On the design, implementation, and feasibility of hospital admission services: The admission lounge case

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JID:OME [m5G;July21,2020;19:9]

Omega xxx (xxxx) xxx

ContentslistsavailableatScienceDirect

Omega

journalhomepage:www.elsevier.com/locate/omega

On

the

design,

implementation,

and

feasibility

of

hospital

admission

services:

The

admission

lounge

case

✩

W. Veneklaas

a

_,

_A.G.

_Leeftink

b ,∗

_,

_P.H.C.M.

_van

_Boekel

a

_,

_E.W.

_Hans

b a Department of Capacity Management, ChipSoft B.V., Amsterdam, the Netherlands

b Center for Healthcare Operations Improvement and Research, University of Twente. PO Box 217, 7500 AE Enschede, the Netherlands

a

r

t

i

c

l

e

i

n

f

o

Article history: Received 20 December 2019 Accepted 10 July 2020 Available online xxx Keywords:

Healthcare facility planning Elective admissions Erlang loss model Decision support system Capacity analysis Case mix optimisation

a

b

s

t

r

a

c

t

Anadmissionloungeisanemergingtypeofhospitalfacilitythatpotentiallyimprovestheefficiencyand efficacyoftheperioperativeprocess.Weproposeafive-stepapproachforthedesign,suitability assess-ment,and optimisationofanadmissionlounge.Theapproachusesacasemixoptimisationmethodto selectpatientsfortheadmissionlounge,clinicalward,orforboth.Also,itdeterminestherequired ad-missionloungeandclinicalwardcapacitiesusinganErlanglossmodelcombinedwithanovelanalytical model.Theapproachisintegratedintoadecisionsupportsystem,whichhelpshospitalstoidentifythe suitabilityoftheadmissionloungeconcept,optimiseitsconfiguration,andidentifythepotentialbed re-ductionintheclinical ward.Thedecisionsupportsystemisvalidatedand testedinacasestudy ofa Dutchhospitalusingtheirhistoricaldata.

1. Introduction

The pressure onhealthcare systemsrises asboth thedemand forhealthcareandexpendituresareincreasing [1] .Itispossibleto significantlyreducehealthcarecoststhroughincreasedefficacyand efficiencyof hospital processes [2] .Withinhospitals, a promising developmenttermed admissions without beds addressesefficiency andefficacyoftheperioperative process.Thenewadmission pro-cedureseparatespreoperativeandpostoperativepatientsby admit-tingelectivepatientstoanewtypeofward:theAdmissionLounge (AL).Forapotentiallylargegroupofelectivepatients,thisreplaces the conventional admission procedure to the Clinical Ward (CW), whichmostlysituatespostoperativepatients.

Fig. 1A depictsthe traditionalpatientadmission process.With theintroductionoftheAL,thisadmissionprocessisadaptedtothe processof Fig. 1B .Thedarkcolouredprocessarrowsdepictprocess stepswhereapatienthasanassignedbed.Asaresultofthe intro-duction oftheAL,bedusageisreduced, whichimproves produc-tivity,reducesbedblocking,andoptimisesthepatientﬂow. More-over,theseparationofpreoperativeandpostoperativepatients

en-✩ This manuscript was processed by Associate Editor Jay Rosenberger. ∗ _{Corresponding author.}

E-mail addresses: wveneklaas@chipsoft.nl (W. Veneklaas), a.g.leeftink@utwente.nl (A.G. Leeftink), pboekel@chipsoft.nl (P.H.C.M. van Boekel), e.w.hans@utwente.nl (E.W. Hans).

ableshospitalsto assignskilled staff torelevantwards more eﬃ-ciently.

Theincreasing shift today-surgery, the focuson effectivebed management, and trend to accommodate admissions without a bed,hasledtotheintroductionofALs.Adedicatedunitfor elec-tivesurgeryadmissionsreducesthepre-surgerylengthofstay [3] , andthenumberofcancellationsduetoinsuﬃcientpreparation [3] , without impacting surgeryoutcomes [4] . From an eﬃciency per-spective,theALisassociatedwithearlierstartingoftheoperating theatre [5] , and increased bed availability for emergency admis-sions [3] .Furthermore,theimplementationofan ALisassociated withincreasedpatientsatisfaction [5] .

Inapreliminaryﬁeld study [6] ,weconductedsemi-structured interviews withthree hospitals to identify their expected effects oftheAL,andtheir strategicdecisions.Twohospitalswereabout tostartanALpilot,andthethirdhospitalhasalreadybeenusing theALforapproximatelyoneyear.Eachofthehospitalsnotedthat therearethreemaindesiredeffectsoftheAL:

-lower workloadforthe CWstaff throughseparation of preop-erativeandpostoperativeelectivepatients;

-lower staﬃng costs throughthe reduction ofbedreservations andseparationoftheaforementionedprocesses;

-increasedpatient friendlinessthrough amorecomfortable ad-missionenvironment.

Strategicdecisionsregardingthe (i) casemixselection,(ii) care unit partitioning,(iii) capacitydimensioning, and(iv)facilitylayout https://doi.org/10.1016/j.omega.2020.102308

0305-0483/© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license. ( http://creativecommons.org/licenses/by/4.0/ ) Please citethisarticleas:W.Veneklaas,A.G.LeeftinkandP.H.C.M.vanBoekeletal.,Onthedesign,implementation,andfeasibilityof

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Fig. 1A. Traditional admission process.

Fig. 1B. Admission Lounge admission process.

forthe AL are likely to affectthe extent in which these desired effectsoccur [1] . Below,we clarifythesedecisions inthecontext oftheALandtheCW.

(i) Casemixselectionreferstothetypesandvolumesofpatients that theALserves(andthe patienttypesandvolumesthat areadmittedtotheCWaccordingly);

(ii) Careunit partitioningaddresses boththe creationofthe AL andCW,anddetermineswhichpatientgroupstoconsolidate ineithertheALorCW.Theseaffectthedecisionsonhowto designatestaff,equipment,andbedstoeachunit;

(iii)Capacity dimensioning occurs in conjunction with (ii), and considers the size of the AL and CW expressed in staffed beds,equipment,andstaff;

(iv)Facility layout concerns the physical positioning of the AL and the CW, based on which facilities should be close to eachoftheunitsandtheavailabilityofsuﬃcientspace. There is a lack of insight into the relations between the ex-pected performance of the AL and the CW, and the four afore-mentioned strategic decisions [6] . This leads to an unbalance in workloadamongst the two facilities andcapacitywaste in terms ofspace,staff,andlogistics.Topreventtheseissues,andtoenable decisionmakerstoanalysetherelationsbetweenstrategicdecision makingandexpectedperformance, wedevelop a decisionsupport system(DSS).ThisDSSisdesignedtoworkwiththehospital infor-mationsystem (HIS) HiX, deliveredby aDutch HISdeveloper.Our DSSfollowsaﬁvestepstrategicdecisionmakingapproach:

Step1: SpecifyinclusionandexclusioncriteriafortheAL.The inclu-sionandexclusioncriteriaarespeciﬁedbyhospital man-agementandtheeffectsoftheassignmentsarevisualised percriterionusingdatavisualisationtechniques.

Step2: Determine theappropriatestaff,equipment,andsupporting processesfortheALandCW.Hospitalmanagementderives the required staff skill mix, appropriate nurse-to-patient ratios,andspecialequipmentrequirementsasaresultof thespeciﬁedcriteriainStep1.

Step3: AnalysisofpotentialbedreductionsfortheCWandrequired capacity fortheAL.Following fromtheinclusion and ex-clusion criteriaof Step1, therequired capacities forthe ALandCWcanbeassessed.TheDSSshowsthepotential bedreductionsfortheCWgivenadesiredblocking prob-ability, andtherequirednumberofbedsfortheALwith itsexpectedperformance.

Step4: Analysis of feasibility of theAL and CWwithin the facility layout. With the required capacities for the AL and CW, hospitalmanagementcanderivewhetherthenew conﬁg-urationﬁtswithintheexistinghospitallayout.

Step5: Optimisation ofthe inclusion and exclusion criteriafor the AL.TheassignmenttotheALandtheCW,whichfollowed fromStep 1,canbe optimised inordertoattain optimal servicelevelsandoccupancyratesinbothfacilities.

Ourproposedﬁve-stepapproachconsecutivelyaddressesa va-rietyofplanningdecisions.HavingthemodelintegratedintoaDSS allowsmanagersandplannerstoquicklyaccessarangeofoptions fortheplanningissueathand,andtotest howperformancemay be affectedby interventionsin theplanningprocess [7] . Fig. 2 is anoverviewoftheinputsandactionsfortheuser,andthe work-ingorderoftheDSSfollowingtheﬁvestepsofourapproach.

The remainder of this paper is structured as follows. Section 2 reviews the literature on each ofthe ﬁve steps of our DSS, andpresents our selection of models that we developed to analyse therelationbetween strategicdecisions andthesystem’s expected performance. In Section 3 , we formulate these models, andSection 4 presentshowthemodelsareintegratedintotheDSS. Section 5 presentsthe results ofa casestudy withourDSS in a Dutchhospital.Finally,in Section 6 wepresentourconclusions. 2. Literaturebasedmodelselection

We review the literature relatedto the five steps of our pro-posedapproach, in Sections 2.1 –2.5 respectively. Section 2.6 con-cludes with the scientific contribution of the proposed five-step approach.

2.1. Step1:specifyinclusionandexclusioncriteriafortheAL The inclusion and exclusion criteria determine the patient groupingoftheALandCW.Inpatient groupingsystems,patients aregenerallygroupedbasedonvarioustypesofdata.Thismay in-clude clinical data (e.g., diagnosis, procedures, ASA classiﬁcation) [8] ,demographic data (e.g., age), andresource consumption data (e.g., costs, LOS) [9,10] . Pooled wards are typically organised ac-cording to patients’ length of stay [11–14] or to patients’ needs [10,15,16] .In theﬁrst case, multi-speciality wards are createdfor patientsofsimilarlengthsofstay.Inthesecondcase,wardscould beorganisedonthebasisofpatientneeds [15] .

Groupingpatients onthe basis of LOSis eﬃcient anda main indicator for both postoperative outcome and satisfaction of the patient [10] .Toaddressboth eﬃciencyoftheALandpatient sat-isfaction,werequireamixofclinicaldataanddemographicdata, which serve asinputsto determine resource consumption levels. The mostrelevantattributes forelective patient selection forthe ALorCWare:ASAscore,age,andthe(sub)specialitythepatient be-longsto.Therelevanceoftheattributesisbasedontheir applica-bilitytoawidevarietyofhospitalsandtheirabilitytoindicatethe patient’sexpectedlengthofstay(LOS) [6] .Basedon these charac-teristics,patientscanbeassignedtotheALortheCW.Patientsfall withina‘greyarea’whentheycouldbeassignedtoboth,orwhen managementcannot decidewhat assignmentismostappropriate. Thisgreyareaforpatientgroupingis,toourknowledge,uniquein theliterature.InStep5(Section 2.5 ),weoptimisetheassignment ofpatientsfromthegreyareatotheALandCW.Withtheuseof datavisualisation,wedemonstratetheeffectsofinclusionand

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Fig. 2. Overview of DSS methodology throughout the ﬁve steps. The top stream represents the user’s inputs and actions, and the bottom stream represents the DSS’s working order.

clusion criteriafor the AL on the volume and complexityof the AL’spatientpopulation.

2.2. Step2:determinetheappropriatestaff andequipment

Appropriate staff and equipment for theAL and CWoptimise thequalityandcostofcare.Workloadisadeterminantforthe ap-propriate staff level [17] ,in conjunctionwiththe available equip-ment [18] .Moreover,theuseofbetterequipmentisfoundtolead to a potential reduction ofthe staff level [19] .Contrarily, invest-mentsinhumanresourcesarearguedtobemoreeﬃcientthanin newer(better) equipment [17] .Todetermine theappropriate mix ofstaff skillsandrequiredequipment,thebestindicatorsare diag-nosisrelatedgroups,casemixgroups,andmedicalspeciality indi-cators [20] .

Acombinationofpatientcharacteristics(includingpatient acu-ity) and organisational factors results in the best model for ex-plaining theuseofhospital careservices [20] .The characteristics found inthereviewby vanOostveen [20] canbe usedas predic-torsiftheyareknownpriortoapatient’sadmission,oras explana-toryfactorsifthey occurduringadmission,forexample,to moni-tortrends intimeregardingthe demandforcare.FortheAL,the requiredstaff canbederivedfromtheinclusionandexclusion cri-teriaspeciﬁedinStep1andtheireffectsonthecasemixdivision. 2.3. Step3:analysisofcapacityrequirements

Capacity dimensioning determines the appropriate number of bedstoadmitpatientstotheALandCW.Theunderlyinglogistical systemoftheadmissionanddischargeprocesscanberegardedas a job shopsystemwithstrong precedenceconstraints.A job shop allowstheprocessingofvariousclassesofproducts(patients)with capacity limitations inherent to the control and handling of the products andthe preparationtimesof themachines(in our case theadmissionfacilities:ALandCW).Thedeterminationofcapacity requirementsfortheCWandAListwofold:wewanttodetermine

the potential bed reduction for the CW, as well as the required bedsfortheAL.Therequiredcapacitiesdependonthepopulation volumesandcomplexityofbothfacilities,determinedinStep1. 2.3.1. PotentialbedreductionfortheCW

Variouspapers study the determination ofthe number of re-quiredbedsforaspeciﬁcclinicaldepartmentsuch thatalmostall patients can be admitted [11 ,14 ,21–24] . The Erlang loss model is oneofthemostwidelyusedqueueing-basedmethods,whichwas ﬁrst introduced forthe assessment of queues in telecommunica-tions, and was later applied to industry and healthcare settings [25–28] .

The Erlang loss model assumes that patient arrivals are Pois-son distributed.Manyauthors haveshown that arrival processes, especially unscheduled, can be approximated by a Poisson pro-cess [11,13,23,28] .Forpracticalpurposes,itisnotrequiredthatthe number ofadmissions follows the laws of a Poisson distribution exactly.Thekeypointforpracticalmodellingpurposesisthat the variabilityinthenumberofadmissionsisgenerallywell captured bythePoissondistribution,makingthisalsoareasonable assump-tionforthearrivaldistributionsthatdonotfollowthePoisson dis-tribution very well [22,23] . Several studies have shown that un-scheduled arrivals perform better under the Poisson distribution than scheduled arrivals [11,29] . However, even scheduled arrivals can be modelled under the Poisson assumption [11,21,30] , espe-ciallyiftheresultsaresolelyrequiredforstrategicandtactical de-cisionmaking [11] .Fordecisionsontheoperationallevel,more ac-curateapproximationsmayberequired [22,31,32] .AstheCWhas asimilarstructure asthe wardsconsidered in [11] ,wewillapply theErlanglossmodeltodeterminethepotentialbedreductionfor theCW,aspresentedin Section 3.1.1 .

2.3.2. RequiredALcapacity

Contrary to the CW, the AL will not reach a steady state on mostworkingdays,astheALisﬁlledwithpatientsinthe morn-ing and is empty by the time the regular operating room (OR) Please citethisarticleas:W.Veneklaas,A.G.LeeftinkandP.H.C.M.vanBoekeletal.,Onthedesign,implementation,andfeasibilityof

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timehaspassed.Therefore,wecannotapplytheErlanglossmodel forthedimensioningoftheAL.Other characteristicsoftheALare thatthepatientarrivalprocessissubjectedtothesurgical appoint-mentplanningandthat patientsrequireabedfora shortperiod of time. This is similar to a hospital’s day care department, but contrarily,thepatient doesnotreturntotheALaftersurgery.We werenotabletoﬁndliteratureaboutcapacitydimensioningforan ALorsimilarfacilities thatdonotreach asteadystate. Therefore, wedevelopedourownmodeltodeterminetherequiredcapacity, basedon historical arrival intensities. This modelis presented in Section 3.2.2 .

2.4.Step4:analysisoffeasibilityoftheALandCWwithinthe facilitylayout

Some choices orrestrictions within theexisting facilitylayout may have a limiting effect on all preceding decisions. Long dis-tancesincrease transportation andtraveltimesbetweenfacilities, which lead to an increase in indirect care activities. The litera-turecontainsawiderangeofmethodstosolve thefacilitylayout problem,in whichthe multitudeoftrips fromandto facilities is minimisedandpenalisedwiththe distancetravelled.We referto [25] and[26] for examples of such models.

2.5.Step5:optimisationoftheinclusionandexclusioncriteriafor theAL

Step5optimisestheassignmentofpatients.InStep1,patients areassignedtoadmissiontoeithertheALortheCW.Patientsthat canbeadmittedtobothunitsareassignedtoagreyarea.The pa-tients fromthegrey area should be assignedto either theAL or theCW. To the best ofour knowledge, methods to optimise the casemixfortheALorcomparablejobshopelementsdonotexist. Ourmethod aimstoassist inchoosingthe mosteffectiveand ef-ficientassignmentsfortheALandtheCW.Efficacyisrepresented bythepopulation sizeof thepatientsassignedtothe AL.Patient friendlinessandreducedworkloadontheCWstaff areinducedby alargerALpopulationsize.Efficiencyisrepresentedbythebed re-ductionfortheCWversusthebedrequirementsfortheAL.A po-tentialbedreductionindicatesincreasedefficiency.Theunderlying modelispresentedin Section 3.3 .

2.6.Scientificcontributionoftheproposedfive-stepapproach We found severalliterature gaps that we aim tofill withthis research.For ourpatient selection methodologyin Step1 we re-quireagreyarea,whichisnewtotheliterature,toourknowledge. InStep3,weneedtodeterminetheexpectedperformance ofthe AL.Becausevery littleiswrittenabouttheAL,we needtodefine a new model forour analysis. Step 5 aims to optimise the case mixwithinthe boundssetby theinclusionandexclusioncriteria setinStep1,a methodwedid notcome acrossintheliterature. Section 3 providesthemodelsforSteps1,3and5.Theintegration ofthefive-stepapproachintoaDSSisdiscussedinSection4. 3. Methodsandmodels

This section describes the case mix division methods of Step 1(Section 3.1 ), andgives themodel formulationforthe capacity dimensioningofStep3 (Section 3.2 ) andthegrey area optimisa-tionofStep 5(Section 3.3 ). Steps 2and4 predominantlyconsist ofqualitativedecisionssupportedbybasicdatavisualisation tech-niques,andarethereforenotdescribedinthissection.Allstepsare integratedinSection4.

3.1. Methodsforstep1

InStep1,theusergivesinputforthecasemixdivision.Weuse datavisualisationtechniquestoindicatetheeffectsofthe patient selection in two ways: the case mix division, and the admission ratetotheCWbothwithandwithouttheAL.

3.1.1. Casemixdivision

The inclusion and exclusion criteriafor the attributeselective status,age,ASAscore,andthe(sub)specialityleadtoadivisioninto the categoriesAL,CW,andgrey area patients. Foreach attribute, the size ofthe patient population foreach category is presented in a stacked bar chart. The total case mix is alsopresented. The patientselectionmethodisbasedonthepatient’sattributes:a pa-tientis markeda CWpatient ifoneor moreattributesfall inthe CWcategory.ApatientisanALpatientifallattributesofthe pa-tientfallintheALcategory.Inothercases,whenthepatient’s at-tributesareacombinationofgreyareaandAL,thepatientis con-sideredagreyareapatient.

3.1.2. Admissionrate

Thecurrentadmissionraterepresentstheadmissionrateofthe CWwithouttheAL.TheaveragenumberofadmissionstotheCW perhourisdetermined.WithanAL,themomentthatALpatients arrivetotheCWispostponedontheday,resultinginabetter dis-tributionoftheadmissionsoverthecourseoftheday.The admis-sionratesarepresentedintheDSSwithabarchart.

3.2. Modelsforstep3

Step 3 focusses on capacity dimensioning of the CW (Section 3.2.1 )andtheAL(Section 3.2.2 ).

3.2.1. CWbedreductionmodel

ForthecapacitydimensioningoftheCWweusetheErlangloss model,alsoknown astheM/G/c/c queueingmodel,asit incorpo-ratessuﬃcientdetailforstrategicandtacticaldecisionmaking.We followthe notationof [11] .Patients arriveaccordingto aPoisson processwithparameter

λ

.TheLOSofan arrivingpatient is inde-pendentandidenticallydistributedwithexpectation 1/μ,andcan followageneraldistribution [11] .Theterm

λ

/μ isoftenreferredto astheoffered load(

ρ

) tothe system.The numberofoperational (occupied)bedsequalsc.Themodelassumesthatthereisno wait-ingarea,whichmeansthatanarrivingpatientwhoﬁndscomplete occupancyattheCWisblocked.Theblockingprobabilityisgiven by: Pc=

(

ρ

)

c_/c! c k=0

(

ρ

)

k/k! (1)

Theoccupancyrateisnowdeﬁnedas:

Occupancyrate=

(

1− Pc

)

ρ

c (2)

whichisequivalentto:

Occupancy= A

v

eragenumbero foccupiedbeds

Numbero foperationalbeds (3)

With Eq. (1) we are able to assessthe blockingprobability fora givennumberofbedstoavoidhighrejectionrates.

Fig. 3 showshowtheLOSintheCWiscalculatedforCWand ALpatients.TheLOSforaCWpatienti(LOSCW

i )ismeasured from

thestartoftheadmissiontotheCWpriortosurgeryuntilthe dis-chargefromtheCW.TheLOSforanALpatientiattheCW(LOSAL

i )

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Fig. 3. Determining the LOS at the CW for AL and CW patients.

The average LOS (ALOS) for the jointsets of ALpatients (sAL)

andCWpatients(sCW)isgivenby:

ALOS= 1

|

sAL

|

i∈sAL LOSAL_i + 1

|

sCW

|

i∈sCW LOSCW_i (4)

This characteristic helps to estimate the potential bed reduc-tion, astheLOS withoutan AL isexpectedto be larger thanthe LOS withan AL.Consequently, asimilar servicelevel forthe CW canbeachievedwithfewerCWbeds.

3.2.2. ALcapacitymodel

AL arrivals will occur according to the appointment schedule oftheoperatingtheatre, andarethereforestronglyrelatedtothe MasterSurgery Schedule(MSS).TheMSSdetermineshowmuchOR time is to be assignedto the variety ofsurgerygroups – onthe highest level representedby specialties– on each weekday [33] . Because capacitydimensioning decisions mainlyfocus on assign-ing OR time to disciplines, resultingin the MSS [34] ,the MSSis leadinginthearrivalsapproximationfortheAL.

We relate the arrivals of the AL patients to the daily total planned OR time forthe specialtieswithin the AL casemix. The dailytotalplannedORtimeforaspecialityisthetotalplanned du-rationofsessionswithintheMSSdedicatedtothesurgeries sched-uled for a speciality. We call days on which common amounts of OR time are allocated to a speciality representative days and use those days as a benchmark for the AL performance assess-ment.

Toestimate thepatients’ LOS inthe ALbefore the ALhas ac-tually been introduced in the hospital, we develop assumptions abouttheLOSinconsultationwiththehospital. Thisallows usto determinetheofferedloadoftheAL.Thegeneralconsensusofour pilot hospitalswastohavethepatientarriveattheALtwohours priortothescheduledstartofsurgery.Basedonthearrivalrateto theORforeachhourtheoperatingtheatreisopened,wecalculate theofferedloadduringworkinghours.

Foreachdayrepresentativedayn∈N,we deﬁnetimebuckets tn ∈Tn withdurationd(in minutes) inwhicharrivalsmayoccur

attheAL.TheexpectedadmissiondurationofDisamultipleofd andrepresentsthetotaltimethat apatientspendsattheAL.The openingtime oftheALisatthebeginning oftn=0,the opening

timeoftheoperatingtheatre(OT)startOT∈Tnisintimebuckettn

andmarksthemomentthatpatientscanleavetheALfortransfer totheholding. Fig. 4 givesagraphicalrepresentationoft,d,D,and startOTonatimeline,omittingnforsimplicity.

Before startOT, the arrivals

λ

tn duringtn∈

{

0,1,2,...,startOT}

remain inthe AL.Ifthe patient hasspent D_d time buckets inthe

ALandtheOTisopen(startOT≤ tn),thepatientleavestheAL.The

offeredALload

ρ

tnduringtimebuckettn onagivendaynis

de-terminedby:

ρ

tn

tn t0

λ

tn, 0≤ tn<startOT tn tn=max

{

tn−

(

Dd

)

,0

}

λ

tn, startOT≤ tn≤ T (5)

Theaverageloadpertimebucket

ρ

tforasetofnrepresentative

daysnisobtainedthrough:

n

ρ

tn

N ,

∀

tn (6)

The average number ofrequired beds to accommodate all AL arrivals on a certain day amounts max

ρ

t

. However, assuming

thatthiswouldsuﬃceastherequirednumberofoperationalbeds wouldmostcertainlyleadtoanunderestimationduetovariability oftheload.

Weassesstheperformance oftheproposedALcapacityto de-terminehowtheALwouldhaveperformedonrepresentativedays. Todoso,wecomparethehistoricalloadontheALbypatientsthat wouldbeassignedtotheALbasedontheircharacteristicsandthe ALinclusioncriteria.Whenevertheload

ρ

tn exceedstheset

num-berof beds,apatient wouldhave beenrejectedandadmitted to theCWinstead.Wedeﬁnethepercentageoftheopeninghoursof theALonwhichrejectionstook place,forall representativedays, astherejected hoursrate.Wealsomeasurethefractionofdayson whichat leastone rejection took place, termed therejected days rate.Bothindicatorsincorporatevariabilityandthereforeassessthe validityofdimensioningtheALaccordingtomax

ρ

t

.

3.3.Modelforstep5

Agreyarea ofpatientselectionisdeﬁned, basedonthe inclu-sion and exclusioncriteria for the AL and CW asdetermined in Step1.Nomodelisavailableintheliteraturetooptimisethecase mixfortheALorcomparablejobshopelements.Therefore,inthis section,wedevelopamodeltochoosethemosteffectiveand eﬃ-cientassignmentsfortheALandtheCW.

WeassignpatientswithinthegreyareatoeithertheALorCW byenumeratingtheassignment possibilitiesinthegreyarea.The ALandCWselectioncriteriaserveasboundsfortheoptimisation method. The selection criteria for the dimensions age, speciality, andASAcanbeuptodiscussioninthecontextofageneral hospi-tal.Thecasemixoptimisationhasadualobjective:optimaluseof theALin termsofoccupancy andrejectionrates,andamaximal bedreductionfortheCW.Thisoptimisationcanbe formulatedas aMILP,whichisabletosolvelargesolutionspacesandoutputs a Please citethisarticleas:W.Veneklaas,A.G.LeeftinkandP.H.C.M.vanBoekeletal.,Onthedesign,implementation,andfeasibilityof

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Fig. 4. Graphical example of time buckets t , the time bucket duration d (60 min), and the admission duration D (120 min) on a timeline. This AL is opened from 06:00 to 17:00.

singleoptimalresult.Giventherelativelysmallsolutionspace (ex-plainedinthenext paragraph) andthe desireto lettheend-user considermultiplesub-optimaloptions,wechoosetousecomplete enumeration.

Theagecategoryisanintervalcategory,andshouldthusbe di-videdinsubcategories.Weproposetousebucketsof5years(e.g., 20–25, 25–30, etc.), asa result of a trade-off between computa-tionalcomplexityandoutcomeprecision.TheordinalcategoryASA consistsofthe threerelevant ASA classiﬁcations(I,II, III)for the AL.Ifa hospitalhasawide varietyofspecialties, orthe modelis reﬁnedtowards subspecialties,thesolution spaceincreases expo-nentially,byafactorof2k_,_with_k_being_the_number_of_specialties

withinthegreyarea.

After theenumeration wecomparethe overallperformance of allassignment rulesets. Becausethere isa widevariety of avail-ableperformanceindicators,weapplya scoringmethodtoassess eachconﬁguration’sperformance, basedonthehospital’s individ-ualgoals.Hence,wecandirectDSSuserstowardspersonalised ef-fectiveandeﬃcientoutcomes, andenablethemtomake compar-isonsrelativelyeasy.

The scoringmethod encompassesefficiencyandservicelevels. Efficiencyisrepresentedbytheoccupancyratiosandtherequired numbersofbedsfortheALandtheCW.Servicelevelsare repre-sentedby theblockingprobability fortheCWandthe hourly ac-ceptancerateforthe AL.Froman economic pointofview,in the analysiswe areparticularly interestedinconfigurations that may leadtoareductioninthetotalnumberofrequiredbeds.Inthese configurations,thebedreductionfortheCWexceedsthenumber ofbeds required for the AL. We propose the following objective functiontoallowbalancingservicelevelandefficiencyofthe solu-tion:

Perf ormance

=

α

β

=1.

4. Decisionsupportsolutiondesign

Variousauthorssolve capacityproblemsinhealthcareand im-plement the solution into a DSS [7,10,35–37] . Our ﬁve step ap-proachisintegratedinaDSS,asshownin Fig. 2 ,toallowmanagers andplanners to easily useour model. The following subsections discusstheDSSdesignforeachoftheﬁvesteps.Tosystematically

Table 1

Patient inclusion and exclusion criteria for the AL speciﬁed for the case hospital.

Category Status Age ASA Specialties CW Non-elective ≥ 86 IV, V –

Grey – 76–85 III BAR

AL Elective 18–75 I, II CHI, KAA, NCH, ORT, PLA, URO

design the DSS, we incorporate the constructs of the technology acceptancemodel(TAM) [38] .

TosetuptheDSS, theuserﬁrsthastospecifywhichhistorical dataisused.Therequiredinputparametersaretheadmissiontype (day patientsand/or clinical patients), the relevantCWs, andthe period to use forthe analysis.After the data isloaded, the user can usethe three tabsin theDSS GUIto go through all theﬁve stepsofALdesigndecisionmaking.

4.1. DSSstep1

The ﬁrsttabinthe DSS(Fig. 5A )showsthe decisionvariables considering thecasemix. Thesevariablesare presentedasa ma-trix,withthecriteriaforinclusion andexclusionshownvertically andtheassignmenttotheAL,CWorgreyareahorizontally.Below thematrix,thepopulationsizesfortheassignmentofeachcriteria arevisualised.Inaddition,thetotalcasemixfractionsassignedto theAL,CWandgreyareaareshown.

4.2. DSSstep2

InStep2,qualitativedecisionvariablesareintroducedfor spec-ifying theappropriate staff,equipment,andsupportingprocesses. ThesevariablesarenotdirectlyincorporatedintheDSS,butcanbe derivedfromthequalitativepatientselectioncriteriain Table 1 . 4.3. DSSstep3

Tab 2 inthe DSS(Fig. 5B ) showshow the ALandCW assign-ments affect the requiredbeds for theCW andAL, fora chosen rejectionrate.Thetableshowsthenumberofbedsneededinthe CW andthe potential bedreductions after the AL is introduced. Inaddition,thesecond tableshowsthehourlyanddailyrejection rates giventhe number of bedsin the AL.Along with the occu-pancy rate, thesenumbers indicate thenumber ofbeds required attheAL.Colourcodesshowhowtheindicatorsperform. 4.4. DSSstep4

TheperformanceoftheALandtheCW,foraspeciﬁednumber ofbeds,isalsopresentedin Table 2 .Fromthis,theusercanderive the requirednumber of ALbeds and potential bedreduction for the CW. The number of required AL beds also implies the need forawaitingarea(thelounge aspectoftheAL)thatissuﬃciently

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Fig. 5A. Tab 1 of the DSS.

Fig. 5B. Tab 2 of the DSS.

Table 2

Inputs for the Erlang loss models and the corresponding required beds and corresponding occupancy (occ.) ratios (case hospital data, 2015–2017, n = 7565).

Current situation With the admission lounge p b = 0.05 p b = 0.01 p b = 0.05 p b = 0.01 speciality λ μ beds occ. beds occ. μ beds occ. beds occ.

BAR 1.38 1.87 6 42% 8 32% – – – – – CHI 3.36 4.57 21 70% 25 61% 4.47 20 72% 24 62% KAA 0.07 1.19 2 4% 2 4% 1.03 2 4% 2 4% NCH 0.29 1.17 2 16% 3 11% 1.09 2 15% 3 10% ORT 1.97 3.03 10 57% 13 46% 2.94 10 56% 12 48% PLA 1.66 2.14 7 49% 9 39% 1.92 7 44% 9 35% URO 1.12 2.21 6 40% 7 35% 2.14 6 39% 7 34% Pooled 9.86 3.17 37 80% 43 72% 3.08 35 80% 41 71%

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Fig. 5C. Tab 3 of the DSS.

Table 3

Performance of the AL in the case hospital calculated with our deter- ministic model (case hospital data, 2015–2017, n = 7565).

Beds Rejected hours (%) Rejected days (%) Occupancy (%)

1 25.1 71.4 82.9 2 12.3 41.9 65.5 3 5.1 20.4 51.8 4 2.9 8.1 41.4 5 0.4 2.1 33.9 6 0 0.2 28.4 7 0 0 24.3

large.Managementcandecideupon thefeasibilityofthesolution withinthehospitallayoutonthebasisoftherequiredcapacities. 4.5.DSSstep5

Table 3 oftheDSS(Fig. 5C )showsoptimisationpossibilitiesfor assigningthepatientsinthegreyareatotheALorCW.Here,the top ﬁve outcomes are presented in a table, including the initial assignment.Notethatwhena differentassignmentischosen,the outputsof Tables 1 and 2 willbeadjustedaccordingly.

5. Casestudy

Thissectionprovidesthecomputationalandpracticalresultsof theintroducedDSS.Thecasestudywascarriedoutincollaboration withanaveragesizegeneralhospitalinTheNetherlands.The hos-pitalis planning toexpand, and simultaneously considers to im-plementan AL. At thetime of research they alreadyhad a ward dedicatedto mainlythe admission ofelective patients, butnot a fullydedicated AL.In Section 5.1 we describe the datainput de-rivedfromthehospitaldata. Section 5.2 thendiscussestheuseof theDSS.

5.1.Datainputs

For the data preparation we select admissions of clinical pa-tients, duringweekdays, froma surgical ward. These admissions took place from 2015 to 2017. This ward admits all adult, elec-tive, surgicalpatients andhada capacity of39 beds on average. Irregularitiesareremovedfromthedatasetbyapplyingathreshold of0.5% ofalladmissionsper speciality.Thisleavesuswithseven surgicalspecialtiesinthe dataset(withtheir Dutch abbreviations mentionedwithinbrackets):

– Bariatrics (BAR)

– Generalsurgery (CHI)

– Jawsurgery (KAA)

– Neuro-surgery (NCH)

– Orthopaedics (ORT)

– Plasticsurgery (PLA)

– Urology (URO)

WeapplyourDSSmethodologytothecasehospital.Recallthe ﬁvesteps:

1. SpecifyinclusionandexclusioncriteriafortheAL;

2. Determine the appropriate staff, equipment, and supporting processesfortheALandCW;

3. Analysis of potential bedreductions forthe CW andrequired capacityfortheAL;

4. Analysisoffeasibilitywithinthefacilitylayout; 5. Optimisation:assignmentofthegreyareapatients. 5.2. UseoftheDSS

5.2.1. Step1casestudyresults

The hospitalindicates that patientsthat are allowed accessto the AL are elective patients, aged between 18 and 75,with ASA classiﬁcationIorII,andfromeveryspecialityofthesurgicalward, exceptBARpatients.Patientsthatarenotallowedaccessare non-elective,86yearsorolder,orbelongtoASAclassIVorV.Allother patients are considered to be in the grey area. BAR patients are generallyoverweightanddiabetic,meaningthatspecialequipment is requiredduringthe admission process. Becausethe hospital is interestedinthedifferenceinperformanceoftheALwithor with-outtheBARpatients,thespecialityisinitiallyassignedtothegrey area. Table 1 summarisesallinclusionandexclusioncriteria.

Thepatientmixdecisionsclassifythepatientsinto44%AL pa-tients,35% greyarea patients,and23% CWpatients. Fig. 6 shows that onlyadultpatientsare admitted tothe AL,andthat asmall portionof thepatientsis non-elective. Theattribute ASA hasthe largest greyarea. The size ofthe grey area deﬁnesthe room for optimisationinStep5.ThelowerboundforthenumberofAL pa-tientsis44%andtheupperboundis77%ofallpatients.

Step2focussesontheselectionoftheappropriatestaff, equip-ment,andsupportingprocesses forthe AL.Thehospital indicates thatallavailablestaff isqualiﬁedtoadmithigher-complexpatients

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Fig. 6. Distribution of the patient mix as a result of the inclusion and exclusion criteria for the AL. The numbers in the bars indicate the percentages (Case hospital data, 2015–2017, n = 7565).

Fig. 7A. Admissions to the CW from 6 AM to 8 PM, without the AL (case hospital data, 2015–2017, n = 7565).

with,e.g.,an ASAIIIclassiﬁcation.Cliniciansindicatedthat an ap-propriatenurse-to-patientratiofortheadmissionprocessis2to1 ifthe admissionshaveto take place overa shortperiod oftime. Withalowernurse-to-patientratiothenurses’workloadbecomes toohigh,andthepatientfriendlinessdecreases.

The hospital has special equipment (larger beds and heavier mattresses)andfacilities(widerdoorsandstandingtoilets)forthe BAR patients.Fortheotherpatientsthereisnoindicationof spe-cial requirements. Currently, a nurse transfers the patient to the holding. Because the CW is one ﬂoor level beneath the OT, the nurse has touse an elevator to transfer the patient to the hold-ing,whichisfoundtobetimeconsuming.

InStep 3,we ﬁrst analyse the plotof the admission and dis-charge moments atthe CW,with andwithout the AL(Figure 7). We observethat the casehospital experiences a prominentpeak loadintheCWinthemorning,causedbynewpatientadmissions. AnALcanstronglyreducethatpeakloadandspreadtheadmission ofpatientsmoreevenlyacrosstheday(Figs. 7A and 7B ).

Next, we dimension the CW with and without the AL. Table 2 shows that the CW can reduce the required number of beds by 2 for a blocking probability of both 5% and 1% in the pooledsituation.The hospitalposedthat a pooledcapacityof37 bedscouldbe anaccurateestimationfortheassessed period. Be-causeallsurgicalspecialtiesare situatedinoneCW,itis not rel-Please citethisarticleas:W.Veneklaas,A.G.LeeftinkandP.H.C.M.vanBoekeletal.,Onthedesign,implementation,andfeasibilityof

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Fig. 7B. Admissions to the CW from 6 AM to 8 PM with the AL (case hospital data, 2015–2017, n = 7565).

evant to comparethe results for theindividual specialties. How-ever,it isrelevanttoanalysethebehaviouroftheindividual spe-cialties:ingeneral,the occupancyratesarerelatively lowgivena blockingprobabilityof5%.Theoccupancyfurtherdecreasesby ap-proximately8–10percentpointsforthelargerspecialtieswhenthe blockingprobabilityof1%isselectedcomparedto5%.

We also plot the blocking probability and occupancy ratio (Figs. 8 and 9 )asafunctionofthenumberofCWbeds.Theplots areavailableforthesituationwithouttheAL(aspresentedinthis paper)andwiththeAL.The curvesshowthesamebehaviour for bothsituations,exceptwithafasterconvergenceforthesituation withouttheAL.Thehospitalindicatedthattheadditional informa-tiongivenbyhooveringoverthelines(notshownintheﬁgures)is ahelpfulextensionoftheplotsbecauseitincreasesthereadability oftheplots.

Withthe currentpatientselection criteria, theperformance of theALwill beasshownin Table 3 (on representativedays),with openinghours from 6:30 AMto 11:00 AM. Theseopening hours mayspanashortperiodoftime,butfewpatientsassignedtothe ALareadmittedafter11:00AM.Withthecurrentcriteriawe rec-ommendto open the AL with 3 or 4 beds. When the hospitals choosestoassignfourbedstotheAL,theymayhavetoclosebeds during periods with lower demand, because the expected occu-pancyratioof41%isrelativelylow.Withthreebeds,theoccupancy ratioismorethan10% higher(51.8%),andtherejectedhoursrate increasesbyonly2.2%.

Table 3 showsthat theoccupancy ratio isrelatively low fora relativelyhighrejectionrate,comparedtotheperformance ofthe CW.This can be explained by the peak load on the AL early in themorning, seen in Fig. 10 .After 8:00 AM, the loadon the AL quicklydecreases,whichisaresultoftheplanningandscheduling methodsof thecasehospital. AL patientsare typicallyscheduled forsurgeryearlyinthemorningandarriveaccordingly.

5.2.4. Step4and5caseresults

The hospital plans on an expansion in the next year, as we mentioned inthis section’sintroduction. It isstill unclear where theAL will be situated, andtherefore there are no limits to the sizeoftheALforouranalysis.Weenumeratethepatientselection criteriatoﬁndimprovementsonthecurrentsolution.

Togetherwiththeinitialcasemixselectionthereare12 selec-tion options to assess(Table 4 ). We use the goal function intro-ducedin Section 3.2 todeterminethetopﬁveperforming conﬁgu-rations.

The goalfunction(see Section 3.2 ) highlightsthetop ﬁve per-forming assignment options: 1, 2, 4, 6, and 12 respectively, as shownin Table 5 .ThenumberofCWbedsisthenumberofbeds thatcorrespondstoablockingprobabilityof5%.ThenumberofAL

Table 4

Patient assignment options for the AL. Option ASA age speciality

1 III – – 2 III 76–80 – 3 III 76–85 – 4 III – BAR 5 III 76–80 BAR 6 III 76–85 BAR 7 † _– _– _– 8 – 76–80 – 9 – 76–85 – 10 – – BAR 11 – 76–80 BAR 12 – 76–85 BAR

† The initial assignment rules used.

bedsisthenumberofbedsthatfirstleadstoarejectedhoursrate lessthan10%.Theassignmentweconsideredintheprevioussteps, assignment7,isnot partofthetop5performing assignment op-tions.Thetop threeassignmentsgive similarperformanceresults. Assignment 1, the best performing configuration, has the lowest patient complexity profile, lowest rejection rate, and the lowest occupancy rateforthe AL.We remarkthat assignment6, ranked fourth,causesthelargestbedreductionfortheCW,witha reduc-tionof3beds.Here,theALrequires4beds,whichis1morethan theothertopfiveassignments.ThishighernumberofALbedsalso comesatthepriceofthesecondlowestoccupancyratiofortheAL. Giventhenursetopatientratioof2:1,webelievethatassignment 4has themostpotential forthe hospital. Ifinclusion ofBAR pa-tientsisnotdesired,werecommendusingassignment1.

6. Conclusionsanddiscussion

AnALhasmanyadvantagesforthehospitaladmissionprocess, suchasoperationalandlogisticalefficiency,cost-efficiency,and in-creased patient friendliness. We have introduced a five-step ap-proachforthedesign,criticalanalysis, andoptimisationofanAL. This framework was implemented into a DSS, and validatedand tested in a case study to obtain computational and practical re-sults.

The DSSenableshospital management tomake strategic deci-sions regarding the selection of patients and both the partition-ing and dimensioning of the AL and the CWs. The DSS follows five steps. In Step 1, hospital management andclinicians specify inclusion andexclusioncriteriafortheAL, whichdivides elective patient populationinthreegroups:ALpatients, CWpatients,and greyareapatients.Withinourcasestudytheinclusionand exclu-sion criteria were based on the patient’s age, ASA classification, andspeciality.The effects oftheinclusion criteriaon assignment toeithertheALortheCWarevisualisedbytheDSS.DuringStep 2,therequiredmaterials,staff skillmix and supportingprocesses for the AL can be derived from the selected patients. In Step 3, the potential bedreductionsforthe CWare calculated usingthe Erlang loss model,in conjunctionwith the calculation ofthe re-quired number of AL beds. During Step 4, hospital management assesses thefeasibility ofthe proposed dimensioningofboth the ALandtheCWwithin thefacilitylayout.In Step5,thecasemix for the AL andCW can be optimised by the assignment of grey area patients to either the AL or the CW. Using a goal function, the results ofall possible assignments are compared interms of efficiency (largest bedreduction) and efficacy(largest AL patient population and highest AL occupancy), weighing cost reductions againstpatientfriendlinessandworkloadreductions.

TheDSSsupportsuserstosystematicallymakedecisionsabout the implementation of the AL. After the AL is implemented, the DSScanbeusedfortacticalplanningpurposesbyresettinginputs

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Fig. 8. Blocking probability (top) and occupancy ratio (bottom) as a function of the number of beds for the individual specialties, without the AL (case hospital data, 2015–2017, n = 7565).

Table 5

Top 5 performing assignment options for the AL’s patient assignment enumeration (case hospital data, 2015–2017,

n = 7565).

Rank Option Beds CW with AL

Reduction CW

Occupancy CW (%)

Beds AL Rejected hours AL (%) Occupancy AL (%) 1 1 35 2 79.6 3 6.9 56.0 2 2 35 2 79.3 3 9.1 59.8 3 4 35 2 79.3 3 9.7 60.1 4 6 34 3 80.1 4 7.5 56.2 5 12 35 2 79.8 3 7.9 57.0

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Fig. 9. Pooled blocking probability (dark) and occupancy ratio (light) as a function of the number of beds calculated with the Erlang loss model (case hospital data, 2015– 2017, n = 7565).

Fig. 10. Expected daily load on the AL per hour (case hospital data, 2015–2017, n = 7565). suchasthewards foranalysis, theanalysisperiod,orthepatient

selectioncriteria.

The proposed systematicimplementationofthe ALusesnovel OM/OR models to determine the AL load and optimise the case mix.The introducedgreyarea forpatientallocationdecisionssets boundariesforthesolutionspaceandenableshospitalstooptimise theALandCWwithintheirstrategicscope.Thecasemix optimisa-tionisparticularlyusefulinsituationswheremanagementis hes-itantaboutthequalitativeimpactsoftheassignment ofapatient, andneeds quantitative supporttojustifycomplexdecisions. Note thatthe casemixoptimisation canbe personalisedforeach hos-pitalby considering additionalrelevant casemix variables inthe inclusion criteria, orforexample by considering other agegroup buckets.

WevalidatedandtestedourDSSinacasestudyinarelatively smallgeneralhospital.Thecasestudywasusedtoobtain compu-tationalandpractical resultsthat arerequiredbefore implement-ingan AL.Notethat, asthesedecisionsupport stepsprecede the actualimplementation ofthe AL,the casestudyhospital hasnot

(yet)implementedanAL.ThishospitalindicatedthattheDSSwas easytointerpretanduse.ApplyingtheDSStoalargeroranother type of hospital will resultin moreknowledge aboutthe usabil-ityoftheDSS.Weexpectthat theDSScanespeciallybe valuable forlarger hospitalswhere thedecisions forpatient selection and wardselection aremorecomplexthanthecontext westudied.In a specialisedhospital, thepatient selection decisions mightfocus onotherattributesthaninourstudy.Inthatcase,attributessuch astreatment typemight beadded tothe inclusionandexclusion criteria,ortheagegroupsmightbedeﬁneddifferently.

TheErlanglossmodelisusedtoquantifythepotentialCWbed reduction. This model is known to lead to an overestimation of therequirednumberofbeds.WeusedtheErlanglossmodel for-mulationtodeterminethepotentialbedreductionfortheCW.To account for the variability inarrivals at the CW,we recommend expandingthemodelwiththe time-dependantErlang lossmodel [22] .The impact of the AL could also be quantiﬁed if the time-dependant arrivalsattheCWare based onthevisualised admis-sionpatternsweincorporatedinourDSS.Inadditiontothe

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titativeeffectsoftheALthereisalsoawidevarietyofqualitative beneﬁtsthat mayoccur. Themaindriverforhospitalsisexpected tobetheimprovedlogisticsandpatientfriendliness,whilethebed reductionsmightbeofmarginalinterest.

Inourmodel,weassumedPoissonpatientarrivals.However,in practice aPoisson distributionmightnot give a perfectﬁt tothe data, as is also the case for some of the specialtiesin our case study. However, when considering the arrivals to the AL, all se-lected specialtiesare combined, andforthe jointarrival ratethe Poisson assumption is valid. Furthermore, the literature suggests that a Poisson distribution is a good assumption in general, but dependingontheplanningrulesofahospital,thearrival distribu-tion might be different. For generaland university hospitals, the Poisson assumption is most likely to give a good ﬁt, especially for larger hospitals. But for example in a highly regulated small sized specialised hospital, arrivals might be uniform distributed. Including various distributions in the model is an area offuture research.

We use representative days to determine the AL load. With thismethodweautomaticallyexcludeoutliersfromtheanalysisof theAL.Thismeansthatwepotentiallyover-orunderestimatethe numberof daysorhours on whichpatientsare rejected. Amore accurate AL load could be modelled with a convolution model, based on the expectedinﬂow fora given MSS.To gain more in-sights aboutthe operational performance of the AL andthe CW combined,asimulationstudymayberequired.Anotherremarkon theuseofrepresentativedaysfortheanalysisoftheAListhatthey mightbenon-existentwhentheMSSchangesdrastically.

Enumerationofthecasemixwasdoneforarelativelysmall so-lution space.The solutionspace increasesexponentially withthe numberof(sub)specialtiesassignedtothegreyareaforAL admis-sioninclusion/exclusion.Wedetermined,undertheassumptionof linearruntimebehaviour,thattheruntimeofthemodelamounts 91 h with15 (sub)specialties assignedto thegrey area, whichis acceptable for strategic decisionmaking. A MILPwill mostlikely bemoreeﬃcientintermsofcomputingtimeandisthereforemore usefulifonlyoneoptimalsolutionisdesired.

The DSS can be used for the implementation of an AL in an existing hospital, or for the design of a new building. In this light, an interesting extension is to add ﬁnancial considerations to themodel, asﬁnancial aspects forexamplehighlyaffect deci-sion making in the design of a newbuilding. In thedesign of a new building, we also advise to decide on the design of the AL in conjunction with the clustering and assignment of specialties towards(e.g.,thoseof [14] ).Infutureresearch,ourmodelshould be integrated withclustering and assignment models of special-tiestowards.Oneofthekeytopicsinoperationsmanagementfor healthcareistobalancethecareburdenacrosswards [20] .TheAL provides such a balance; the preoperativepatients are no longer amongst thepostoperativepatientsandthereforethecareburden atboth theAL andCWismorebalanced than itwouldbe with-outtheAL.Tofurtherreducetheunbalancedcareburden,research shouldanalyseassigningpatientstotheALorCWonthebasis of theirdiagnosis.

Funding

This research did not receive any speciﬁc grant fromfunding agenciesinthepublic,commercial,ornot-for-proﬁtsectors.

DeclarationofCompetingInterest None.

CRediTauthorshipcontributionstatement

W.Veneklaas:Conceptualization, Methodology,Software, Vali-dation,Formalanalysis,Investigation,Datacuration,Writing- orig-inaldraft,Writing -review &editing,Visualization. A.G.Leeftink: Conceptualization, Methodology, Investigation, Writing - original draft,Writing-review&editing,Visualization,Supervision,Project administration.P.H.C.M. vanBoekel:Conceptualization, Investiga-tion,Resources,Datacuration,Writing-originaldraft,Supervision. E.W.Hans: Conceptualization, Methodology, Resources,Writing -originaldraft,Supervision.

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