Repair Floor

Strip Room

Rough in Plumbing &Electrical

Repair Wall & Ceiling

Fume Hood

Base Cabinet

Chemical Sink

Vinyl Flooring

Walls

Electrical

Plumbing

j Act ivity Descript ion T ( Days) ES D EFD LS D LFD2 4 S trip room 3 0 3 1 4

2 12 Obtain fume hood 10 0 10 4 14

2 14 Obtain cabinet 10 0 10 3 13

2 20 Obtain chem ical s ink 10 0 10 7 17

2 24 Painter availability 20 0 20 0 20

2 28 Obtain vinyl floor covering 5 0 5 21 26

4 6 Rough-in plum bing and electrical 5 3 8 4 9

4 8 Replace existing fume d uct 3 3 6 6 9

6 8 Dumm y 0 8 8 9 9

6 10 Repair floor 1 8 9 12 13

8 10 Repair walls and ceiling 4 8 12 9 13

10 12 Dumm y 0 12 12 14 14

10 14 Dumm y 0 12 12 13 13

12 16 Install new fume hood 1 12 13 14 15

14 16 Dumm y 0 12 12 15 15

14 22 Install wall cabinets 5 12 17 13 18

16 18 Install 1/3 base cabinets 1 13 14 15 16

18 20 Dumm y 0 14 14 17 17

18 22 Install 2/3 base cabinets 2 14 16 16 18

20 22 Install chem ical s ink 1 14 15 17 18

22 24 Finish plumbing and electrical 2 17 19 18 20

24 26 Dumm y 0 20 20 23 23

24 28 Paint cabinets 6 20 26 20 26

26 28 Paint walls and ceiling 3 20 23 23 26

28 30 Lay vinyl floor 1 26 27 26 27

Forward Pass Computations - Remodeling Chemical Laboratory

Total float: Can change the successor activity times & bring new critical path

Free Float: Can delay without any problem. No change in successor activities.

Independent Float: Can delay even if the previous activities are late

j Act ivity Descript ion T ( Days) ES D EFD LS D LFD TF FF INTF INDF

2 4 S trip room 3 0 3 1 4 1 0 1 -

2 12 Obtain fume hood 10 0 10 4 14 4 2 2 2

2 14 Obtain cabinet 10 0 10 3 13 3 2 1 2

2 20 Obtain chem ical s ink 10 0 10 7 17 7 4 3 4

2 24 Painter availability 20 0 20 0 20 0 - - -

2 28 Obtain vinyl floor covering 5 0 5 21 26 21 21 0 21

4 6 Rough-in plumbing and electrical 5 3 8 4 9 1 0 1 -

4 8 Replace existing fume d uct 3 3 6 6 9 3 2 1 1

6 8 Dummy 0 8 8 9 9 1 0 1 -

6 10 Repair floor 1 8 9 12 13 4 3 1 2

8 10 Repair walls and ceiling 4 8 12 9 13 1 0 1 -

10 12 Dummy 0 12 12 14 14 2 0 2 -

10 14 Dummy 0 12 12 13 13 1 0 1 -

12 16 Install new fume hood 1 12 13 14 15 2 0 2 -

14 16 Dummy 0 12 12 15 15 3 1 2 0

14 22 Install wall cabinets 5 12 17 13 18 1 0 1 -

16 18 Install 1/3 base cabinets 1 13 14 15 16 2 0 2 -

18 20 Dummy 0 14 14 17 17 3 0 3 -

18 22 Install 2/3 base cabinets 2 14 16 16 18 2 1 1 0

20 22 Install chem ical s ink 1 14 15 17 18 3 2 1 0

22 24 Finish plumbing and electrical 2 17 19 18 20 1 1 0 0

24 26 Dummy 0 20 20 23 23 3 0 3 -

24 28 Paint cabinets 6 20 26 20 26 0 - - -

26 28 Paint walls and ceiling 3 20 23 23 26 3 3 0 3

28 30 Lay vinyl floor 1 26 27 26 27 0 - - -

Forward Pass Computations - Remodeling Chemical Laboratory

0

FLOATS : Flexibility in delaying an activity

Critical PathCritical Path

In In project managementproject management, a , a critical critical pathpath is the sequence of is the sequence of project networkproject network activities with the activities with the longest overall longest overall durationduration, determining , determining the shortest time possible to the shortest time possible to complete the project. Any delay of complete the project. Any delay of an activity on the critical path an activity on the critical path directly impacts the planned project directly impacts the planned project completion date (i.e. there is no completion date (i.e. there is no floatfloat on the critical path)..on the critical path)..

Critical PathCritical Path

A project can have several, parallel critical A project can have several, parallel critical paths. An additional parallel path through paths. An additional parallel path through the network with the total durations shorter the network with the total durations shorter than the critical path is called a than the critical path is called a sub-critical sub-critical or non-critical path and the activities are or non-critical path and the activities are non-critical activities.non-critical activities.

If the float of activity is negaive: If the float of activity is negaive: supercritcial activites; need more resources, supercritcial activites; need more resources, Special attention.Special attention.

Originally, the critical path method Originally, the critical path method considered only logical considered only logical dependenciesdependencies among among terminal elements. Since then, it has been terminal elements. Since then, it has been expanded to allow for the inclusion of expanded to allow for the inclusion of resources related to each activity resources related to each activity

Update CPM DiagramUpdate CPM Diagram

As the project progresses, the actual As the project progresses, the actual task completion times will be known task completion times will be known and the network diagram can be and the network diagram can be updated to include this information. A updated to include this information. A new critical path may emerge, and new critical path may emerge, and structural changes may be made in structural changes may be made in the network if project requirements the network if project requirements change.change.

Time CrashingTime Crashing

Normally project is planned for the completion period Normally project is planned for the completion period of the network. of the network.

Increasing the duration of the project increase project Increasing the duration of the project increase project costs.costs.

But, under some circumstances, may compel to But, under some circumstances, may compel to reduce the completion time:reduce the completion time:• To avoid delay which attract heavy penalty or loss of To avoid delay which attract heavy penalty or loss of

goodwill.goodwill.• To venture on another projectTo venture on another project• To earn bonus for early completion, if found feasible.To earn bonus for early completion, if found feasible.• To transfer the resources needed elsewhere.To transfer the resources needed elsewhere.

Project Cost ComponentsProject Cost Components

Direct & Indirect CostsDirect & Indirect Costs

Direct cost : For Accomplishing the workDirect cost : For Accomplishing the work Indirect Cost : Related to control & direction of Indirect Cost : Related to control & direction of

work, financial overheads, lost production, work, financial overheads, lost production, insurance claimsinsurance claims

Direct project CostDirect project Cost

Variation of Cost with TimeVariation of Cost with Time

Indirect CostIndirect Cost

Only considering overheads and supervision

Indirect CostIndirect Cost If there isIf there is

• loss in profitsloss in profits• Penalty due to delayPenalty due to delay

OUTAGE LOSSOUTAGE LOSS

Indirect Cost (Overhead + Outage Indirect Cost (Overhead + Outage Loss)Loss)

Total Project CostTotal Project Cost

CPM Cost ModelCPM Cost Model

In CPM- Time is related to cost ---- In CPM- Time is related to cost ---- Therefore objective is to develop optimum Therefore objective is to develop optimum time-cost relationship.time-cost relationship.

The project duration can be reduced by The project duration can be reduced by reducing the duration of critical activities.reducing the duration of critical activities.• By deploying more resourcesBy deploying more resources• By relaxing the technical specificationsBy relaxing the technical specifications

Cost Variation with TimeCost Variation with Time

Normal & Crash EstimatesNormal & Crash Estimates

Normal Estimate: Emphasis is on Normal Estimate: Emphasis is on costcost with time with time being associated with minimum cost.being associated with minimum cost.

Crash Estimate: Absolute minimumCrash Estimate: Absolute minimum time time required required for the job and the cost necessary to achieve it.for the job and the cost necessary to achieve it.

Cost –Time CurveCost –Time Curve

Normal Time (tNormal Time (tnn): Normal time is the standard time that an ): Normal time is the standard time that an estimator would usually allow for an activity.estimator would usually allow for an activity.

Crash Time (tCrash Time (tcc): Minimum possible time in which an activity ): Minimum possible time in which an activity can be completed by deploying extra resources.can be completed by deploying extra resources.

Normal Cost (CNormal Cost (Cnn): This is the direct cost required to ): This is the direct cost required to complete the activity in normal time durationcomplete the activity in normal time duration

Crash Cost (CCrash Cost (Ccc) : This is the direct cost corresponding to the ) : This is the direct cost corresponding to the completion of the activity within crash time.completion of the activity within crash time.

Generalized Generalized directdirect cost-time cost-time curvecurve

Direct Direct Cost CurveCost Curve

Total Project Cost & Optimum Total Project Cost & Optimum DurationDuration

Total Cost Curve Linear Approximation

Cost SlopeCost SlopeThe slope of each cost versus time trade-off for each activity as follows:

Time-Cost Model Time-Cost Model AssumptionsAssumptions

The time-cost model described above relies on The time-cost model described above relies on the following assumptions:the following assumptions:

The normal cost for an activity is lower than The normal cost for an activity is lower than the crash cost. the crash cost.

There is a linear relationship between activity There is a linear relationship between activity time and cost. time and cost.

The resources are available to shorten the The resources are available to shorten the activity. activity.

Project CrashingProject Crashing

The activities having the lowest cost per unit The activities having the lowest cost per unit of time reduction should be shortened first. of time reduction should be shortened first. In this way, one can step through the critical In this way, one can step through the critical path activities and create a graph of the total path activities and create a graph of the total project cost versus the project time. project cost versus the project time.

Project CrashingProject Crashing

Attention should be given to the critical path to Attention should be given to the critical path to make sure that it remains the critical path after the make sure that it remains the critical path after the activity time is reduced. If a new critical path activity time is reduced. If a new critical path emerges, it must considered in subsequent time emerges, it must considered in subsequent time reductions.reductions.

To minimize the cost, those activities that are not To minimize the cost, those activities that are not on the critical path can be extended to minimize on the critical path can be extended to minimize their costs without increasing the project their costs without increasing the project completion time.completion time.

ActivityActivity Normal Normal Duration Duration

(Days)(Days)

Normal Cost Normal Cost (Rs. )(Rs. )

Crash Crash Duration Duration

(Days)(Days)

Crash Cost Crash Cost (Rs.)(Rs.)

1-21-2 99 80008000 66 95009500

2-32-3 55 50005000 33 55005500

Project Overhead costs are @ Rs 300/day

Determine:

3. Direct Cost-duration relationship

4. Total cost –duration relationship and corresponding least cost plan

1 2 39 (6) 5 (3)

1. Find out the cost slope for each activity ?

2. Find out Normal Duration Direct Cost ?

3. Crash the activity with least cost slope ?

4. Find out the extra cost of crashing ?

5. Add to the normal direct cost of the project

6. Crash another activity ?

7. Find out the extra cost of crashing ?

8. Add to the normal direct cost of the project ?

Critical PathCritical Path

Normal Duration & Direct Cost Normal Duration & Direct Cost

Cost SlopeCost Slope

First Stage crashing: Critical First Stage crashing: Critical Activity with minimum cost -slopeActivity with minimum cost -slope

Not 3 weeks: (The path should remain critical)

Second-Stage crashing 2-3, 2-4 or 2-4, Second-Stage crashing 2-3, 2-4 or 2-4, 3-4. minimum cost slope Simultaneously3-4. minimum cost slope Simultaneously

Third Stage of Crashing: Activity Third Stage of Crashing: Activity 2-4 & 3-42-4 & 3-4

Fourth Stage of CrashingFourth Stage of Crashing

33000