Construction Scheduling Using Constraint Satisfaction Problem Method

Construction Scheduling Using Constraint Satisfaction Problem Method

Seminar Report - 2014

CHAPTER – 1 INTRODUCTION 1.1.

GENERAL

Construction projects are characteried b! their comple"it!# uni$ueness# and the fact that there there are %ariou %ariouss t!pes t!pes of constra constraint intss impose imposed d b! sta&eho sta&eholde lders' rs' (his (his includ includes es numero numerous us constraints of %arious t!pes# including contractual due dates# resource limitations# safet!# financ financial# ial# and manage managerial rial constra constraint ints' s' Satisf! Satisf!ing ing project project constra constraint intss is one of the most most challen challengin ging g tas&s tas&s in the constru constructio ction n schedu schedulin ling g process process'' (he (he practic practicalit alit! ! of a schedu schedule le depend dependss consid considerab erabl! l! on the degree degree to )hich )hich these these constra constraint intss are satisfie satisfied' d' Pre%iou Pre%iouss scheduling s!stems primaril! emplo!ed the critical path method to produce schedules' CPM in its present form has pro%en inade$uate for the consideration of constraints in real-life construction projects' (his paper %ie)s construction scheduling as a constraint satisfaction problem' CSP graduall! generates %alid schedules using constraint propagation and constraint consistenc! chec&ing techni$ues' (hese techni$ues are useful for handling constraints that are predetermined as )ell as those that become apparent during schedule s chedule de%elopment' * CSP based scheduling method has been de%eloped to facilitate e"pressi%e constraint representation and to pro%ide effecti%e generation of practical# %alid project schedules' (he nature of the constraints %aries' (he most commonl! encountered constraints in the case of high + rise buildings includes time# technological# managerial# logistic# resource and space constraints' (echnological constraints# such as ,the placement of form)or& and rebar must be completed before pouring concrete# are rigid' Some constraints are imposed to ensure that certain acti%ities cannot be e"ecuted concurrentl! for safet! reasons' (hese constraints do not specificall! specificall! dictate )hich acti%it! is the predecessor or successor' successor' (he! can be classified classified as conditional constraints' .rganiational policies can be regarded as managerial constraints' Some of them are rigid )hile others ma! be treated as preferential /i'e'# soft constraints' Constraints pla! an important role in the scheduling generation process' Rigid constraints impose a fi"ed logic# )hereas conditional and preferential ones signifies fle"ible and multiple logics in the project net)or&' (he $ualit! of schedules produced depends largel! on the degree to )hich project constraints are satisfied'

ept' .f Ci%il ngineering

1

M''S'C'# 3uttippuram

thj&hj



Construction scheduling has been an acti%e research area o%er the last fi%e decades' Man! of the pre%ious efforts use the critical path method /CPM to determine the o%erall project duration as )ell as the acti%it! start and finish times' CPM is based on the assumption that the duratio duration n and cost of acti%it acti%ities ies in a project project net)or net)or& & are determ determinis inistic tic'' (radi (raditio tional nal CPM scheduling methods ha%e pro%en to be helpful onl! )hen the project deadline is not fi"ed and the resources are not constrained b! either a%ailabilit! or time' (hese methods ha%e been )idel! criticied for their inabilit! to cope )ith non technological constraints' n addition# CPM-based methods can primaril! handle a predetermined and rigid logic' n the later stage# Precedence 5et)or& *nal!sis /P5* frame)or& is de%eloped to manage constraints that arise from static and d!namic d!namic construction construction re$uirements' re$uirements' (his P5* techni$ue is commonl! commonl! used used for time time planni planning ng of constru constructio ction n project projects' s' (he! (he! introd introduce uce a concep conceptt called called meta meta inter%als to represent the comple" re$uirements that cause conditional relationships' (he P5* frame)or&# frame)or&# ho)e%er# ho)e%er# does not address the treatment treatment of constraints constraints in the situation in )hich the! cannot be satisfied. n this stud!# a ne) scheduling method called Constraint Satisfaction Problem /CSP method is discussed )ith the intent of o%ercoming this major dra)bac& inherent to most CPM-based methods' (he proposed method %ie)s construction scheduling as a constraint satisfaction problem /CSP' CSP %ie)s this problem as a set of decision %ariables# each ha%ing a set of possible %alues and a set of constraints restricting restr icting the %alues to %ariables' (he tas& of CSP is to instantiate the %ariables %ariables )ith the %alues )hile satisf!ing all the constraints' constraints' fficient CSP formulation formulation and solution solution generation techni$ues techni$ues are described' described' * practical practical case e"ample that incorporates both technological and non technological constraints is used to demonstrate the practicalit! of the proposed method 1.2.

OBJECTIVES 

(o de%elop a comprehensi%e &no)ledge about the %arious categories of constraints faced in a construction project'



(o &no) about the %arious scheduling processes processe s emplo!ed in construction projects'



(o identif! the inade$uacies of construction scheduling using Critical Path Method


2


thj&hj





(o de%elop a comprehensi%e &no)ledge about the construction scheduling using the constraint satisfaction problem'



(o compare the schedules de%eloped using Critical Path Method and Constraint Satisfaction problem Method'

CHAPTER – 2 LITERATURE REVIEW Construction projects are subjected to numerous constraints of %arious t!pes including contractual due dates# resource limitations# safet!# financial# and managerial constraints' Satisf!ing project constraints is one of the most challenging tas&s in the construction scheduling process' (he practicalit! of a schedule depends considerabl! on the degree to )hich these constraints are satisfied' 6or the literature re%ie) related to the current stud!# articles from the follo)ing journals )ere re%ie)ed' *ccording to Pasit Lorterao!" a!# $o!"%o& Ussa'a#i&o%rit (2)1*+, Construction projects are characteried b! their comple"it!# uni$ueness# and the fact that there are %arious t!pes of constraints imposed b! sta&eholders' (he nature of these constraints %aries' (he! identified si" t!pes of constraints that are commonl! encountered in most high-rise building constructions# including time# technological# managerial# logistic# resource# and space constraints' (echnological constraints# such as ,the placement of form)or& and rebar must be completed before pouring concrete# are rigid' Some constraints are imposed to ensure that certain acti%ities cannot be e"ecuted concurrentl! for safet! reasons' (hese constraints do not specificall! dictate )hich acti%it! is the predecessor or successor' (he! can be classified as conditional constraints' .rganiational policies can be regarded as managerial constraints' Some of them are rigid )hile others ma! be treated as preferential /i'e'# soft constraints' Constraints pla! an important role in the scheduling generation process' Rigid constraints impose a fi"ed logic# )hereas conditional and preferential ones signif! fle"ible /i'e'# soft and multiple logics in the project net)or&' (he $ualit! of schedules produced depends largel! on the degree to )hich project constraints are satisfied' C&a-#e Le Pae defined Constraint Satisfaction Problem as a programming method based on

three principles' (he problem to be sol%ed is e"plicitl! represented in terms of %ariables and ept' .f Ci%il ngineering

7


thj&hj



constraints on these %ariables' n a constraint-based program# this e"plicit problem definition is clearl! separated from the algorithm used to sol%e the problem' 8i%en a constraint-based definition of the problem to be sol%ed and a set of decisions# themsel%es translated into constraints# a purel! deducti%e process referred to as ,constraint propagation is used to propagate the conse$uences of the constraints' (his process is applied each time a ne) decision is made# and is clearl! separated from the decision-ma&ing algorithm' (he o%erall constraint propagation process results from the combination of se%eral local and incremental processes# each of )hich is associated )ith a particular constraint or a particular constraint class' Construction scheduling has been an acti%e research area o%er the last fi%e decades' Man! of the pre%ious efforts use the critical path method /CPM to determine the o%erall project duration as )ell as the acti%it! start and finish times' CPM is based on the assumption that the duration and cost of acti%ities in a project net)or& are deterministic (Sa%%a a!# E&Sa/e"0 2))+. (raditional CPM scheduling methods ha%e pro%en to be helpful onl! )hen the project

deadline is not fi"ed and the resources are not constrained b! either a%ailabilit! or time (He"a/ 1333+. (hese methods ha%e been )idel! criticied for their inabilit! to cope )ith

nontechnological constraints (Jaa4ari 13567 P-&tar 133)7 E&Bi8a!/ 1337 C0oo et a&. 1333+. n addition# CPM-based methods can primaril! handle a predetermined and rigid

logic' C0-a a!# 9eo0 (2)11+ de%elop a PM99 frame)or& to manage constraints that arise from static and d!namic construction re$uirements' (he! introduce a concept called metainter%als to represent the comple" re$uirements that cause conditional relationships' (he PM99 frame)or&# ho)e%er# does not address the treatment of constraints in the situation in )hich the! cannot be satisfied' Pasit Lorterao!" a!# $o!"%o& Ussa'a#i&o%rit (2)1*+ de%eloped a ne) scheduling

method )ith the intent of o%ercoming this major dra)bac& inherent to most CPM-based methods' (he proposed method %ie)s construction scheduling as a constraint satisfaction problem /CSP' CSP %ie)s this problem as a set of decision %ariables# each ha%ing a set of possible %alues and a set of constraints restricting the %alues to %ariables' (he tas& of CSP is to instantiate the %ariables )ith the %alues )hile satisf!ing all the constraints' fficient CSP formulation and solution generation techni$ues are described' * practical case e"ample that


4


thj&hj



incorporates both technological and non technological constraints is used to demonstrate the practicalit! of the proposed method'

CHAPTER – * CONSTRAINT SATIS:ACTION PROBLE$ *.1. CSP – AN OVERVIEW

n general# a Constraint Satisfaction Problem or CSP is defined b! a set of %ariables X i = {x 1 , x2 , x 3 ,..........xn }# and a set of constraints C 1 , C 2 , C 3.........C m' ach %ariable X i has a non empt! domain i of possible %alues' ach constraint is defined o%er a subset of %ariables# and it restricts the combination of %alues that these %ariables can assume' * CSP can be %isualied as a constraint graph consisting of nodes and arro)s' * state of the problem is defined b! an assignment of %alues to some or all of the %ariables# : X i = v ,i X j = v j ,…….;' (he nodes of the graph correspond to %ariables# and the arcs correspond to project constraints' (!pical %ariables in the scheduling problem are the start and finish times of project acti%ities'

>


thj&hj



scheduling %ariables' 6or instance# the unar! constraint S * ? 20 indicates that the domain of S* must be greater than da! 20' (he non unar! constraints S * 9 2 @ 6 *# 6 = A SC# and S= 9 > @ 6 =# each represented b! an arc# signif! a constraint from one %ariable to another' Conditional constraints# such as ,acti%it! C can be performed after * or = is finished# can effecti%el! be incorporated using a node .R in the constraint graph' n some situations# it is possible that acti%ities * and = cannot be e"ecuted simultaneousl!' (heir precedence relationships are interchangeable' (his situation generates a condition b! )hich * can precede = or %ice %ersa . Bogical operators such as A# # =# and D are used to specif! the relationships bet)een %ariables' * solution to the CSP problem is the assignment of a %alue from its domain to e%er! %ariable in such a )a! that all imposed constraints are satisfied' Partial solutions are progressi%el! generated and tested through the use of CSP and search techni$ues' ()o )idel! used CSP techni$ues# node and arc consistenc! chec&ing# are emplo!ed to ensure that all imposed constraints are locall! satisfied' n a net)or&-t!pe problem# ho)e%er# the assignment of a %alue to one %ariable can affect the domain of the others' * techni$ue called constraint propagation is then used to disseminate the effect of such an assignment to others' (he effecti%eness of an! CSP depends on ho) )ell constraints are represented and the techni$ues used to propagate them'

Figure. 3.1. Project Constraint Graph (Pasit Lorterapong et.al – 2013) ept' .f Ci%il ngineering

E


thj&hj



*.2. DEVELOP$ENT O: CSP – BASED SCHEDULING $ETHOD

(his stud! demonstrates a ne)l! de%eloped CSP-based scheduling method capable of satisf!ing %arious t!pes of constraints encountered in construction projects' (he proposed method utilies *llenFs constraint modeling techni$ues and emplo!s )idel! used searching techni$ues to produce schedules that satisf! project constraints' *cti%it! start /S i and finish /6i times are set as scheduling %ariables' Project constraints that are predetermined and rigid as )ell as those conditional and situational in nature can be incorporated' (ables 7'1 and 7'2 sho) the scheduling %ariables and constraint representations utilied in the proposed method' Table 3.1. che!uling "ariables #epresentation (Pasit Lorterapong et.al – 2013) S;0e#-&i!" Varia8&es

CSP $o#e&

Re
*cti%it! Start /Si

Si @ Gl # uH

B# u are lo)er and upper bounds of S i

*cti%it! 6inish /6i

6i @ Gl # uH

B# u are lo)er and upper bounds of 6 i

Table. 3.2. che!uling Constraint #epresentations (Pasit Lorterapong et.al – 2013) U!ar/ Co!strai!t

E=a<&es

Co!strai! t

(ime

Project

start

and

finish

dates#

acti%it! duration# milestones Precedence relationships bet)een

No! -!ar/ Co!strai! t

I

Co!#itio!a & Co!strai!t

I

acti%ities e"ists due to re$uirements (echnological

for structural integrit!# regulations#

I

and other technical re$uirements signifies that the acti%ities must

Managerial

ta&e place in a particular se$uence Managerial constraints are

I

I

dependenc! relationships emerged because

of

a

decision

b!

management' (his often occurs in the form of polic! or preferences re$uired ept' .f Ci%il ngineering

b! clients

preferential J


thj&hj



constraints allo) multiple planning alternati%es Bogistic constraints are numerous interferences bet)een configuration of Bogistic

construction

construction

)or&

site such

and as

in

I

I

I

I

I

I

I

I

I

I

conse$uence disorganied material storage causes e"tra time for the search of material or to rearrange storage areas Site safet! rulesK pipe )elding acti%ities must be performed in

Safet!

isolation

because

it

produces

spar&s# )hich might be haardous for others Resource constraints relate to lac& Resource

Space

of needed resources# )hich ma! force

parallel

acti%ities

to

be

performed in se$uence Space constraints are introduced to pre%ent an! trade interference

ach %ariable is characteried b! its domain inter%al /i'e'# its lo)er and upper bounds Gl# uH' CSP scheduling in%ol%es modif!ing the domains of all scheduling %ariables b! successi%el! imposing project constraints in a step)ise manner' * CSP scheduling procedure is generall! performed in the fi%e stagesK initialiation# propagation# bac&trac&ing search# rela"ation# and realiation' Sta"e 1> I!itia&iatio!

6ormulate the problem b! identif!ing project constraints and acti%ities' Scheduling %ariables /i'e'# Si and 6 i are generated' (he o%erall project duration specified in the contract is used to generate the initial domain %alues Gl# uH of S i and 6i' Sta"e 2> Proa"atio!


L


thj&hj



mpose project constraints input in Stage 1 in a se$uential manner' (he order in )hich those constraints are imposed is not restricted' (o facilitate faster schedule generation# ho)e%er# it is recommended that acti%it! duration constraints are imposed first' (hen# proceed )ith rigid constraints /i'e'# constraints that cannot be rela"ed such as technological# safet!# and managerial# conditional# and soft constraints# respecti%el!' (he )idel! &no)n depth-first search algorithm is emplo!ed to identif! the rele%ant constraints' ach constraint is chec&ed to ensure its consistenc!' (he successful constraint is then propagated to the scheduling %ariables in%ol%ed )here their domain %alues are updated /i'e'# being reduced' ach time a ne) domain %alue of an! scheduling %ariable is obtained# the related node and arc chec&s must be performed to ensure consistenc!' Sta"e *> Ba;%tra;%i!" Sear;0

n the situation in )hich no possible domain %alues can be found# a bac&trac&ing search is performed to locate the decision point at )hich a non e"plored alternati%e path e"ists /i'e'# the .R gate in the project constraint graph' Stage 2 is then repeated for the ne) path' Sta"e 6> Re&a=atio!

n the situation in )hich a %alid schedule cannot be obtained# some constraints )ill ha%e to be rela"ed' (his stage allo)s planners to in%ol%e in the constraint rela"ation process' (he ne)l! rela"ed constraint must then be re-propagated b! repeating Stage 2' (he scheduling process ends )hen all project constraints ha%e been satisfied and Si and 6i ha%e been assigned %alid domain inter%als' Upon e"hausting all paths in the constraint graph# and still# some constraints are not satisfied# it can be stated that the project is so constrained that no %alid schedule can be obtained' Sta"e 6> Rea&iatio!

f a solution e"ists# the ne"t step is to con%ert the final domains of each Si and 6 i to the common acti%it! start and finish times# GS i# 6iH# respecti%el!' *ccordingl!# Si ta&es the lo)er bound of S i# )hile 6 i assumes the lo)er bound of 6 i' Similarl!# the latest possible timeline of acti%it! i# GBSi# B6iH# can be determined using the upper bounds of Si and 6 i'





thj&hj



Figure. 3.2. CP base! sche!uling $lgorith% (Pasit Lorterapong et.al – 2013)

CHAPTER 6 CASE STUD9 ept' .f Ci%il ngineering

10


thj&hj



6.1. DE:INITION

(he management of a general hospital has decided to construct ne) buildings just opposite to the old buildings' (he figure gi%en belo) sho)s the site la!out of this project' * solid line di%ides the e"isting buildings from the ne) construction area' *t present# the e"isting road R1 and 8ates 81 and 82 are used to ser%e the hospital# )hile 87 is used as a spare gate' (he scope of the )or& described in this case stud! includes o%erhauling the e"isting road R1 /Sections 1-1# 1-2# 1-7 and constructing t)o ne) roads# R2 /Sections 2-1# 2-2# 2-7# 2-4 and R7 /Sections 7-1# 7-2# 7-7# 7-4# 7->' (he management of this hospital demands that e"isting hospital buildings must be full! accessible during the t)ent!-)ee& construction period /i'e'# time constraint' n other )ords# at least one road and one gate must be a%ailable to ser%e the hospital at an! time' ecisions regarding )hich road and )hich gates be in-ser%ice at )hat time are left to the authorit! at the project le%el' Such a polic! can be regarded as managerial constraints' (hese managerial constraints ha%e created se%eral planning alternati%es for this project' Construction acti%ities that ta&e place in front of an! gate necessitates the closure of that gate' 6or demonstration purposes# onl! the time# managerial# and the common technological constraints are imposed on the case e"ample'

Figure. &.1. Project ite La'out (Pasit Lorterapong et.al – 2013)

Table. &.1. Technological Constraints a%ong Project $ctiities ept' .f Ci%il ngineering

11


thj&hj


Roa# Se;tio!s

1-1 R1

R2

R7


(Pasit Lorterapong et.al .– 2013) D-ratio! (Di+ Pre#e;essors (?ee%s+ 2 -

Re
.%erhaul the

1-2

2

1+1

1-7

7

1-2

2+1

2

-

2+2

4

2+1

Construct a ne)

2+7

7

2+2

road

2+4

2

2-7

7+1

4

2+1

7+2

>

7+1

7+7

7

7+2

7+4

2

7+7

7+>

1

7-4

e"isting road

Construct a ne) road

6.2. SOLUTIONS GENERATED USING CP$

(he CPM has been used to generate project plans in this case e"ample' (he CPM allo)s planners to e"plore one project plan at a time' (o enable a realistic schedule# ho)e%er# the planner must generate a comprehensi%e project net)or& as input for CPM calculations' * schedule is then generated and assessed for its practicalit!' *lternati%e schedules necessitate %arious degrees of modifications to the original project net)or&' (he pre%ious process can be repeated in a trial manner until acceptable schedules are obtained' (he CPM solutions for the case e"ample are described subse$uentl! Tria& 1> t is decided that 81 and 82 )ill be opened such that construction can begin at R2

and R7' Upon completion of R7# 81 and 87 )ill be in ser%ice and construction can begin on R1' (he calculated project duration is 24 )ee&s# 4 )ee&s greater than the re$uired 20 )ee& project duration' (herefore# this alternati%e is not acceptable' Tria& 2> Similar to the first trial# construction )ill start on R2 and R7 simultaneousl!' (his

time# R1 )ill start once R2 is finished' (he construction of section R7 /7-> re$uires the closing of 82' (o maintain the gi%en managerial constraints# section R1 /1-7 can begin once section R7 /7-> is completed' CPM calculations !ield 20 - )ee& project duration' (his


12


thj&hj



alternati%e satisfies the gi%en project constraints' *ctuall!# the planning process can end once a satisfied schedule is disco%ered' More alternati%es can# ho)e%er# be e"plored if desired' Tria& *> Suppose that the planner )ould li&e to e"plore other planning option based on (rial

2' (his time# it is decided that R1 /1-7 is the predecessor of R7 /7->' (he project duration is calculated to be 1 )ee&s /i'e'# one )ee& shorter than the re$uired project duration'

Figure &.2. Project netor*s using the Critical Path +etho! , (a) Project -etor* – Trial 1 (b) Project -etor* – Trial 2  (c) Project -etor* – Trial 3 (Pasit Lorterapong et.al – 2013)

*s illustrated# the critical path method can be emplo!ed to calculate project schedules' No)e%er# the challenging tas& of generating a project net)or& that satisfies all project constraints is still borne b! the planner' (his tas& is %er! challenging# especiall! for the projects that are complicated# subjecting it to numerous and a %ariet! of constraints' 6.*. SOLUTIONS GENERATED USING CSP

(he proposed CSP-based scheduling procedure has been applied to the case e"ample' (echnological constraints are also considered along )ith the other constraints' (he managerial constraints regarding the accessible road and gates needed to maintain the hospitalFs functionalit! are formulated# and their representations modeled in the CSP format ept' .f Ci%il ngineering

17


thj&hj



are illustrated in tables 4'2 O 4'7 sho)s the CSP functions classified b! the t!pes of constraints' Table &.2. +anagerial Constraints an! their CP representations (Pasit Lorterapong et.al – 2013) $a!a"eria& Co!strai!t

Res-&ti!" Pre;e#e!;e

Des;ritio!

Re&atio!s0i •

Co!strai!t :-!;tio!

Section R1 / 1 + 1can start after •

Section R2 /2 + 4 or Section R7 *t least one road /R1# R2 or R7 must be a%ailable to ser%e the

hospital

during

1

/7-> has finished •

the

62-4 A S1-1 % 67-> A S1-

ue to ph!sical constraint# the o%erhauling of R1 )ill al)a!s

construction period

begin at section R1 /1 + 1 and

•

61-1 A S1-2 # 61-2 A S1-7

•

67-> A S1-7 % 61-7 A S7-

proceed to)ard section R1 / 1 + 7 •

Conse$uentl!# Section R1 /1 + 7 and Section R7 /7 + > cannot

*t least one gate /81 or 82

be constructed simultaneousl!'

must be a%ailable at an! time

GConstructing Section R1 /1 + 7

for hospital entrance and e"it

caused 81 to be closed )hile

>

constructing Section R7 /7 + > causes 82 to be closedH


14


thj&hj



Table &.3. CP Constraint /unctions o/ the Case tu!' (Pasit Lorterapong et.al – 2013) Co!strai!t N-<8er

Co!strai!t :-!;tio!

T/e o4 Co!strai!t

1

*ll
(ime - related

2

S2-1 9 2-1 @ 62-1

(ime - related

7

S2-2 9 2-2 @ 62-2

(ime + related

4

S2-7 9 2-7 @ 62-7

(ime + related

>

S2-4 9 2-4 @ 62-4

(ime + related

E

S7-1 9 7-1 @ 67-1

(ime + related

J

S7-2 9 7-2 @ 67-2

(ime + related

L

S7-7 9 7-7 @ 67-7

(ime + related



S7-4 9 7-4 @ 67-4

(ime + related

10

S7-> 9 7-> @ 67->

(ime + related

11

S1-1 9 1-1 @ 61-1

(ime + related

12

S1-2 9 1-2 @ 61-2

(ime + related

17

S1-7 9 1-7 @ 61-7

(ime + related

14

62-1 A S2-2

(echnological

1>

62-1 A S7-1

(echnological

1E

62-2 A S2-7

(echnological

1J

62-7 A S2-4

(echnological

1L

67-1 A S7-4

(echnological

1

67-2 A S7-7

(echnological

20

67-7 A S7-4

(echnological

21

67-4 A S7->

(echnological

22

61-1 A S1-2

(echnological


1>


thj&hj



27

61-2 A S1-7

(echnological

24

62-4 A S1-1 % 67-> A S1-1

Managerial

2>

67-> A S1-7 % 61-7 A S7->

Managerial

6.6. SCHEDULE DEVELOP$ENT USING THE PROPOSED CSP $ETHOD

(he schedule of the project is de%eloped using the CSP method b! follo)ing the fi%e procedural stages' Sta"e 1> I!itia&iatio! 1. nitiate the domain of all acti%it! start and finish times /i'e'# S i and 6i b! imposing

Constraint 1 /project duration constraint# resulting in the initial domains of G0# 20H for all scheduling %ariables' Sta"e 2> Proa"atio! 1. mpose the acti%it! duration constraints /i'e'# Constraints 2+17 on all scheduling %ariables'

Constraint 2 /i'e'# S2-1 9 2-1 @ 62-1 is selected for demonstration purposes' (he initial domains of S2-1 and 6 2-1 obtained from step 1 are G0# 20H' Upon imposing Constraint 2# the lo)er bound of S 2-1 remains unchanged' (he upper bound of S 2-1# ho)e%er# must be reduced b! 2 )ee&s /i'e'#  2-1 @ 2 )ee&s' Conse$uentl!# the upper bound of S 2-1 is reduced to )ee& 1L after constraint propagation# resulting in a ne)l! reduced domain G0# 1LH' 5ode and arc consistenc! are then chec&ed to ensure that other constraints associated )ith S 2-1 are satisfied' Similarl!# the upper bound of 6 2-1 remains unchanged at )ee& 20' (he lo)er bound of 6 2-1 is increased b! the amount specified b!  2-1# to )ee& 2' (he resulting domains for 6 2-1 are G2# 20H' (his process is repeated for Constraints 7+17' 2. 5e"t# impose the technological constraints /14 + 27' Considering# for e"ample# Constraint

14 /i'e'# 6 2-1 A S2-2# the domains of 6 2-1 and S 2-2 obtained from the pre%ious process are G2# 20H and G0# 1EH# respecti%el!' =! propagating Constraint 14# the domains of 6 2-1 and S2-2 are further reduced to )ee&s G2# 1EH' 5ode and arc are chec&ed and found to be consistent' (his propagation is considered to be successful' (his process is repeated for Constraints 1>+27 ept' .f Ci%il ngineering

1E


thj&hj



Figure &.3. atis/action o/ $ctiit' uration Constraints (Constraint 2) (Pasit Lorterapong et.al – 2013)

Figure &.&. atis/action o/ Technological Constraints (Constraint 1&) (Pasit Lorterapong et.al – 2013)

*. mpose managerial constraint /i'e'# 24# the ser%ice road re$uirement' (o maintain at least

one accessible road during the construction# R 1/1 - 1 can start once R 2/2 - 4 or R 7/7 - > has completed /i'e'# 6 2-4 A S1-1 or 6 7-> A S 1-1' (a&e# for e"ample# the scenario in )hich R 1 /1 - 1 can begin once R 2 /2 - 4 has finished' (he figure gi%en belo) illustrates the domains of 62-4 and S1-1 before and after Constraint 24 is propagated' =efore propagation# the domains of 62-4 and S1-1 )ere G11# 20H and G0# 17H# respecti%el!' Constraint 24 /i'e'# 6 2-4 A S1 indicates that the domain of 62-4 must be smaller than or e$ual to that of S

1

' *s a

1-1

result# the domains of both 6 2-4 and S1-1 are reduced to G11# 17H' 5ode and arc consistenc! is chec&ed to ensure that these ne) domains do not cause an! %iolation to other constraints' (his process is repeated for Constraint 2>'


1J


thj&hj



Figure &.. atis/action o/ +anagerial Constraints (Constraint 1&) (Pasit Lorterapong et.al – 2013) Sta"e *> Ba;%tra;%i!" Sear;0 a!# Sta"e 6> Re&a=atio! 1. =ac&trac&ing search and rela"ation are re$uired )hen an! constraint is %iolated' 6or this

case# no %iolation has been encountered' *s such# there is no need to perform bac&trac&ing or rela"ation'


1L


thj&hj



Figure &.. Final o%ains o/ all sche!uling ariables (Pasit Lorterapong et.al – 2013) Sta"e @> Rea&iatio! 1. 6inall!# it is necessar! to con%ert the domain of all S i and 6i to their respecti%e start and

finish times' *s this figure demonstrates# the final domains of S2-2 and 6 2-2 for this alternati%e are G2# 7H and GE# JH# respecti%el!' (hus# section 2-2 can start at an! time bet)een the end of )ee&s 2 and 7# and it can finish at an! time bet)een the end of )ee&s E and J' 2. Combine the domains of the acti%it! start and finish times into earl! or late 8antt charts'

6igure 4'J illustrates the resulting earl! 8antt chart obtained from the combination' *s ept' .f Ci%il ngineering

1


thj&hj



e"plained in Stage ># the earl! start time /S for R 2 /2-2 assumes the lo)er bound of domains of S 2-2 G2#7H# )hich is da! 2' Similarl!# the earl! finish time /6 ta&es the lo)er bound of 62-2 GE# JH# )hich is da! E' 6igure 4'J also illustrates the earliest possible start and finish times of all acti%ities'

Figure &.. #esulting earliest possible ti%es /or all project actiities (Pasit Lorterapong et.al – 2013) 6.@. DISCUSSIONS

Construction projects are )ell &no)n for their comple"ities# and the! are subject to numerous constraints of %arious t!pes' (he proposed CSP-based scheduling method focuses on the satisfaction of project constraints# )hereas most CPM-based methods focus on scheduling acti%ities according to a predefined and fi"ed logic' *s indicated in the case e"ample# CPM generall! re$uires planners to comprehend all project constraints at the outset of the scheduling process' (hese constraints are then used to formulate a project net)or& for ept' .f Ci%il ngineering

20


thj&hj



for)ard and bac&)ard CPM calculations' Conditional constraints# such as ,Road 1 can begin as soon as Road 2 or Road 7 is finished# cannot be incorporated into one net)or& logic' Multiple logics )ill ha%e to be modeled separatel! in different net)or&s' 6or large projects# this process can be time consuming' More importantl!# this dra)bac& can limit the opportunit! to obtain schedules of better $ualit!' (he CSP-based scheduling method# on the other hand# allo)s constraints to be imposed in a more fle"ible and e"pressi%e manner' (he conditional constraints can be effecti%el! incorporated' (he less rigid constraint such as ,81 and 82 cannot be closed at the same time can effecti%el! be modeled' (his t!pe of constraint naturall! causes multiple logics that cannot be effecti%el! modeled b! CPM-based methods' (o produce schedules# the proposed CSP based method propagates constraints and performs consistenc! chec&ing to ensure the production of a %alid schedule' hen inconsistencies are detected# bac&trac& searching can be performed to find an alternati%e logic


21


thj&hj



CHAPTER  CONCLUSION Construction projects are subjected to numerous constraints of %arious t!pes including contractual due dates# resource limitations# safet!# financial# and managerial constraints' Satisf!ing project constraints is one of the most challenging tas&s in the construction scheduling process' (he practicalit! of a schedule depends considerabl! on the degree to )hich these constraints are satisfied' Most scheduling methods based on Critical Path Method re$uire that all projects constraints should be arranged in to a single logical net)or& for de%eloping project schedule' CPM in its present form has pro%en inade$uate for the consideration of constraints in real-life construction projects' (his stud! considered construction scheduling as a constraint satisfaction problem' CSP graduall! generates %alid schedules using constraint propagation and constraint consistenc! chec&ing techni$ues' (hese techni$ues are useful for handling constraints that are predetermined as )ell as those that become apparent during schedule de%elopment' * CSP-based scheduling method has been de%eloped to facilitate e"pressi%e constraint representation and to pro%ide effecti%e generation of practical# %alid project schedules' CSP method can be performed in fi%e stages + initialiation# propagation# bac&trac&ing search# rela"ation# and realiation' *n application e"ample is anal!ed to illustrate the use of the proposed method and to demonstrate its capabilit! in comparison to CPM' CSP e"hibits a close resemblance to construction scheduling problemsQ the %ariables of the CSP correspond directl! to the scheduling information related to project acti%ities' n addition# CSP allo)s constraints to be e"plicitl! e"pressed and satisfied' (his process helps to facilitate the formulation of solutions and the selection of search algorithms to guide the solution' (he present method is superior to CPM because of its more e"pressi%e constraint representations and abilit! to handle multi logic project net)or&s' *lternati%e schedules can be obtained )ith relati%e ease' Comparing )ith the traditional CPM-based methods# the proposed method has the potential to transform the ept' .f Ci%il ngineering

22


thj&hj



)a! construction schedules are generated and managed' * computeried CSP method supports human+machine interactions in generating a more realistic schedule'

RE:ERENCES 1' Pasit Borterapong and Mong&ol Ussa%adilo&rit /2017# Construction Scheduling Using the Constraint Satisfaction Problem MethodF + ournal of Construction ngineering and Management# 2017'17 /*SC# pp' 414 + 422 /' 2' oana Cobeanu# 17+>21/ 4' Biliana Cucu - 8rosjean O .li%ier =uffet# 8lobal Multiprocessor Real-(ime Scheduling as a Constraint Satisfaction ProblemF# pp' 01 + 0L >'

Claude Be Pape# Constraint-=ased SchedulingK * (utorialF pp' 01 - 77


27


thj&hj

Construction Scheduling Using Constraint Satisfaction Problem Method

Recommend Documents