drools

Geoffrey De Smet

Nurse rostering and
hospital bed planning
with Drools Planner

Agenda

Bin packagingWhat is NP complete?

Employee shift rosteringAKA Nurse rostering

Hard constraints

Soft constraints

Patient admission scheduleAKA Hospital bed planning

How many possible solutions?

Other use cases

Hard constraint implementation

// a nurse can only work one shift per dayrule "oneShiftPerDay" when $left : EmployeeAssignment( $employee : employee, $shiftDate : shiftDate, $leftId : id ); $right : EmployeeAssignment( employee == $employee, shiftDate == $shiftDate, id > $leftId); then // Lower the hard score with a weight ...end

Soft constraint implementation

rule "dayOffRequest" when $dayOffRequest : DayOffRequest( $employee : employee, $shiftDate : shiftDate, $weight : weight ); $employeeAssignment : EmployeeAssignment( employee == $employee, shiftDate == $shiftDate ); then // Lower the soft score with the weight $weight ...end

Patient admission schedule

Hard constraintsNo 2 patients in same bed in same night

Room gender limitation

Department minimum or maximum age

Patient requires specific room equipment(s)

Soft constraintsPatient prefers maximum room size

Department specialization

Room specialization

Patient prefers specific room equipment(s)

Needle in a haystack

How many possible solutions?310 bedsin 105 rooms

in 4 departments

84 nights

2750 patients (admissions)

Numbers from a real dataset

Needle in a haystack

How many possible solutions?310 bedsin 105 rooms

in 4 departments

84 nights

2750 patients (admissions)

> inhabitants of Gent (BE)?250000 inhabitants

Source: wikipedia

Needle in a haystack

How many possible solutions?310 bedsin 105 rooms

in 4 departments

84 nights

2750 patients (admissions)

> humans?7000000000 humans

Source: NASA (wikipedia)

Needle in a haystack

How many possible solutions?310 bedsin 105 rooms

in 4 departments

84 nights

2750 patients (admissions)

> minimum atoms in the observable universe?10^80

Source: NASA and ESA (wikipedia)

Needle in a haystack

How many possible solutions?310 bedsin 105 rooms

in 4 departments

84 nights

2750 patients (admissions)

> atoms in the universe
if every atom is a universe
of atoms?(10^80)^80 = 10^6400

Source: NASA and ESA (wikipedia)

Needle in a haystack

How many possible solutions?310 bedsin 105 rooms

in 4 departments

84 nights

2750 patients (admissions)

A little over 10^6851

Do the math

1 patient310 beds

310 ways to schedule 1 patient

2 patients310 * 310 = 96100

3 patients310 * 310 * 310 = 29791000

2750 patients310 * 310 * ... * 310

310^2750= a little over 10^6851

A little over 10^6851

17565400009613647714189309909847019528176031676612802408947467896773536824694320253771058944295328388965847321421820520338269384218763243353186553203291774156243401969717704429199723195574019731357439221586010900901318775661618988149185744289903563474940721372704649669447515706252843900344472960295273324597346780837674886972275338744554737771986776337765496773882810395955542351928331414378439283405132892358744224215499792287586474426914111457027335258269167103194692790665217766902628732489519488236496931246157419949856522543510386164584826962224171420152255658502323853504643497053252922727924406406179159327025274968691052425818270121710670552641837503435108794481961062422002729288737980404185875233912428178009558605680683578864680145557998942327371019832139824665975180911386722774004539981342785523851686636374432671601485496423110930175953308580416767966832068095365964656939583089443708945844323888227816296382464122209980716936990539499472027590738400791514217875461942733015467480308665074008529461146577114465977072581447925882122906827160570007228017056499674188148507908716786164922536467490587163626945689452927061532150637454615233641645612791027410608416476380642469085143980464067453971429400369608313929289399595696359958354101721624055729520838609453039985592726289376243856941429063767903919977138724432513602703448146045970566585076809576476984036923221553270878279574239866657156729051295085970100212856025787345034666683590797377984104207041334053480226788236770435009014979334517769826461063281178894554527012859966520606253098788699367180806367012372895824963357992764969799123361044456461687410981522493093316910464937089299655880447014074876397812210684054337706530175130912335567383560436635091489083375525519539844805718811296858076507685112192499405286337668107046095023999871224655107877174220679360212410573001491104381221662138764756898834588381340410892158544837200229008533930816794663631470201197595487045022087615873490295940409113638894083753062801416644858

A little over 10^6851

70757942487218045035508810158461046502812782292385633846174494690914238485407798379765738528402484632449685642401410897637632172694954465509230907381501728706686840208173164426348468614134650930610728341876292346711310677332648553951422991989751468506508069513397904821612697383659788320905691994864296149528670873271380180066507702490525594196383327289726362280241278856579591895744202499646581373849829964867870738964842426372580420928473929652466453066089306581572745139056256181505240205578741292314133858985615181677968313683876880079649763914095651402272047776108451445066888366968448972791816669030945790810396895725248399188822034667566483522327685006195080178525107491255245054238976705620547582329759857450557583834141364747838395082871684183199560673441708538602779816347949276957201268066627372831370768073558934679410276824283049183299518869516908654179971718550810202675628457097617280232889096038128616543128200089047813223519902714196694639844273986565523012106816309974964021700560537928432528631741787455155275823033005847637107210747721372066369346754152090839849611389908167353907349234368276522287410730637555342957452428266968002573227849933691449063418286501311036314048960528249465982665132492491072491788618403253474529440348798670244615185355092357283764936387607076234181916670755269421546530337284689838773122323053171794271444358533638806848969871884168582847613016398013006633016140503743175611255484273419291435502775849577615159921009571496639402549077872124227731739936370100132762333353473908080215719004335487157010620020523763648856692728699459471603410776592535816520745995861336577877431293776796124264697049418795186010546056975226424227455446011031581123438684685838655333776830823720356749120051129394691394743488410658613543537795455760655157849602214428915084056181314465895075924498263846040474495622654552157933867572542745838370889391243702358459244386561081479905545570084491443709439642235090455604548030317754849613813010298858282615659336373785985294

A little over 10^6851

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A little over 10^6851

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The search space is big!Compare with WWW size 22020000000 pages

Each possible solution2750 patients scheduled into 310 beds

Still need to calculate the score!

Throw hardware at it?

Calculate 10^9 scores per msImpossible today!

31579200000 ms in 1 year< 10^11 ms in 1 year

10^9 * 10^11 scores per year= 10^20 scores per year

How many years? 10^6851 / 10^20= 10^6831 years

CPU 1000 times fasterIt becomes 10^6828 years

A dose of reality

Find the optimal solution?Of a real world planning problem?

Not in our lifetimes!

Who cares?Beat the human planner(s): easy!Spend less resourcesSave more money

Save the environment

Make more people happy

Always room to improve our algorithms

Thanks for your attention

Useful linksWebsitehttp://www.jboss.org/drools/

Reference manualhttp://www.jboss.org/drools/documentation.html

Bloghttp://blog.athico.com/

Mailing lists (forum through nabble)http://www.jboss.org/drools/lists.html

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