Resou ce Alloca ion wi h Dependencies
in Business P ocess Managemen Sys ems
Gi ay Ha u , C is ina Cabanillas, Jan Mendling, and Axel Polle es
Vienna Uni e si y o Economics and Business, Vienna, Aus ia
{gi ay.ha u ,c is ina.cabanillas,jan.mendling,axel.polle es}@wu.ac.a
Abs ac . Business P ocess Managemen Sys ems (BPMS) acili a e
he execu ion o business p ocesses by coo dina ing all in ol ed esou ces.
T adi ional BPMS assume ha hese esou ces a e independen om one
ano he , which jus ifies a g eedy alloca ion s a egy o offe ing each wo k
i em as soon as i becomes a ailable. In his pape , we de elop a o -
mal echnique o de i e an op imal schedule o wo k i ems ha ha e
dependencies and esou ce con lic s. We build ou wo k on Answe Se
P og amming (ASP), which is suppo ed by a wide ange o efficien
sol e s. We apply ou echnique in an indus y scena io and e alua e i s
effec i eness. In his way, we con ibu e an explici no ion o esou ce
dependencies wi hin BPMS esea ch and a echnique o de i e op imal
schedules.
Keywo ds: Answe Se P og amming ·Op imali y ·Resou ce
alloca ion ·Resou ce equi emen s ·Wo k scheduling
1 In oduc ion
Business P ocess Managemen Sys ems (BPMS) ha e been designed as an in e-
g al pa o he business p ocess managemen (BPM) li ecycle by coo dina ing
all esou ces in ol ed in a p ocess including people, machines and sys ems [1].
A design ime, BPMS ake as inpu a business p ocess model en iched wi h
echnical de ails such as ole assignmen s, da a p ocessing and sys em in e aces
as a specifica ion o he execu ion o a ious p ocess ins ances. In his way, hey
suppo he efficien and effec i e execu ion o business p ocesses [2].
I is an implici assump ion o BPMS ha wo k i ems a e independen om
one ano he . I his assump ion holds, i is fine o pu wo k i ems in a queue and
offe hem o a ailable esou ces igh away. This app oach o esou ce alloca-
ion, can be summa ized as a g eedy s a egy. Howe e , i he e a e dependencies
be ween wo k i ems, his s a egy can easily become subop imal. Some domains
like enginee ing o heal hca e ha e a ich se o ac i i ies o which a ious
Funded by he Aus ian Resea ch P omo ion Agency (FFG) g an 845638 (SHAPE).
esou ces, human and non-human, a e equi ed a he same ime. Resou ce con-
flic s ha e o en he consequence ha wo king on one wo k i em blocks esou ces
such ha o he wo k i ems canno be wo ked on. This obse a ion emphasizes
he need o echniques o make be e use o exis ing esou ces in business
p ocesses [3].
In his pape , we add ess cu en limi a ions o BPMS wi h espec o aking
such esou ce cons ain s in o accoun . We ex end p io esea ch on he in e-
g a ion o BPMS wi h calenda s [4] o ake dependencies and esou ce conflic s
be ween wo k i ems in o accoun . We de elop a echnique o speci ying hese
dependencies in a o mal way in o de o de i e a globally op imal schedule o
all esou ces oge he . We define ou echnique using Answe Se P og amming
(ASP), a o malism om logic p og amming ha has been ound o scale well
o sol ing p oblems as he one we ackle [5]. We e alua e ou echnique using
an indus y scena io om he ailway enginee ing domain. Ou con ibu ion o
esea ch on BPMS is an explici no ion o dependence along wi h a echnique o
achie e an op imal schedule.
The pape is s uc u ed as ollows. Sec ion 2p esen s and analyzes an indus-
y scena io. Sec ion 3concep ually desc ibes he esou ce alloca ion p oblem.
Sec ion 4explains ou ASP-based solu ion and how i can be applied o he
indus y scena io. Sec ion 5e alua es he solu ion. Sec ion 6discusses ela ed
wo k. Sec ion 7summa izes he conclusions o he wo k and he u u e s eps.
2 Mo i a ion
In he ollowing, we desc ibe an indus y scena io ha leads us o a mo e de ailed
defini ion o he esou ce alloca ion p oblem and i s complexi y.
2.1 Indus y Scena io
A company ha p o ides la ge-scale echnical in as uc u e o ailway au oma-
ion equi es igo ous es ing o he sys ems deployed. Each sys em consis s o
diffe en ypes and numbe o ha dwa e ha a e fi s se up in a labo a o y. This
se up is execu ed by some employees specialized in diffe en ypes o ha dwa e.
A e wa ds, he simula ion is un unde supe ision.
Figu e 1depic s wo p ocess models ep esen ing he se up and un phases
o wo es s. We use ( imed) Pe i ne s [6] o ep esen ing he p ocesses. The
p ocess ac i i ies a e ep esen ed by ansi ions (ai). The numbe wi hin squa e
b acke s nex o he ac i i ies indica es hei (de aul maximum) du a ion in
gene ic ime uni s (TU). The numbe s unde p ocess names indica e he s a -
ing imes o he p ocess execu ions: 8 TU o Tes -1 and 12 TU o Tes -2.
The p ocesses a e simila o all he es ing p ojec s bu diffe in he ac i i ies
equi ed o se ing up he ha dwa e as well as in he esou ce equi emen s asso-
cia ed wi h hem. Ce ain esou ces can only be alloca ed o ac i i ies du ing
wo king pe iods, i.e., we wan o en o ce ime in e als (so called b eaks) whe e
Fig. 1. Wo kflow o wo p ojec s
some esou ces a e no a ailable. In ou scena io, no esou ce is a ailable in he
in e als [0,8), [19,32), [43,56), and [67,80).
Fo comple ing es s, he a ailable non-human esou ces in he o ganiza ion
include 13 uni s o space dis ibu ed in o 2 labo a o ies (Table 1) and se e al
uni s o 3 ypes o ha dwa e (Table 2). The human esou ces o he company
a e specialized in he execu ion o specific phases o he wo es ing p ojec s,
whose ac i i ies a e able o comple e in a specific ime. Table 3shows a ailable
esou ces in diffe en p ocess phases and he e o e, hei abili y o conduc ce -
ain ac i i ies along wi h hei yea s o expe ience in he company in squa e
b acke s.
The equi emen s on he use o such esou ces in he p ocess ac i i ies a e
showninTable4. Each p ocess ac i i y equi es a specific se o esou ces o i s
comple ion. Fo ins ance, h ee o he ac i i ies in ol ed in he se up o Tes -1
equi e 1 employee wo king on 1 uni o he ha dwa e HW-1 in a labo a o y; 1
se up ac i i y equi es 1 employee wo king on 1 uni o he ha dwa e HW-2 in
a labo a o y; and he un ac i i y equi es 4 employees. Besides, a es can only
be execu ed i he whole se up akes place in he same labo a o y.
The aim in his scena io is o op imize he o e all execu ion ime o simul-
aneous es s and consequen ly, he space usage in he labo a o ies.
2.2 Insigh s
The esou ce alloca ion p oblem1deals wi h he assignmen o esou ces and
ime in e als o he execu ion o ac i i ies. The complexi y o esou ce allo-
ca ion in BPM a ises om coo dina ing he explici and implici dependencies
1Commonly e e ed as scheduling.
ac oss a b oad se o esou ces and ac i i ies o p ocesses as well as om sol ing
po en ial conflic s on he use o ce ain esou ces. As we obse e in ou indus y
scena io, such dependencies include, among o he s: (i) esou ce equi emen s,
i.e., he cha ac e is ics o he esou ces ha a e in ol ed in an ac i i y (e.g.,
oles o skills) (c . Table 3); (ii) empo al equi emen s. Fo ins ance, he du a-
ion o he ac i i ies may be s a ic o may depend on he cha ac e is ics o he
se o esou ces in ol ed in i , especially o collabo a i e ac i i ies in which se -
e al employees wo k oge he (such as o he ac i i ies o he un phase o a
es ing p ocess). Fu he mo e, esou ce a ailabili y may no be unlimi ed (e.g.,
b eak calenda s). In addi ion, esou ce conflic s may eme ge om in e depen-
dencies be ween equi emen s, e.g., ac i i ies migh need o be execu ed wi hin
a specific se ing which may be associa ed wi h (o sha e esou ces wi h) he
se ing o o he ac i i ies (e.g., all he se up ac i i ies o a es ing p ocess mus
be pe o med in he same labo a o y).
A esou ce alloca ion is easible i (1) ac i i ies a e scheduled wi h espec o
ime cons ain s de i ed om ac i i y du a ions and con ol flow o he p ocess
model, and (2) esou ces a e alloca ed o scheduled ac i i ies in acco dance wi h
esou ce a ailabili y and esou ce equi emen s o ac i i ies. This combina o-
ial p oblem o finding a easible esou ce alloca ion unde cons ain s is an
NP-Comple e p oblem [7]. Howe e , o ganiza ions gene ally pu sue an op imal
alloca ion o esou ces o p ocess ac i i ies aiming a minimizing o e all exe-
cu ion imes o cos s, o maximizing he usage o he esou ces a ailable. In
p esence o objec i e unc ions he esou ce alloca ion p oblem becomes ΔP
2[8].
3 Concep ualiza ion o he Resou ce Alloca ion P oblem
Figu e 2illus a es ou concep ualiza ion o he esou ce alloca ion p oblem. We
di ide i in o h ee complexi y laye s ela ed o he a o emen ioned dependencies
and esou ce conflic s. Op imiza ion unc ions can be applied o all ypes o allo-
ca ion p oblems. This model has been defined om he cha ac e is ics iden ified
in ou indus y scena io as well as in ela ed li e a u e [9].
Table 1. A ailable space in labs
LAB −1LAB −2
Space 4 9
Table 2. A ailable ha dwa e (HW)
Type Uni s
HW1 hw1a, hw1b, hw1c
HW2 hw2a, hw2b, hw2c, hw2d
HW3 hw3a, hw3b, hw3c
Table 3. Specializa ion o employees
Tes −1Tes −2
Se up Run Se up Run
Glen[7]  
D ew[7] 
E an[3] 
Ma y[5]  
Ka e[6]  
Amy[8]   
Table 4. Ac i i y equi emen s
Ac i i ies Requi emen s
Tes -1 a1−a31Employee:Se up-1, 1 Ha dwa e:HW-1, 1 Lab:a1-a4same lab
a41Employee:Se up-1, 1 Ha dwa e :HW-2, 1 Lab:a1-a4same lab
a54Employee:Run-1, a e execu ion(a.e.) elease he lab o a1-a4
Tes -2 a6−a81Employee:Se up-2, 1 Ha dwa e:HW-2, 1 Lab:a6-a11 same lab
a9−a11 1Employee:Se up-2, 1 Ha dwa e :HW-3, 1 Lab:a6-a11 same lab
a12 2Employee:Run-2 (hasExp>5), a.e. elease he lab o a6-a11
Fig. 2. Resou ce alloca ion in business p ocesses
Fig. 3. Resou ce on ology and example ins an ia ion

3.1 Basic Resou ce Alloca ion
Th ee elemen s a e in ol ed in a basic esou ce alloca ion, namely: a model ha
s o es all he in o ma ion equi ed abou he esou ces a ailable, in o ma ion
abou he expec ed du a ion o he p ocess ac i i ies, and a language o defining
he es ic ions ha cha ac e ize he alloca ion.
Resou ce On ology. As a uni o m and s anda dized ep esen a ion language,
we sugges he use o RDF Schema (RDFS) [10] o model o ganiza ional in o -
ma ion and esou ces. Figu e 3illus a es a sample RDFS on ology, in which
a esou ce is cha ac e ized by a ype and can ha e one o mo e a ibu es.
In pa icula , any esou ce ype (e.g. Employee) is a subclass o d s:Resou ce.
The a ibu es a e all o ype d :P ope y; domain ( d s:domain) and ange o
a ibu es a e indica ed wi h s aigh a ows labeled wi h he a ibu e name,
whe eas dashed a ows indica e an d s:subclassO . The e a e h ee diffe en ypes
o esou ces: Employee,Ha dwa e and Lab, whe e Ha dwa e has h ee esou ce
sub ypes. Employees ha e a ibu es o hei name (hasName), ole(s) (has-
Role) and expe ience le el (hasExp) in he o ganiza ion (numbe o yea s). Labs
p o ide a ce ain amoun o space o expe imen s (hasSpace). An ins an ia ion
o he on ology is desc ibed a he bo om o he figu e using he RDF Tu -
le syn ax [11]. This ins an ia ion ep esen s Tables 1,2and 3o he indus y
scena io.
Ac i i y Du a ion. Resou ce alloca ion aims a p ope ly dis ibu ing a ail-
able esou ces among unning and coming wo k i ems. The main empo al aspec
is de e mined by he expec ed du a ion o he ac i i ies. The du a ion can be
p edefined acco ding o he ype o ac i i y o calcula ed om p e ious execu-
ions, usually aking he a e age du a ion as e e ence. This in o ma ion can be
included in he execu able p ocess model as a p ope y o an ac i i y (e.g. wi h
BPMN [12]) o can be modelled ex e nally. In ei he case, i has o be accessible
by he alloca ion algo i hm.
Resou ce Alloca ion. Resou ce alloca ion can be seen as a wo-s ep defini ion
o es ic ions. Fi s , he so-called esou ce assignmen s mus be defined, i.e., he
es ic ions ha de e mine which esou ces can be in ol ed in he ac i i ies [13]
acco ding o hei p ope ies. The ou come o esou ce assignmen is one o
mo e2 esou ce se s wi h he se o esou ces ha can be po en ially alloca ed o
an ac i i y a un ime. The second s ep assigns ca dinali y o he esou ce se s
such ha diffe en se ings can be desc ibed, e.g. o he execu ion o ac i i y
a1, 1 employee wi h ole se up-1, 1 ha dwa e o ype HW2, and 1 uni space o
a labo a o y a e equi ed.
The e exis languages o assigning esou ce se s o p ocess ac i i ies [13–
16]. Howe e , ca dinali y is gene ally dis ega ded unde he assump ion ha
2Since se e al se s o es ic ions can be p o ided, e.g. o ac i i y a1 esou ces wi h
ei he ole 1o skill s1a e equi ed.
only one esou ce will be alloca ed o each p ocess ac i i y. This is a limi a ion
o cu en BPMS ha p e en s he implemen a ion o indus y scena ios like he
one desc ibed in Sec . 2.1.
3.2 Ad anced Time Managemen
This laye ex ends he empo al aspec o esou ce alloca ion by aking in o
accoun ha : (i) esou ce a ailabili y affec s alloca ion, and ha (ii) he esou ce
se s alloca ed o an ac i i y may affec i s du a ion. Rega ding esou ce a ail-
abili y, calenda s a e an effec i e way o speci ying diffe en esou ce a ailabili y
s a us, such as a ailable, una ailable, occupied/busy o blocked [9]. Such in o -
ma ion mus be accessible by he esou ce alloca ion module. As o he a iable
ac i i y du a ions depending o he esou ce alloca ion, h ee specifici y le els
can be dis inguished:
–Resou ce-se -based du a ion, i.e., a iple (ac i i y, esou ceSe , du a ion)
s a ing he (minimum/a e age) amoun o ime ha i akes o he esou ces
wi hin a specific esou ce se (i.e., ca dinali y is dis ega ded) o execu e
ins ances o a ce ain ac i i y. Fo ins ance, (a1, echnician, 6) specifies ha
people wi h he ole echnician need (a leas /on a e age) 6 TU o comple e
ac i i y a1, assuming ha echnician is an o ganisa ional ole.
–Resou ce-based du a ion, i.e., a iple (ac i i y, esou ce, du a ion) s a ing
he (minimum/a e age) amoun o ime ha i akes o a conc e e esou ce
o execu e ins ances o a ce ain ac i i y. Fo ins ance, (a1,John,8) specifies
ha John needs (a leas /on a e age) 8 TU o comple e ac i i y a1.
–Agg ega ion-based du a ion, i.e., a iple (ac i i y, g oup, du a ion) s a ing
he (minimum/a e age) amoun o ime ha i akes o a specific g oup o
execu e ins ances o a ce ain ac i i y. In his pape , we use g oup o e e
o a se o human esou ces ha wo k oge he in he comple ion o a wo k
i em, i.e., ca dinali y is conside ed. The e o e, a g oup migh be composed
o esou ces om diffe en esou ce se s which may no necessa ily sha e a
specific esou ce-se -based du a ion. An agg ega ion unc ion mus be imple-
men ed in o de o de i e he mos app op ia e du a ion o an ac i i y when
a g oup is alloca ed o i . The defini ion o ha unc ion is up o he o ganiza-
ion. Fo ins ance, a g oup migh be composed o (John,Clai e), whe e John
has an associa ed du a ion o 8 TU o ac i i y a1and Clai e does no ha e a
specific du a ion bu she has ole echnician, wi h an associa ed du a ion o
6 TU o ac i i y a1. S a egies o alloca ing he g oup o he ac i i y could
be o conside he maximum ime needed o he esou ces in ol ed (i.e., 8
TU), o o conside he mean o all he du a ions (i.e., 7 TU) assuming ha
he join wo k o wo people will be as e han one single esou ce comple ing
all he wo k.
3.3 Ad anced Resou ce Managemen
The basic esou ce alloca ion laye conside s esou ces o be disc e e, i.e. hey
a e ei he ully a ailable o ully busy/occupied. This applies o many ypes o
esou ces, e.g. people, so wa e o ha dwa e. Howe e , o ce ain ypes o non-
human esou ces, a ailabili y can be pa ial a a specific poin in ime. Mo eo e ,
hey may ha e o he fluen a ibu es. Fo ins ance, cumula i e esou ces a e
hence cha ac e ized by hei dynamic a ibu es and hey can be alloca ed o
mo e han one ac i i y a a ime, e.g. in Fig. 2 he e is a esou ce oom 1 whose
occupancy changes o e ime.
We use he ASP sol e clasp [17] due o i s efficiency o ou expe imen s. This
allows us o use in ege a iables as a ibu es. The e a e also o he ex ensions
o ASP such as FASP [18] ha adds he powe o model con inuous a iables.
3.4 Op imiza ion Func ion
Sea ching o ( he exis ence o ) a easible esou ce alloca ion ensu es ha all he
wo k i ems can e en ually be comple ed wi h he a ailable esou ces. Howe e ,
ypically schedules should also ulfill some kind o op imali y c i e ion, mos
commonly comple ion o he schedule in he sho es possible o e all ime. O he
op imiza ion c i e ia may in ol e o ins ance cos s o he alloca ion o ce ain
esou ces o pa icula ac i i ies, e c.
Gi en such an op imiza ion c i e ion, he e a e g eedy app oaches [19]p o-
iding a subs an ial imp o emen s o e choosing any easible schedule, al hough
such echniques depend on heu is ics and may no find a globally op imal solu-
ion o complex alloca ion p oblems.
We e e o [20] o u he in o ma ion on a ious op imiza ion unc ions,
bu emphasize ha ou app oach will in p inciple allow a bi a y op imiza ion
unc ions and finds op imal solu ions – simila in spi i o encodings o cos
op imal planning using ASP [21].
4 Implemen a ion wi h ASP
Answe Se P og amming (ASP) [17] is a decla a i e (logic-p og amming-s yle)
pa adigm. I s exp essi e ep esen a ion language, ease o use, and compu a ional
effec i eness acili a e he implemen a ion o combina o ial sea ch and op imiza-
ion p oblems (p ima ily NP-ha d). Modi ying, efining, and ex ending an ASP
p og am is uncomplica ed due o i s s ong decla a i e aspec .
An ASP p og am Πis a fini e se o ules o he o m:
A0←A1,...,A
m,no A
m+1,...,no A
n.(1)
whe e n≥m≥0 and each Ai∈σa e ( unc ion- ee fi s -o de ) a oms; i A0is
emp y in a ule , we call a cons ain , and i n=m= 0 we call a ac .
Whene e Aiis a fi s -o de p edica e wi h a iables wi hin a ule o he
o m (1), his ule is conside ed as a sho cu o i s g ounding g ound( ), i.e.,
he se o i s g ound ins an ia ions ob ained by eplacing he a iables wi h all
possible cons an s occu ing in Π. Likewise, we deno e by g ound(Π) he se
o ules ob ained om g ounding all ules in Π. Se s o ules a e e alua ed in
ASP unde he so-called s able-model seman ics, which allows se e al models,
so called answe se s (c . [22] o de ails).
ASP Sol e s ypically fi s compu e a subse o g ound(Π) and hen use
a DPLL-like b anch and bound algo i hm o find answe se s o his g ound
p og am. We use he ASP sol e clasp [17] o ou expe imen s as i has p o ed
o be one o he mos efficien implemen a ions a ailable [23].
As syn ac ic ex ension, in place o a oms, clasp allows se -like
choice exp essions o he o m E={A1,...,A
k}which a e ue o any sub-
se o E; ha is, when used in heads o ules, Egene a es many answe se s,
and such ules a e o en e e ed o as choice ules. Ano he ex ension suppo ed
in clasp a e op imiza ion s a emen s [17] o indica e p e e ences be ween possible
answe se s:
#minimize{A1:Body1=w1,...,A
m:Bodym=wm@p}
associa es in ege weigh s (de aul ing o 1) wi h a oms Ai(condi ional o Bodyi
being ue), whe e such a s a emen exp esses ha we wan o find only answe
se s wi h he smalles agg ega ed weigh sum; again, a iables in Ai:Bodyi=wi
a e eplaced a g ounding w. . . all possible ins an ia ions. Se e al op imiza ion
s a emen s can be in oduced by assigning he s a emen a p io i y le el p. Rea-
soning p oblems including such weak cons ain s a e ΔP
2-comple e.
Finally, many p oblems con en ien ly modelled in ASP equi e a bounda y
pa ame e k ha eflec s he size o he solu ion. Howe e , o en in p oblems like
planning o model checking his bounda y (e.g. he plan leng h) is no known
up on , and he e o e such p oblems a e add essed by conside ing one p oblem
ins ance a e ano he while g adually inc easing his pa ame e k. Re-p ocessing
epea edly he en i e p oblem is a edundan app oach, which is why inc emen-
al ASP (iASP) [17] na i ely suppo s inc emen al compu a ion o answe se s;
he in ui ion is oo ed in ea ing p og ams in p og am slices (ex ensions). In
each inc emen al s ep, a successi e ex ension o he p og am is conside ed whe e
p e ious compu a ions a e e-used as a as possible.
A o me e sion o ou echnique is de ailed in [5]. We enhance ou encoding
in h ee olds: (1) basic esou ce alloca ion suppo ing mul iple business p ocesses
wi h mul iple unning ins ances, (2) defini ion o ad anced esou ce managemen
concep s, and (3) defini ion o ad anced ime managemen concep s. The en i e
ASP encoding can be ound a h p://goo.gl/Q7B2 4.
4.1 Basic Resou ce Alloca ion
This p og am schedules he ac i i ies in business p ocesses desc ibed as imed
Pe i ne s (c . he gene ic o mula ion o 1-sa e Pe i Ne s [5, Sec . 4]) and allo-
ca es esou ces o ac i i ies wi h espec o ac i i y- esou ce equi emen s. To
achie e his, he p og am finds a fi ing sequence be ween ini ial and goal places
o gi en p ocesses, schedules he ac i i ies in be ween, and alloca es esou ces
by complying wi h esou ce equi emen s. In ou p og am, a fi ing sequence is
ep esen ed as p edica es i e(a,b,i,k), which means ha an ac i i y ao a
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