Data Driven Ambulance Optimization

49 Pages·2014·11.47 MB·English

Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Time-dependent ambulance allocation considering
data-driven empirically required coverage
Lara Wiesche, Dirk Degel, Brigitte Werners
Management,OperationsResearch–Ruhr-UniversityBochum,Germany
1stInternationalWorkshoponPlanningofEmergencyServices: TheoryandPractice
CWI, Amsterdam, 25–27 June 2014
LaraWiesche (RUB) DataDrivenAmbulanceOptimization 25–27June2014 1/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Outline
1. Motivation
2. Basic idea and models
3. Data driven optimization model for tactical ambulance planning
4. A real world EMS planning problem in the city of Bochum
5. Conclusions and Outlook
LaraWiesche (RUB) DataDrivenAmbulanceOptimization 25–27June2014 2/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Motivation
(cid:73) Aging population
(cid:73) Age class of 70+ causes 50% of ambulance operations
(cid:73) EMS demand increases
source:StatistischesBundesamt2013
LaraWiesche (RUB) DataDrivenAmbulanceOptimization 25–27June2014 3/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Motivation
(cid:73) Aging population
(cid:73) Age class of 70+ causes 50% of ambulance operations
(cid:73) EMS demand increases
source:StatistischesBundesamt2013
LaraWiesche (RUB) DataDrivenAmbulanceOptimization 25–27June2014 3/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Motivation
1. Access to emergency medical services (EMS) is crucial
2. Ensuring optimal supply quality
(cid:73) Short arrival time
(cid:73) Coverage of entire demand area
(cid:73) High degree of achievement y
nc
=⇒ Dependent on location and number of Efficie
ambulances
3. Efficiency
Q.uality
(cid:73) Reduction of fixed costs (avoid
overcapacity)
(cid:73) Utilization of ambulances
LaraWiesche (RUB) DataDrivenAmbulanceOptimization 25–27June2014 4/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Quality criteria and objectives
Evaluation of emergency medical services (objective of EMS provider):
(cid:73) Degree of achievement (ex post):
# operations within a time standard T
# total number of operations
.
Objectives in literature (ex ante): ZeitabhängigerRadiusbei25(cid:20)khm(cid:21)
A B C D E F G H J K L M N O P Q R
(cid:73) single coverage models
1 129 1
2 55 67 92 105118130140148 2
(cid:73) double coverage models 3 44 56 68 80 93 106119131141 3
4 12 22 33 45 57 69 81 94 107120132142149 4
(cid:73) busy fraction models 56 1 5 1134 2234 3345 4467 5589 7701 W88236 9956 11008911221211333411W44343115501115556160 56
7 2 6 15 25 36 48 W602 72 84 97 110123135145152157161 7
(cid:73) queue models 8 3 7 16 W261 37 49 61 73 85 98 111124136146153158162 8
9 4 8 17 27 38 50 62 74 86 99 112125137147154159163 9
(cid:73) hypercube models 1101 190 1189 2289 3490 5512 W66344 7756 W88785 110001111134112267113389 1101
12 11 20 30 41 53 65 77 89 102115128 12
13 21 31 42 54 66 78 90 103116 13
14 32 43 79 91 104117 14
A B C D E F G H J K L M N O P Q R
LaraWiesche (RUB) DataDrivenAmbulanceOptimization Wache Ra2die5n–in2Ab7hänJgiugkeniteder2Ge0sc1hw4indigkeitv(t)5/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Optimal quality in emergency medical services
Research project: 2 years (work in progress)
Focus:
(cid:73) Analysis of required resources for EMS
(cid:73) Analysis of time-dependent demand and speed fluctuations for EMS
(cid:73) Tactical and strategic planning horizon
(cid:73) Stochastic influences, uncertain parameters (demand, speed)
Goal:
(cid:73) Dynamic (and robust) optimization model
=⇒ IT-based decision support tool for local EMS providers
LaraWiesche (RUB) DataDrivenAmbulanceOptimization 25–27June2014 6/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Decision support tool
Decision support
Optimization Simulation Forecast

location, degree of trends,
allocation and achievement, development
resource planning resources,
utilization

empirical demand, evaluations population,
required/adequate experts
coverage

LaraWiesche (RUB) DataDrivenAmbulanceOptimization 25–27June2014 7/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Decision support tool
Decision support
Optimization Simulation Forecast

location, degree of trends,
allocation and achievement, development
resource planning resources,
utilization

empirical demand, evaluations population,
required/adequate experts
coverage

LaraWiesche (RUB) DataDrivenAmbulanceOptimization 25–27June2014 7/28
Motivation Basicmodels Optimizationmodel Arealworldproblem Outlook
Basic covering location models
Idea: Demand nodes i have to be covered within a time standard T
M.H.FazelZarandietal./ScientiaIranica,TransactionsE:IndustrialEngineering18(2011)1564–1570 1565
2. Literaturereview
The large number of publications in the area of MCLP
preventsacomprehensivereviewinthispaper.Thus,some
of the main contributions to the field are discussed in this
section.TwovaluableandrecentreviewsbyReVelleetal.[3]
andBermanetal.[4]maybeconsultedforfurtherinformation
regardingthesubject.
MCLP was first presented by Church and ReVelle [1] in
the mid 70s. Since then, numerous papers about various
types of the problem have appeared. Some examples are
theproposalofhierarchicalMCLPbyMooreandReVelle[5],
modelingtheMCLPincompetitiveenvironmentsbyPlastria
and Vanhaverbeke [6], gradual covering models by Church
andRoberts[7],andBermanetal.[8,9],usingGISinMCLP
byAlexandrisandGiannikos[10],andcoveringnodes,using
parallelogramsbyYouniesandWesolowski[11],tonameafew.
Another stream of research in the field of MCLP deals
with employing heuristics and metaheuristics to tackle the
computationalhurdleofsolvingMCLPmodels.Table1presents
Figure1: Asamplesolutiontothecoveringlocationproblem. some of the main non-exact solution algorithms that have
been used in order to solve variants of MCLP from the
thesetofnodesandthesetofpotentialfacilitiesareidentical.
source:Zarandietal.2011–Thelargescalemaximalcoveringlocationproblem;page1565 beginningofthe21stcentury.Thisreviewapparentlyshows
Also,itisassumedthateachnodehasaspecificamountofde-
LaraWiesche (RUB) mandtobeDmateat.DBreivseidneAs,mpbruolxainmceitOypotfimthizeatpioonpulationtothese25–2t7haJtumnee2ta0h14euristi8cs/h2a8vebeenanattractiveareaofresearchto
facilitiesisdesirable.Thismeansthatfacilitiessuchaslandfills solveMCLPmodels.
areexcludedfromthescopeofthispaper.Inaddition,anexoge- Asfarasweareconcerned,theliteratureonreal-worldcase
nousversionofMCLPisconsidered.Hereby,themathematical studiesofMCLPiscomparativelylimited.Acasetoameliorate
programofMCLPisgiven.First,wedefineproblemparameters theaccessibilityofdemandnodestofixedfacilitieshasbeen
andvariablesasdiscussedin[2](forfurtherinformationabout considered by Murawski and Church [25], which is called
theformulation,interestedreaderscanreferto[2]): the‘‘maximalcoveringnetworkimprovementproblem’’,and
i,I Theindexandsetofdemandnodes, whichhasbeenemployedinGhanaasareal-worldcase.In
another paper, Curtin et al. [26] studies the distribution of
j,J Theindexandsetofeligiblefacilitysites, policepatrolareasinDallas,USA.Inaddition,Raticketal.[27]
ai Thepopulationordemandatnodei can be considered as another real-world case study in the
dij Theshortestdistance(ortime)fromdemandnodei Kohat district of Pakistan, by applying the model of Moore
tofacilityatnodej, andReVelle[5].Recently,Basaretal.[24]surveyedthemulti-
S Thedistance(ortime)standardwithinwhich periodversionofMCLPtolocateemergencyservicesinIstanbul,
coverageisexpected, Turkey.
Ni o{jf|Sdtioj≤noSd}e=i,thenodesjthatarewithinadistance ofpAarraemceentterisn,tseurcehstaisndMemCLaPndhsaosraerviseennthabeolouctatthioenuonfcdeertmaianntdy
nodes.Batanovicetal.[28]suggestedaMCLPinnetworkswith
p Thenumberoffacilitiestobeestablished,
uncertainty,andstudiedtheproblemwiththreedifferenttypes
xj Abinaryvariablethatequalsonewhenafacilityis ofdemandnodeweight:
sitedatthejthnodeandzerootherwise,
yi Abinaryvariablewhichequalsoneifnodeiis (a)Equalweights.
coveredbyoneormorefacilitiesstationedwithinS (b)Relativedeterministicweights.
andzerootherwise, (c)Linguistictermsasthedemandweights.
Moreover,Corrêaetal.[21]isanotherrecentpublicationwhich
Maximizez=aiyi, (1) addresses the problem of MCLP, considering congestion in
i∈I queuelines.Arazetal.[29]presentedafuzzygoalprogramming
Subjectto:yi≤xj, i∈I, (2) appappreoracbhyfBoerrmloacnatinetgaelm. e[3rg0e]nsctyudsieersvictheefagcrialidtiueasl. Acovreecreinngt
j∈Ni problemwithuncertaindemands.Inanotherpublicationby
xj=p, (3) BermanandWang[31],theysurveyedacaseinwhichthe
j∈J demands are random variables with unknown probability
0≤yi≤1 i∈I, (4) dinistmriboudteiloinngs.FcaozveelrZinarganpdrioebtleaml.[s32in]istahneotfhuezrzyrecseenntsaet.teTmhepyt
xj∈{0,1} j∈J. (5) modeledaclosed-loopsupplychainnetworkwithcoverage
Therestofthepaperisorganizedasfollows:aconciseliterature considerations,andusedfuzzygoalprogrammingtosolveit.
reviewofcoveringproblemsandrelatedissuesispresented Tothebestoftheauthors’knowledge,theonlyattempts
inSection2.Section3isdedicatedtotheproposedsolution tomodelandsolveMCLPoflargersizesareReVelleetal.[2]
algorithm.NumericalexamplesappearinSection4.Finally, andParkandRyu[15].Althoughthesetwopapersarevaluable
conclusionsandoutlooksforpotentialfutureresearcharegiven contributionstotheliterature,theproblemsizeswhichwere
inSection5. targetedarebelow900nodes,inbothpapers.Moreover,itis