CPMPERT Critical Path Method Project Evaluation Review Technique

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CPM/PERT Critical Path Method Project Evaluation Review Technique Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn

CPM/PERT Critical Path Method Project Evaluation Review Technique Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 1

CPM/PERT Tools for Project Management – Minimum Project Duration – Scheduling – Time-cost Trade-offs

CPM/PERT Tools for Project Management – Minimum Project Duration – Scheduling – Time-cost Trade-offs – Resoruce Leveling (not to be discussed( Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 2

Critical Path Method • Network-based (to be seen why ( • An LP Problem

Critical Path Method • Network-based (to be seen why ( • An LP Problem but much more simple that it can be solved by hand • Deterministic (all the parameters are known or assumed with certainty( Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 3

Project Evaluation Review Technique • Extension of CPM • Probability Concept is added to

Project Evaluation Review Technique • Extension of CPM • Probability Concept is added to CPM • Good for a project which has never been done before. Some uncertainty involved Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 4

PROJECTS • There are many activities. Each activity takes time. • Some activities (successors)

PROJECTS • There are many activities. Each activity takes time. • Some activities (successors) cannot start until the other activities (predecessors) finish. • Can be represented by a directed network • Examples are construction, scientific project and thesis Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 5

Activity-on-Node (Ao. N( Act. A Act. B Act. C Act. D Pongsa Pornchaiwiseskul, Faculty

Activity-on-Node (Ao. N( Act. A Act. B Act. C Act. D Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 6

Activity-on-Arc (Ao. A( activity A S activity B F activity C activity D Pongsa

Activity-on-Arc (Ao. A( activity A S activity B F activity C activity D Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 7

EXAMPLE OF CPM Activity DIG FOUND POURB JOISTS WALLS RAFTERS FLOOR ROUGH ROOF FINISH

EXAMPLE OF CPM Activity DIG FOUND POURB JOISTS WALLS RAFTERS FLOOR ROUGH ROOF FINISH SCAPE Time 34 2 3 5 3 4 6 7 5 2 Predecessors DIG FOUND WALLS, POURB JOISTS FLOOR RAFTERS, JOISTS ROUGH, ROOF POURB, WALLS Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 8

MINIMUM PROJECT DURATION • Network Method – by hand – by computer programs, e.

MINIMUM PROJECT DURATION • Network Method – by hand – by computer programs, e. g. , Microsoft Project (not to be discussed( • Solving its corresponding LP problem – by computer or by hand Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 9

Network Method by Hand • Determine Longest route between start and end • Performed

Network Method by Hand • Determine Longest route between start and end • Performed in two steps. – Forward Pass(from start to end( – Backward Pass (from end back to start( Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 10

FORWARD PASS (1)The project starts at time zero (2)Every starting activity has an Earliest

FORWARD PASS (1)The project starts at time zero (2)Every starting activity has an Earliest Start(ES) at zero (3)Earliest Finish(EF) of an activity is ES + activity time EFj = ESj + Dj (4)For an activity j w/ predecessors, ESj = max{ its predecessors’ EF { Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 11

FORWARD PASS (cont’d( (5)The minimum project duration (T( T = max{EF of activities w/o

FORWARD PASS (cont’d( (5)The minimum project duration (T( T = max{EF of activities w/o successors{ Note that (1 The project can earliest finish at time T (2 It can finish later than time T but not before Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 12

BACKWARD PASS (1)The project finishes at time T (2)All the activities w/o successors can

BACKWARD PASS (1)The project finishes at time T (2)All the activities w/o successors can Latest Finish(LF) at time T. Their LF = T (3)Latest Start(LS) of an activity j is its LF minus activity duration (D), I. e, . LSj = LFj - Dj (4)LF of an activity w/ successors = min {LS of its successors{ Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 13

Ao. N Representation DIG(3( FOUND(4( JOISTS(3( FLOOR(4( ROUGH(6( POURB(2( RAFTERS(3( ROOF(7( WALLS(5( SCAPE(2( Pongsa

Ao. N Representation DIG(3( FOUND(4( JOISTS(3( FLOOR(4( ROUGH(6( POURB(2( RAFTERS(3( ROOF(7( WALLS(5( SCAPE(2( Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University FINISH(5( 14

AON Legend ES EF ACTIVITY (D( LS LF Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn

AON Legend ES EF ACTIVITY (D( LS LF Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 15

Ao. N Representation 1420 JOISTS(3( 10 14 FLOOR(4( ROUGH(6( 7 9 1215 1522 22

Ao. N Representation 1420 JOISTS(3( 10 14 FLOOR(4( ROUGH(6( 7 9 1215 1522 22 27 ROOF(7( FINISH(5( 7 10 9 12 0 3 DIG(3( 0 3 3 7 FOUND(4( 3 7 12 16 POURB(2( RAFTERS(3( 7 12 1214 10 12 WALLS(5( 7 12 1215 16 22 15 22 2227 SCAPE(2( 2527 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 16

Ao. A Representation 3 WA LLS 5 RB I 3 FTERS 2 G POU

Ao. A Representation 3 WA LLS 5 RB I 3 FTERS 2 G POU RA FOUND B C 4 ROUGH H 6 RO OF 7 0 JOI S DIG A 3 F SIH FIN 5 TS D FLOOR 4 E SCAPE 2 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 17

RESULT Activity DIG FOUND POURB JOISTS WALLS RAFTERS FLOOR ROUGH ROOF FINISH SCAPE Time

RESULT Activity DIG FOUND POURB JOISTS WALLS RAFTERS FLOOR ROUGH ROOF FINISH SCAPE Time Predecessors ES 3 0 4 DIG 3 2 FOUND 7 3 FOUND 7 5 FOUND 7 3 WALLS, POURB 12 4 JOISTS 10 6 FLOOR 14 7 RAFTERS, JOISTS 15 5 ROUGH, ROOF 22 2 POURB, WALLS 12 EF 3 7 9 10 12 15 14 20 22 27 14 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University LS 0 3 10 10 7 12 12 16 15 22 25 LF 3 7 12 12 12 15 16 22 22 27 27 18

LP Representation MAX 3 DIG+4 FOUND+2 POURB+3 JOISTS+5 WALLS 3 RAFTERS+4 FLOOR+6 ROUGH+7 ROOF+5

LP Representation MAX 3 DIG+4 FOUND+2 POURB+3 JOISTS+5 WALLS 3 RAFTERS+4 FLOOR+6 ROUGH+7 ROOF+5 FINISH+ 2 SCAPE+ SUBJECT TO (2 DIG <=1 (3 FOUND - DIG = 0 (4 JOISTS + POURB + WALLS - FOUND =0 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 19

LP Representation(cont’d( (5 FLOOR + DUMMY - JOISTS =0 (6 RAFTERS + SCAPE -

LP Representation(cont’d( (5 FLOOR + DUMMY - JOISTS =0 (6 RAFTERS + SCAPE - POURB - WALLS = 0 (7 ROUGH - FLOOR = 0 (8 ROOF - RAFTERS - DUMMY = 0 (9 FINISH - ROUGH - ROOF = 0 END Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 20

SCHEDULING WITH BAR CHART Activity 5 10 15 20 25 DIG FOUND POURB JOISTS

SCHEDULING WITH BAR CHART Activity 5 10 15 20 25 DIG FOUND POURB JOISTS WALLS RAFTERS FLOOR ROUGH ROOF FINISH SCAPE Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 21

CRITICAL ACTIVITIES • activities with zero slack = LS -ES or = LF -

CRITICAL ACTIVITIES • activities with zero slack = LS -ES or = LF - EF • critical activities form a Critical Path Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 22

TIME COST TRADE-OFFS Choose to shorten the critical activity with lowest cost until the

TIME COST TRADE-OFFS Choose to shorten the critical activity with lowest cost until the activity becomes non-critical. Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 23

CRASHING THE PROJECT Decrease the project duration by shortening the activities. Activity Normal Duration

CRASHING THE PROJECT Decrease the project duration by shortening the activities. Activity Normal Duration Max. Crash $/day DIG 3 1 50 JOIST 3 1 30 WALLS 5 3 40 FINISH 5 2 80 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 24

UNCERTAINTY Activity duration could be uncertain A - optimistic time estimate B - pessimistic

UNCERTAINTY Activity duration could be uncertain A - optimistic time estimate B - pessimistic time estimate M - most likely time estimate (mode( Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 25

DURATION ESTIMATES A M B time Mean D = (A+4 M+B)/6 Standard Deviation SD

DURATION ESTIMATES A M B time Mean D = (A+4 M+B)/6 Standard Deviation SD = (B-A)/6 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 26

PERT Method • Do CPM using its Mean D for the duration of each

PERT Method • Do CPM using its Mean D for the duration of each activity • CPM yields the Mean project duration • The variance of project duration T Var(T) = sum of Var(D) for all the critical activities in a CP Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University 27

Activity DIG FOUND POURB JOISTS WALLS RAFTERS FLOOR ROUGH ROOF FINISH SCAPE RESULT Time

Activity DIG FOUND POURB JOISTS WALLS RAFTERS FLOOR ROUGH ROOF FINISH SCAPE RESULT Time Predecessors ES 34 DIG 2 FOUND 3 FOUND 5 FOUND 3 WALLS, POURB 4 JOISTS 6 FLOOR 7 RAFTERS, JOISTS 5 ROUGH, ROOF 2 POURB, WALLS EF Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University LS LF 28

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