,changes and 32 in sites demand two when sub-figures would the budget not werebe isconsidered morecompared, important in i.e.Instance with and without periodic Constraints (1) - (7), and wShanghai.= 1,αⅣ = 0The with 30case Constraints is31 discussed32 (1)1 -with (2)30 anddifferent5 (4)29 - (7).parameter30 27 7 12 23 8 3 25 Constraints (1) - (7),changeswhen and w in= 1 demand,., αFurthermore,= 0 in with each Constraintstwo of Figuressub-figures (1)2 and - (2) 3.were and compared, (4) - (7). i.e. with and without periodic changesIn order in demand, to analyse in eachthis problem8 settings, more for comprehensively, example,61 62 when63 four the64 instancesdesign65 66 is withmore67 68service- 69 70 71 72 73 74 75

of Figures 2 and 3. More specifically,oriented the settingⅠ or cost-oriented,w 10= 1.0 22 implies 23and thatwhether7 the16 design the9 time-dependent in2 Instance3 9 I 26 8 11 172 10 26 More specifically,The results the reveal setting another w = differentcritical1.0 implies fact settings that that the varying weredesign demandtested, in Instance i.e.complicates wI = 1.0 ,thαe =planning1 with Constraints (1) - (7), The results reveal another criticaland II fact is service-oriented, that varying butrestrictions changesⅡ inexist demand103 or not.29 would 30 not23 be 21considered 21 2 in Instance8 15 26 16 26 9 10 9 and II is service-oriented,problem, but aschanges the number in demand of selected would locationsnot be considered for I and inIIIare Instance greater than those for II demand complicates the planning problem, as the number SomeⅢ interesting10 5 conclusions15 22 23 are 26reached 26 from8 10 the 21 9 9 33 21 w = 1.0 , α = 0 with Constraints (1) - (2) and (4) - (7), w = 1 , 1 with 8 and IV. Under similar situation in two settings of w , the authoranalysis.8 ities need Firstly, to set both up the weight inα the= objective function of selected locations for I and III are greater than those for Ⅳ 22 4 25 15 9 316 33 16 23 10 8 10 21 15 21 more stations to satisfy the time-dependent demands of ambulanceand the services. time-dependent It is constraints change the result of II and IV. Under similar situationConstraints in two (1) settings- (7), and of w,= the1,α = 0 with Constraints 76 (1) - (2) and (4) - (7). worth mentioning the results in II and III that the solutions are exactlylocations the and same allocation with of service sites to demand nodes. authorities need to set up more stations to satisfy the time- Ⅰ 26 existing emergency service sites in N More0 . That specifically, is to say, the the setting existing w =facilitie1.0 impliess in the that the design in Instance I and II is service-oriented, but changes in demand would not be considered in Instance 10 central region of Shanghai can meet the requirements for such services if the 013 population would not vary periodically, or if the authorities have to consider budget 8 HKIE Transactions | Volume 26, Number 1, pp.9–19 constraints. They could even remove one site from these existing sites in the setting of IV, i.e. the cross as shown in Figure 3.

Next, the results from the prospect of a covering level were explored, i.e.

' ∑∑α i zh ij + ∑∑ ( −α)1 i zh ij ∈∈Mi Nj ∈∈Mi Nj . αhi + ∑∑ ( −α )1 h' i ∈Mi ∈Mi

The results of the covering level for four instances, i.e. I, II, III and IV, are 100%, 100%, 91.99% and 98.61%, respectively. That is to say, all demands are covered by M K LI AND J W ZHANGthe 37 service sites in Instance I and by 33 sites in Instance II. The authorities reduce the number of locations in Instances III and IV, but at the cost of service level, i.e. 91.99% and 98.61%. It is interesting to note that the covering level of IV is greater than that of III, even with fewer service sites. More detailed results of the allocation of facilities to demand nodes are presented as follows. Table 2. The allocation of facilities to demand nodes. Table 2. The allocation of facilities to demand nodes. Demand Facility 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Instance Ⅰ 27 16 3 8 24 4 33 2 7 25 1 18 19 5 15 Ⅱ 24 11 24 29 33 8 22 11 2 4 3 28 5 19 18 Ⅲ 11 4 8 23 7 16 15 24 33 22 18 6 1 18 2 Ⅳ 11 2 24 11 4 6 1 33 5 18 17 25 2 6 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Ⅰ 12 1 14 20 25 18 29 24 13 103 20 6 5 32 124 Ⅱ 12 17 20 5 19 28 18 19 20 18 20 14 31 13 27 Ⅲ 28 19 20 24 17 5 4 17 31 13 32 31 Ⅳ 27 19 12 12 7 20 29 17 17 29 18 6 14 13 31 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Ⅰ 124 124 31 28 17 30 30 15 17 31 13 22 14 19 28 Ⅱ 12 14 32 7 6 12 6 30 4 14 13 3 17 25 1 Ⅲ 31 14 27 28 25 13 20 6 19 32 27 1 Ⅳ 28 31 32 3 28 7 5 33 22 20 28 24 14 19 13 48 46 47 49 50 51 52 53 54 55 56 57 58 59 60 Ⅰ 6 32 12 4 103 118 6 27 33 172 118 29 23 21 11 Ⅱ 2 31 32 33 27 6 1 27 22 5 25 23 16 7 30 Ⅲ 30 12 14 16 7 30 11 25 30 12 29 2 3 29 Ⅳ 30 31 32 1 30 5 29 30 27 7 12 23 8 3 25 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Ⅰ 10 22 23 7 16 9 2 3 9 26 8 11 172 10 26 Ⅱ 10 29 30 23 21 21 2 8 15 26 16 26 9 10 9 Ⅲ 10 5 15 22 23 26 26 8 10 21 9 9 33 21 Ⅳ 22 4 25 15 9 16 33 16 23 10 8 10 21 15 21 76 Ⅰ 26 Ⅱ 15 Ⅲ 21 10

Ⅳ 9 "

Figure 11.. TThehe change of population in subsub-districts.-districts. The detailed allocation pattern for the four instances given in Table 2 was

compared, and thus more properties for this realistic problem could be explored.

(a) (b)

Under the same settings to w and other parameters, the allocation of facilities to

demand nodes in I and III is quite different to the result of II and IV, respectively.

This result implies that the allocation pattern of service sites to demand nodes needs

to be rearranged when attempting a satisfactory covering level, but with periodic

changes in demand.

5. Concluding remarks

In this research, the location problem for emergency medical services with

time-dependent demand restrictions was investigated. Multiple factors in the decision I) with periodic changechangess in demands II) without periodic changechangess in demands making process were considered, i.e. periodic changes in demand, costs and the Figure 2. Results of locations of emergency medical sites when w = 0.1. (a) with periodic changes in demands; and (b) capacity of the facilities. Time-dependent demand restrictions into the formula were without periodic changes in demands.FFigureigure 22.. Results of locations of emergency medical sites wwhenhen w = 0.11.0 . introduced, and maximising the coverage of emergency services while minimising the

total cost of providing the services were aimed.

The formula is used to study a real problem in Shanghai. The case is 014 discussed with differentHKIE parameter Transactions settings, | Volume for 26, Numberexample, 1, pp.9–19 when the design is more

service-oriented or cost-oriented, and whether the time-dependent restrictions exist or

not.

Some interesting conclusions are reached from the analysis. Firstly, both the weight in

the objective function and the time-dependent constraints change the result of

locations and allocation of service sites to demand nodes. Furthermore, the time-dependent constraints could affect the final decision on the locations. More !'16" service" sites are required to satisfy varying demands, but the service coverage level is still unfavourable in one test instance.

This study highlights a specific focus on the location problem with time-dependent aspects. The mobility of the population has put growing pressure on medical services in many cities in China which are going through the mega changes of rapid urbanisation.

This study does not consider more features, e.g. some locations may have higher accident rates than others. But the design shows a framework for optimising facility locations for emergency medical services in cities and a basis for relocating and dispatching ambulances. Hence, further research work can be conducted in future, for instance, when the change of demand appears to be more dynamic or when more

" Figure 11.. TThehe change of population in subsub-districts.-districts.

I) with periodic changechangess in demands II) without periodic changechangess in demands

FFigureigure 22.. Results of locations of emergency medical sites wwhenhen w = 0.1.0 1.

(a) (b)

features are considered.

Acknowledgements

This work is supported by the National Social Science Fund of China [grant number: 16BGL083].

Notes on Contributors

!'16" " Figure 3. Results of locations of emergency medical sites when w = 1. (a) with periodic changes in demand; and (b) without periodic changes in demand.

Dr Ming-Kun Li received his Ph.D. degree from The University of Hong Kong. He is currently an Associate Professor at the Shanghai University, People’s Republic of China. His research interests are in supply chain management and terminal planning.

Furthermore, the time-dependent constraints could affect Mr Jia Wei Zhang received his master the final decision on the locations. More service sites degree from Shanghai University, are required to satisfy varying demands, but the service People’s Republic of China. He is a coverage level is still unfavourable in one test instance. Senior Operation Analyst for multiple This study highlights a specific focus on the location supply chain operators. problem with time-dependent aspects. The mobility of the population has put growing pressure on medical services in many cities in China which are going through the mega changes of rapid urbanisation. MrReferences Jia Wei Zhang received his master degree from Shanghai University, People’s This study does not consider more features, e.g. some Republic of China. He is a Senior Operation Analyst for multiple supply chain operators. locations may have higher accident rates than others. But [1] Aringhieri R, Bruni ME, Khodaparasti S and the design shows a framework for optimising facility Essen JTV (2017). Emergency medical services locations for emergency medical services in cities and a and beyond: Addressing new challenges through a basis for relocating and dispatching ambulances. Hence, wide literature review. Computers and Operations further research work can be conducted in future, for Research, Volume 78 (C), pp. 349-368. instance, when the change of demand appears to be more [2] Basçar A, Çatay B and Ünlüyurt T (2012). A dynamic or when more features are considered. taxonomy for emergency service station location features are considered. problem. Optimization Letters, 6(6), pp. 1147–1160. 12 Acknowledgements [3] Batta R, Dolan JM and Krishnamurthy NN (1989). Acknowledgements The maximal expected covering location problem: This work is supported by the National Social Science revisited. Transportation Science, 23(4), pp. 277-287. Fund ofThis China work [grant is supported number: by 16BGL083].the National Social Science Fund of[4] China Budge [grant S, Ingolfsson A and Zerom D (2010). number: 16BGL083]. Empirical analysis of ambulance travel times: Notes on Contributors The case of calgary emergency medical services. Notes on Contributors Management Science, 56(4), pp. 716–723. Dr Ming Kun Li received his Ph.D. [5] Chung C, Schilling D and Carbone R (1983). The degree from The University of Hong capacitated maximal covering problem: A heuristic. Kong. He is currently an Associate In: Proceedings of the fourteenth annual Pittsburgh Professor at the Shanghai University, conference on modeling and simulation. Pittsburgh, People’s Republic of China. His research pp. 1423-1428. interests are in supply chain management [6] Church R and ReVelle C (1974). The maximal and terminal planning. covering location problem. Papers in Regional Science, 32(1), pp. 101-118. Dr Ming-Kun Li received his Ph.D. degree from The University of Hong Kong. He is currently an Associate Professor at the Shanghai University, People’s Republic of China. His research interests are in supply chain management and terminal planning.

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Mr Jia Wei Zhang received his master degree from Shanghai University, People’s Republic of China. He is a Senior Operation Analyst for multiple supply chain operators.

M K LI AND J W ZHANG

[7] Current JR and O’Kelly ME (1992). Locating [22] Qi TF and Jing J (2017). Response time of pre- emergency warning sirens. Decision Sciences, 23(1), hospital first aid in urban regions in China, 1996- pp. 221-234. 2015: A meta-analysis. Chinese Journal of Public [8] Current JR and Storbeck JE (1988). Capacitated Health, 33(10), pp. 1466-1468. covering models. Environment and Planning B: [23] Rajagopalan HK, Saydam C and Xiao J (2008). Planning and Design,15, pp. 153-164. A multi-period set covering location model for [9] Daskin MS (1983). A maximum expected covering dynamic redeployment of ambulances. Computers & location model: Formulation, properties and heuristic Operations Research, 35(3), pp. 814–826. solution. Transportation Science, 17(1), pp. 48-70. [24] Schmid V and Doerner KF (2010). Ambulance [10] Farahani RZ, Asgari N, Heidari N, Hosseininia location and relocation problems with time-dependent M and Goh M (2012). Covering problems in travel times. European Journal of Operational facility location: A review. Computers & Industrial Research, 207(3), pp. 1293-1303. Engineering, 62(1), pp. 368-407. [25] Shanghai Civil Affairs Bureau (2015). 2014 report [11] Garey MR and Johnson DS (1979). Computers of elderly population and public affairs. Shanghai: and intractability: A guide to the theory of Shanghai Civil Affairs Bureau. NPCompleteness. New York: Freeman. [26] Shanghai Health and Family Planning Commission. [12] Gendreau M, Laporte G and Semet F (1997). The twelfth 5-years plan on the development of Solving an ambulance location model by tabu search. Shanghai emergency medical services. [online]. Location Science, 5(2), pp. 75-88. Available at . dynamic model and parallel tabu search heuristic for [Access on 30 April 2015]. real-time ambulance relocation. Parallel Computing, [27] Sorensen P and Church R (2010). Integrating Volume 27, pp. 1641-1653. expected coverage and local reliability for emergency [14] Griffin PM, Scherrer CR and Swann JL (2008). medical services location problems. Socio-Economic Optimization of community health center locations Planning Sciences, 44, pp. 8-18. and service offerings with statistical need estimation. [28] Statistics Department (2003). The criteria of setting IIE Transactions, 40(9), pp. 880-892. up emergency medical site in districts of Shanghai. [15] Hill AV and Benton WC (1992). Modelling intra-city Shanghai. time-dependent travel speeds for vehicle scheduling [29] Statistics Department (2009). Report of occupational problems. The Journal of the Operational Research composition of employed population in Shanghai. Society, 43(4), pp. 343–351. Shanghai. [16] Hogan K and ReVelle C (1986). Concept and [30] Statistics Department (2011a). The demographic applications of backup coverage. Management yearbook in Changnin district. Shanghai: Academia Science, 32, pp. 1434-1444. Press. [17] Ichoua S, Gendreau M and Potvin JY (2003). Vehicle [31] Statistics Department (2011b). The demographic dispatching with time-dependent travel times. yearbook in Hongkou district. Shanghai: Shanghai European Journal of Operational Research, 144(2), Academy of Social Sciences Press. pp. 379–396. [32] Statistics Department (2011c). The demographic [18] Indriasari V, Mahmud AR, Ahmad N and Shariff yearbook in Huangpu district. Shanghai: Shanghai ARM (2010). Maximal service area problem for Cultural Publishing House. optimal siting of emergency facilities. International [33] Statistics Department (2011d). The demographic Journal of Geographical Information Science, yearbook in Jingan district. Shanghai: Academia Volume 24(2), pp. 213-230. Press. [19] Loo PY and Lam WY (2012). Geographic [34] Statistics Department (2011e). The demographic accessibility around health care facilities for elderly yearbook in Putuo district. Shanghai: Shanghai residents in Hong Kong: A microscale walkability Academy of Social Sciences Press. assessment. Environment and Planning B: Planning [35] Statistics Department (2011f). The demographic and Design, 39, pp. 629 – 646. yearbook in Xuhui district. Shanghai: Academia [20] Malandraki C and Daskin MS (1992). Time- Press. dependent vehicle routing problems: Formulations, [36] Statistics Department (2011g). The demographic properties and heuristic algorithms. Transportation yearbook in Yangpu district. Shanghai: Shanghai Science, 26(3), pp. 185–200. Higher Education Electronic & Audio-visual Press. [21] Murray AT and Gerrard RA (1997). Capacitated service and regional constraints in location-allocation modeling. Location Science, 5(2), pp. 103-118.

016 HKIE Transactions | Volume 26, Number 1, pp.9–19 [37] Statistics Department (2011h). The demographic Appendix 1. Candidates for setting up emergency medical yearbook in Zhabei district. Shanghai: Shanghai sites. Academy of Social Sciences Press. [38] Toregas C, Swain R, ReVelle C and Bergman L No. Name of Location (1971). The location of emergency service facilities. 1 Huajing Community Hospital Operations Research, 19 (6), pp. 1363-1373. 2 Shanghai Xuhui Changqiao Community Hospital [39] Tuzkaya UR, Heragu SS, Evans GW and Johnson M 3 Shanghai Sports Hospital (2014). Designing a large-scale emergency logistics 4 Shanghai Xuhui Xinle Community Hospital network - A case study for Kentucky. European 5 Shanghai Xuhui Maternal and Child Health-Care Journal of Industrial Engineering, Volume 8, pp. Center 513-532. [40] Yin P and Mu L (2012). Modular capacitated 6 Shanghai Xuhui Tianlin Community Hospital maximal covering location problem for the optimal 7 The Sixth People’s Hospital of Shanghai Jiaotong siting of emergency vehicles. Applied Geography, 34, University pp. 247-254. 8 Wanping Hospital of Shanghai Xuhui District [41] Zarandi MHF, Davari S and Sisakht SAH (2013). 9 The Hospital North Caoxi Road The large-scale dynamic maximal covering location 10 Shanghai Changning Chengjiaqiao Community problem. Mathematical and Computer Modelling, Hospital 57(3-4), pp. 710–719. 11 Shanghai Gamma Knife Hospital 12 Tumour Hospital Affiliated to Fudan University 13 Shanghai Bokang Reproductivity Hospital 14 The Second Pulmonary Hospital of Shanghai 15 Shanghai Xujiahui District Hospital 16 Zunyi Hospital of Shanghai Changning District 17 International Welfare Association International Peace Maternity and Child Health Hospital 18 Branch of No.455 Hospital of the PLA 19 Rihui Hospital of Shanghai Xuhui District 20 Shanghai Xuhui Yixian Hospital 21 Zhongshan Hospital Affiliated to Fudan University 22 Shanghai Thoracic Hospital Affiliated to Shanghai Jiaotong University 23 Paediatric Hospital Affiliated to Fudan University 24 Shanghai Civil Aviation Hospital 25 Southeast Hospital of Shanghai Luwan District 26 Shanghai Ganghua Hospital 27 Shanghai Xuhui District City Tianping Road Lot Hospital 28 Shanghai Xuhui Dental Disease Prevention Center 29 No.455 Hospital of PLA 30 Shanghai Jiangnan Shipyard workers hospital 31 Shanghai Stomatological Medical Center 32 The Ninth People’s Hospital Affiliated to Shanghai Jiaotong University School of Medicine 33 Shanghai Guanghua Hospital (Traditional Chinese and Western Medicine Hospital) 34 Shanghai Changning Xinhua Community Hospital 35 Shanghai Maternal and Child Health Hospital of Luwan District 36 Shanghai Dapuqiao Lot Hospital 37 Shanghai Xuhui Yongjia Lot Hospital 38 Xianxia Hospital of Shanghai Changning District 39 The Third Hospital of Shanghai textile Shanghai Friendship Hospital

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40 Otolaryngological Hospital Affiliated to Fudan 79 Shanghai Huangpu Jinling Road Lot Hospital University 80 Changzheng Hospital of Second Military Medical 41 Shanghai Second People’s Hospital University in Shanghai 42 Shanghai Huangpu Bansongyuan Community 81 Renji Hospital of Shanghai Jiaotong University (West Hospital Campus) 43 Shanghai Oriental Breast Disease Hospital 82 Central Hospital of Shanghai Huangpu District 44 Chinese Medicine Hospital of Shanghai Changning 83 Shanghai Ophthalmological Hospital Tianshan District 84 Shanghai Occupation Disease Prevention and 45 Wuyi Hospital of Shanghai Changning District Treatment Institute 46 Maternal and Child Health Hospital of Changning 85 Shanghai Jingan Shimener Road Lot Hospital District 86 Shanghai Huangpu East Nanjing Road Hospital 47 Shanghai Skin and Venereal Disease Prevention and 87 Shanghai Putuo Jade Street Hospital Treatment Center 88 The Branch of Huangpu Central Hospital (traditional 48 Shanghai Luwan Shunchang District Hospital Chinese Medicine) 49 Obstetrics and Gynecology Hospital of Fudan 89 Shanghai Jingan Jiangning Road Lot Hospital University 90 The Bund Hospital at Huangpu District 50 Shanghai Electric Power Hospital 91 Caoyang Red Cross Hospital 51 Shanghai Luwan Ruijin Erlu Community Hospital 92 Shanghai Stomatosis Prevention and Treatment 52 Shanghai Yuanyang Hospital Center 53 Shanghai Xiangshan Hospital of Traditional Chinese 93 Shanghai Haining Hospital Medicine 94 Haining Community Hospital of Zhabei District 54 Shanghai Changning Beixinjing District Hospital 95 Changzhen United Hospital of Putuo District 55 Shanghai Huangpu District Hospital of Traditional 96 Shanghai Putuo District City Hospital of traditional Chinese and Western Medicine Chinese Medicine 56 Central Huaihai Road Hospital of Luwan District 97 Shanghai Hongkou Zapu Community Hospital 57 Huashan Hospital Affiliated to Fudan University 98 Shanghai Seaman’s Hospital 58 Central Hospital of Shanghai Xuhui District 99 Shanghai Hongkou Tilanqiao Community Hospital 59 Shanghai Changning Zhoujiaqiao Community 100 Shanghai Yangpu Pingliang Subdistrict Hospital Hospital 101 Shanghai Maternal and Child Health Hospital of 60 Luwan Branch of Ruijin Hospital (Center Hospital Yangpu District of Luwan District) 102 Shanghai Yangpu East Hospital (Shanghai Second 61 Shanghai City Huangpu District Dongjiadu Area Textile Hospital) Hospital 103 Shanghai Putuo Zhongshan North Subdistrict 62 Shanghai Post and Telecommunications Hospital Hospital 63 Shanghai South City Maternal and Child Health 104 The Center Hospital of Shanghai City Labor Bureau Hospital 105 Shanghai Hudong Nursing Centre 64 Shanghai First Maternal and Infant Health-Care 106 Shanghai Hangdao Hospital Hospital 107 Baoshan Hospital of Shanghai Zhabei District 65 Tongren Hospital of Shanghai 108 Shanghai Yangpu District City Hospital of traditional 66 Huayang Hospital of Shanghai Changning District Chinese Medicine 67 Yu Garden Hospital for the Elderly 109 Shanghai Zhabei District City Zhi Jiangxi District 68 Shuguang Hospital (West Part) Hospital 69 Shanghai Huangpu Xiaodongmen Lot Hospital 110 Jiaxing Hospital of Shanghai Hongkou District 70 Shanghai West Nanjing Road Hospital 111 Shanghai Hospital of Traditional Chinese Medicine 71 The children’s Hospital Affiliated to Shanghai 112 Shanghai Yichuan Hospital Jiaotong University 113 Geriatric Hospital of Shanghai Yangpu District 72 District Hospital of Jingan Temple 114 Branch of Shanghai First People’s Hospital (Fourth 73 The Square Hospital of Huangpu District People’s Hospital of Shanghai) 74 Shanghai Hongguang Hospital 115 No.411 Hospital of the PLA 75 Workers’ Hospital of Shanghai for Public Services 116 Shanghai Hongkou Ouyang Community Hospital 76 Shanghai Jingan Maternal and Child Health Care 117 Shanghai Hongkou District Xingang Road Lot Centre Hospital 77 Shanghai Jingan Caojiadu Community Hospital 118 Shanghai Yangpu Dentistry 78 Geriatrics Hospital of Shanghai Jing’an District 119 Shanghai City Bridge Community Hospital

018 HKIE Transactions | Volume 26, Number 1, pp.9–19 120 Ganquan Hospital of Shanghai Putuo District 121 Shanghai Zhabei District City Hospital of Traditional Chinese Medicine 122 Shanghai Yangpu Jiangpu Community Hospital 123 Gonghexin Community Hospital of Shanghai Zhabei District 124 Public Health Center affiliated to Fudan University (Shanghai Infectious Disease Hospital) 125 Shanghai Zhabei Women’s Health Institute 126 Health Service Center of Siping Community (Siping Hospital of Shanghai Yangpu District) 127 Dinghai Hospital of Shanghai Yangpu District 128 Shanghai Yangpu Fengcheng District Hospital 129 Shanghai Hongkou Guangzhong District Hospital 130 Shanghai Putuo District Taopu Area Hospital 131 Wanrong Hospital of Shanghai Zhabei District 132 Kongjiang Hospital of Shanghai Yangpu District 133 The Hospital of Tongji University 134 Yanji Hospital of Shanghai Yangpu District 135 Yonghe Branch of Huashan Hospital Affiliated to Fudan University 136 Health Care Center, Medicine College at the Fudan University 137 Shanghai Hongkou Liangcheng Community Hospital 138 Shanghai Yangpu Wujiaochang Community Hospital 139 Shanghai Occupation Disease Hospital (Pulmonary Hospital of Tongji University) 140 Shanghai Jiangwan Hospital 141 Shanghai Zhabei Pengpu Community Hospital 142 Oriental Hepatobiliary Surgical Hospital of the Second Military Medical University 143 Shanghai Yangpu Minxing Community Hospital 144 Shanghai Skin and Venereal Disease Hospital (Shanghai Zunyi Hospital) 145 Central Hospital of Shanghai Yangpu District of Central Plains Branch 146 Shanghai Yangpu Yinhang Community Hospital

019 HKIE Transactions | Volume 26, Number 1, pp.9–19