© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 8-1

© McGraw-Hill/Irwin 2004

Information Systems Project Management—David Olson8-1



Chapter 8: Network Scheduling Methods

Critical path method (CPM)

Buffers

Leveling & Smoothing



why networks?

• Gantt charts don’t explicitly show task relationships

• don’t show impact of delays or shifting resources well

• network models clearly show interdependencies



Logic Diagrams

• network of relationships

elements & relationships (sequence)this is ACTIVITY-ON-NODE

can have ACTIVITY-ON-ARC

researchwhat’s

been done

researchwhat needs

doing pickfinaltopic

internetresearch

write print



Network Diagrams

• activity duration

• milestone

• immediate predecessors

identified by arrows leading into• durations can include in parentheses• dummy activities need for AOA networks

activity(duration)

milestone



networks

• networks make a good visual

• they are TOTALLY UNNECESSARY for identifying – early starts earliest an activity can be begun– late finishes latest an activity can finish– slack spare time– critical paths activities with no slack



Project Scheduling

MODEL COMPONENTS• activities from WBS• predecessors what this activity waits on• durations how long

– durations are PROBABILISTIC– CPM DETERMINISTIC– PERT considers uncertainty, but UNREALISTIC– simulation

• all assume unlimited resources



Critical Path Method

• INPUTS: activities, durations, immediate predecessors

• ALGORITHMforward pass schedule all activities with no unscheduled predecessors

ES/EF determine early starts & early finishes (start ASAP, add duration)

backwards pass schedule in reverse (schedule all activities with no unscheduled FOLLOWERS)

LF/LS determine late finishes, subtract duration to get late starts

slack difference between LS-ES (same as LF-EF)

critical path all chains of activities with no slack



CPM Example

FORWARD PASSactivity duration predecessorA requirements analysis 3 weeks -B programming 7 weeks AC get hardware 1 week AD train users 3 weeks B, Cschedule A start 0 finish 0+3 =3schedule B 3 3+7 =10

& C 3 3+1 =4schedule D 10 10+3 =13



CPM Example

backward passschedule D finish 13 late start= 13-3 = 10schedule B 10 10-7 = 3

& C 10 10-1 = 9schedule A 3 3-3 = 0slack A LF= 3 EF= 3 3-3 = 0

B LF= 10 EF= 10 10-10= 0C LF= 10 EF= 4 10-4 = 6D LF= 13 EF= 13 13-13= 0

critical path: A-B-D



Gantt Chart

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A x x x

B x x x x x x x

C x

D x x x



CPM

• can have more than one critical pathactivity duration predecessorA requirements analysis 3 weeks -B programming 7 weeks AC get hardware 7 weeks AD train users 3 weeks B, C

• critical paths A-B-DA-C-D

both with duration of 13 weeks



Buffers

• Assure activities completed on time (Goldratt, 1997)

• Project Buffers: after final project task• Feeding Buffers: where non-critical

activities lead into critical activities• Resource Buffers: before resources

scheduled to work on critical activities• Strategic Resource Buffers: assure key

resources available



Project Buffer

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A x x x

B x x x x x x x

C x

D x x x b b



Resource Limitations

critical path crashing

(cost/time tradeoff)

other methods



Crashing

• can shorten project completion time by adding extra resources (costs)

• start off with NORMAL TIME CPM schedule

• get expected duration Tn, cost Cn• Tn should be longest duration• Cn should be most expensive in

penalties, cheapest in crash costs



Time Reduction

• to reduce activity time, pay for more resources

• develop table of activities with times and costs

• for each activity, usually assume linear relationship for relationship between cost & time



Crash Example

Activity: programming

Tn: 7 weeks

Cn: $14,000 (7 weeks, 2 programmers)if you add a third programmer, done in 6 weeksTc: 6 weeks

Cn: $15,000

cost slope = (15000-14000)/(6-7)=-$1000/week



Example Problem

activity Pred TnCn Tc Cc slope maxA requirements none 3 can’t crashB programming A 7 14000 6 15000 -1000 1 weekC get hardware A 1 50000 .5 51000 -2000 .5

weekD train users B,C 3 can’t crashCrashing Algorithm:1 crash only critical activities B only choice2 crash cheapest currently critical B is cheapest

3 after crashing one time period, recheck critical



Crash Example

Import critical software from Australia: late penalty $500/d > 12 dA get import license 5 days no predecessorB ship 7 days A is predecessorC train users 11 days no predecessorD train on system 2 days B,C predecessorscan crash C: $2000/day more than current for up to 3 days

B: faster boat 6 days $300 more than current bush plane 5 days $400 more than current commercial 3 days $500 more than current



Crash Example

Original schedule: 14 days, $1,000 in penalties = $1000

crash B to 6 days:13 days, $500 penalties, $300 cost = $800*

crash B to 5C to 10: 12 days, no penalties, $400+2000 cost = $2400

to 11 days is worseNOW A SELECTION DECISIONrisk versus cost



Crashing Limitations

• assumes linear relationship between time and cost– not usually true (indirect costs don’t change at

same rate as direct costs)

• requires a lot of extra cost estimation

• time consuming

• ends with tradeoff decision



Resource Constraining

• CPM & PERT both assume unlimited resources

NOT TRUE– may have only a finite number of systems analysts,

programmers

• RESOURCE LEVELING - balance the resource load

• RESOURCE CONSTRAINING - don’t exceed available resources



Resource Leveling

unleveled leveled

1stQtr

2ndQtr

3rdQtr

4thQtr

0

5

10

15

20

25

1stQtr

2ndQtr

3rdQtr

4thQtr

analystsprogrammerstrainers

1stQtr

2ndQtr

3rdQtr

4thQtr

0

5

10

15

20

25

30

35

40

1stQtr

2ndQtr

3rdQtr

4thQtr

analysts

programmers

trainers



Work Patterns

• natural resource demands tend to have lumps

• maintaining a stable work force works better if demand leveled

• HOW TO LEVEL: split each activity into smaller activities, schedule them at different times

• USUALLY NOT THAT EASY



Resource Leveling

this leveling often works for specific activities, but complicated even more when resources shared



Resource Leveling Methods

• split up work, stagger

• eliminate some activities (subcontract)

• substitute less resource consuming activities (use CASE tools)

• substitute resources (hire spot work programmers)



Resource Smoothing

• Adjust schedules to level workload– expand duration for peak load– compress durations where load low

• Fill in gaps of work

• Requires balancing resources– for activities with heavier load, use multiple

crews



Resource Loading

• MUST schedule activities to not overschedule critical resource

• If there is only one training room, and it includes the only delivery system– can’t speed up training– can’t conduct two training activities at once

• LINEAR PROGRAMMING• heuristics



Recap

• cost/time tradeoff– time consuming, still makes assumptions

• resource leveling– manual shuffling

• resource constraining– pure solution to optimality a research issue– heuristics have been applied in software

• NO IDEAL SOLUTION METHOD



Criticisms of CPM

• Rarely to activities proceed as planned– critical path therefore very volatile

• options to speed some activities available– crashing

• resource limits not reflected– resource leveling

• schedule likely to be very lumpy– resource smoothing



Summary

• Critical path provides managers valuable information– What activities interfere with project completion– Estimate of project duration

• Buffers a means to manage risk• Crashing a means to analyze cost/time tradeoff• Resource management

– Leveling– smoothing

Documents

© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 8-1