lecture 8. budget, cash flow, and uncertainty

8/3/2019 Lecture 8. Budget, Cash Flow, And Uncertainty

1/33

Project and Portfolio

Management (PPM)

Sudhir M Chadha

(Course of 20 lectures)

01/2011 1sudhir chadha


2/33

Uncertainty

01/2011 sudhir chadha 2


3/33

Questions

Given the uncertainties in accurately

estimating project durations, what is the

probability of completing the project by the

deadline (47 weeks)?



4/33

PERT Three Estimate Approach

The duration of each activity is a randomvariable having some probability distribution.

The three estimates to be obtained for each

activity are: Most likely estimate (m) = estimate of the most

likely value of the duration;

Optimistic estimate (o) = Estimate of the durationunder the most favourable conditions;

Pessimistic estimate (p) = Estimate of the durationunder the most unfavourable conditions



5/33

= Mean of probability distribution

2 = Variance of the probability distribution

is the average of the various activity durations and is the standarddeviation that measures the variability of the durations about the mean.

Model of Probability Distribution

Beta distribution

o pm Elapsed time



6/33

Approximate Formulas for and 2

For most probability distributions, such as the -distribution, essentially all the durations would liein the interval -3 and +3, i.e., the spread ofdurations is about 6. (For example, for a normal

distribution 99.73% of the distribution lies insidethis interval).

2 = [(p-o)/6 ]2

= (o+4m+p)/6

Note that the mean and the most likely estimateis not the same, because the possibility of muchhigher durations pushes the mean up.



7/33

and For Activity DurationsActivity o m p = (o+4m+p)/6 =(p-o)/6

A 1 2 3 2 B 2 3.5 8 4 1

C 6 9 18 10 4

D 4 5.5 10 6 1

E 1 4.5 5 4

F 4 4 10 5 1

G 5 6.5 11 7 1

H 5 8 17 9 4

I 3 7.5 9 7 1

J 3 9 9 8 1

K 4 4 4 4 0

L 1 5.5 7 5 1

M 1 2 3 2

N 5 5.5 9 6 01/2011 7sudhir chadha


8/33

Path Lengths When Duration = p

Path Length (weeks)

StartABCDGHMFinish 70

Start

A

B

C

E

H

M

Finish 54

StartABCEFJKNFinish 66

StartABCEFJLNFinish 69

StartABCIJKNFinish 60

StartABCIjLNFinish 63



9/33


10/33

Three Simplifying Approximations

Approximation 1: Assume that the mean critical path will turn outto be the longest path through the project network. As we havejust seen this may not be true. This implies that

p = Sum of the means of the durations for the activities on the meancritical path.

Approximation 2: Assume that the duration of the activities on themean critical path are statistically independent. This would not betrue if the same cause produces deviations in the durations of twoor more activities. p

2 = Sum of the variances of the durations for the activities on themean critical path.

Approximation 3: Assume that the form of the distribution of theproject duration is the normal distribution (one form of the central-limit theorem). This is justified if the number of activities for themean critical path is, say, 5.



11/33

p and p for Reliable Project

Activities on Mean Critical Path Mean Standard Deviation

A 2

B 4 1

C 10 2

E 4

F 5 1

J 8 1

L 5 1

N 6 Project Duration p = 44 p = 3



12/33

Probability of

Meeting the Deadline

The three simplifying

approximations lead to theprobability duration of theproject being approximatedby a normal distribution.

d = 47 weeks

= Deadline for the project;Number of standarddeviations by which dexceeds p

= (d - p)/p = 1.

P(T d) = Probability thatthe project duration (T)does not exceed thedeadline (d) = 0.84.

47 (Deadline)44 (Mean)

Project Duration

(in weeks)



13/33

Managerial Evaluation of PERT/CPM

The P(T d) is only a rough approximation of the true probability ofmeeting the project deadline. Since the true critical path of the project isusually longer than the mean critical path (i.e., more than 44 weeks), thereal probability of meeting the deadline is less than that obtained fromusing the simplifying assumptions.

The approximations made in estimating the mean and variance of activity

durations, as well as the simplifying approximations to get to the projectduration probability distribution are questionable. Nevertheless, themethod allows an understanding of uncertainty in activity durations.

Another deficiency is that PERT/CPM does not allow an activity to beginuntil all its immediate predecessors are completely finished. However, anextension called theprecedence diagramming methoddoes allow dealing

with overlapping activities. For example, although activity H (do theexterior painting) follows activity G (put up the exterior siding) in Reliablesproject network, it would be better to have a start-to-start relationshipwith some lag.



14/33

In Summary

Project Rules Scope and deliverablesPLANNING

From project definition

STEP 6Develop

budget

STEP 5Assign and

level resources

STEP 4Calculate an initial schedule

STEP 3Estimate the work packages

STEP 2Sequence the tasks

STEP 1Develop a work

breakdown structure

PREPLANNINGRisk management

Development approach

Risk management tasks

Resource

constraints

Realistic schedule

Resource forecast

Materials cost from

product specifications



15/33


16/33

Time-Cost Trade-off



17/33

Questions

If extra money is spent to expedite the

project, what is the least expensive wayof

attempting to meet the target completion

date (40 weeks)?



18/33

Time-Cost Trade Offs

Crashing an activityrefers to special costly measures toreduce the duration of an activity below its normal value.

These special measures might include using overtime,hiring additional temporary help, using special time-savingmaterials, obtaining special equipment, or anything else toexpedite an activity.

Crashing the projectrefers to crashing a number ofactivities to reduce the duration of a project to below itsnormal value.

The CPM method of time-cost tradeoffs is concerned withdetermining how much (if any) to crash each of theactivities to reduce the anticipated duration of the projectdown to a desired value.



19/33

Crashing

The normal pointon thetime-cost graph shows thetime (duration) of an activitywhen it is performed in thenormal way.

The crash pointshows thetime and cost when the

activity isfully crashed; i.e.,it is fully expedited with nocost spared to reduce itsduration as much aspossible.

The options for eachactivity are to be at its crashpoint, its normal point, orsomewhere on the linesegment between these twopoints.

Normal timeCrash time

Normal

Activity duration

Crash cost

Normal cost

Crash

A typical time-cost graph for

an activity



20/33

Time-Cost Trade-Off DataActivity Normal

weeks

Crash

weeks

Normal

Cost

Crash Cost Max Reduction

in Time

Crash Cost per

Week Saved

A 2 1 $180,000 $280,000 1 $100,000

B 4 2 320,000 420,000 2 50,000

C 10 7 620,000 860,000 3 80,000

D 6 4 260,000 340,000 2 40,000

E 4 3 410,000 570,000 1 160,000F 5 3 180,000 260,000 2 40,000

G 7 4 900,000 1,020,000 3 40,000

H 9 6 200,000 380,000 3 60,000

I 7 5 210,000 270,000 2 30,000

J 8 6 430,000 490,000 2 30,000

K 4 3 160,000 200,000 1 40,000

L 5 3 250,000 350,000 2 50,000

M 2 1 100,000 200,000 1 100,000

N 6 3 330,000 510,000 3 60,00001/2011 20sudhir chadha


21/33

Marginal Cost Analysis

Summing the normal costand the crash costin the time-cost trade-off table gives: Sum of normal costs = $4.55 million;

Sum of crash costs = $6.15 million;

Anticipated duration of the project if all the activities areperformed in the normal way = 44 weeks;

Ifallthe activities arefully crashed, then the project duration(assuming no delays) = 28 weeks.

Marginal cost analysis (MCA) finds the least expensive wayto reduce project duration one week at a time.

MCA becomes unwieldy for large networks.

Linear programming (LP) provides a more efficientalternative to marginal cost analysis, for large projects.



22/33

Performing MCA on Reliable Project

Activity

to

Crash

Crash

Cost

ABCDGHM

ABCEHM

ABCEFJKN

ABCEFJLN

ABCIJKN

ABCIJLN

40 Weeks 31 43 44 41 42

J $30,000 40 31 42 43 40 41

J 30,000 40 31 41 42 39 40

F 40,000 40 31 40 41 39 40

F 40,000 40 31 39 40 39 40

Cost of the partially crashed project = $4.69m



23/33

Linear Programming

Restatement of the problem: Consider the total cost of the project, including the extra cost of crashing

activities. The problem then is to minimize the total cost, subject to theconstraint that the project duration is less than or equal to the time desired bythe project manager.

The following decisions will appear in the changing cells:

The start time of each activity; The reduction in the duration of each activity due to crashing;

The finish time of the project (must not exceed 40 weeks for Reliable).

The start-time constraints specify that an activity cannot start until each ofits immediate predecessors have finished.

Although the start-time constraints allow a delay in starting an activity, an

optimal solution would not allow this to happen for any activity on thecritical path.



24/33

Mr Pertys Conclusions

The CPM method of time-cost trade-offs ignores the considerable uncertainty inactivity times, so the predicted project duration under any crashing plan may missthe actual duration by a considerable amount.

Conclusion 1. The plan for crashing the project only provides a 50% chance ofactually finishing the project within 40 weeks, so the extra cost of the plan($140000) is not justified. Therefore Mr Perty rejects any crashing at this stage.

It is sometimes useful to postpone a decision on crashing an activity until near itsstart time. Information on how well the project schedule is progressing can theninfluence this decision.

Conclusion 2. The extra cost of the crashing plan can be justified if it almostcertainly would earn the bonus of $150000 for finishing the project within 40weeks. Therefore Mr Perty will hold the plan in reserve to be implemented if theproject is running well ahead of schedule before reaching activity F.

Conclusion 3. The extra cost of part or all of the crashing plan can be easilyjustified if it likely would make the difference in avoiding the penalty of $300000 fornot finishing the project within 47 weeks.. Therefore Mr Perty will hold thecrashing plan in reserve to be partially or wholly implemented if the project isrunning far behind schedule before reaching activity F or activity J.



25/33

Budget and Cash Flow



26/33

Questions

How should ongoing costs be monitoredto try

to keep the project within budget?



27/33

Project Costs

The following terminology is used for project costs: Baseline costs. The original planned task, resource, or assignment

costs saved as part of a baseline plan;

Current (or scheduled) tasks. The calculated costs of tasks, resources,and assignments in a project plan. As adjustments are made to thebaseline plan (such as assigning or removing resources) , therecalculated costs are the current costs. The current cost equals theactual cost plus the remaining cost per task, resource, or assignment.

Actual costs. The costs that have been incurred for tasks, resources orassignments. After the project incurs actual costs (typically by trackingactual work), the current cost equals the actual cost plus theremaining cost per task, resource, or assignment.

Remaining costs. The difference between the current or scheduledcosts and the actual costs for tasks, resources, or assignments.



28/33

Scheduling Project Costs

PERT/Cost is a systematic procedure (included within Project) tohelp the project manager plan, schedule, and control project costs.

A common assumption when using PERT/Cost is that the costs ofperforming an activity are incurred at a constant rate throughout itsduration, i.e., prorated. This assumption can be changed.

PERT/Cost provides a weekly schedule of expenses so that theproject manager can monitor whether the project is staying withinbudget.

Postponing activities to their latest start times also postpones thecosts of these activities, which is helpful when cash is short, but thisalso increases the riskof missing the scheduled project completion

date.



29/33

Project budget for Reliable ProjectActivity Est. Duration (Weeks) Estimated Costs Cost per week of its

Duration

A 2 $180,000 $90,000

B 4 320,000 80,000

C 10 620,000 62,000

D 6 260,000 43,333

E 4 410,000 102,5000

F 5 180,000 36,000

G 7 900,000 128,571

H 9 200,000 22,222

I 7 210,000 30,000

J 8 430,000 53,750

K 4 160,000 40,000

L 5 250,000 50,000

M 2 100,000 50,000

N 6 330,000 55,00001/2011 29sudhir chadha


30/33

Earliest Time Project Cost ScheduleID Task Name Fixed Cost Fixed Cost

Accrual

0 Reliab le Co nst ructio n 0 Prorated

1 Excavate 180,000 Prorated

2 Lay the foundation 320,000 Prorated

3 Put up the rough wall 620,000 Prorated

4 Put up the roof 260,000 Prorated

5 Install the exteriorplumbing

410,000 Prorated

6 Install the interior plumbing 180,000 Prorated

7 Put up the exter ior s id ing 900,000 Prorated

8 Do the ex te ri or pai nti ng 200, 000 Prorated

9 Do the electrical work 210,000 Prorated

10 Put up the wallboard 430,000 Prorated

11 Install the flooring 160,000 Prorated

12 Do the i nte ri or pai nti ng 250, 000 Prorated

13 Install the exterior fixtures 100,000 Prorated

14 Install the interior fixtures 330,000 Prorated

Details

CostCum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

CostCum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

CostCum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

25/04 02/05 09/05 16/05 23/05 30/05 06/06 13/06 20/06

May June

175,833 175,83 175,83 175,833 109,33 109,33 194,571 164,571 164,571,295,833 1,471,66 1,647,50 1,823,333 1,932,66 2,042,00 2,236,571 2,401,143 2,565,71

180,000 180,00 180,00 180,000 180,00 180,00 180,000 180,000 180,00

320,000 320,00 320,00 320,000 320,00 320,00 320,000 320,000 320,00

620,000 620,00 620,00 620,000 620,00 620,00 620,000 620,000 620,00

43,333 43,33 43,33 43,333 43,33 43,33

43,333 86,66 130,00 173,333 216,66 260,00 260,000 260,000 260,00

102,500 102,50 102,50 102,500102,500 205,00 307,50 410,000 410,00 410,00 410,000 410,000 410,00

36,00 36,00 36,000 36,000 36,00

36,00 72,00 108,000 144,000 180,00

128,571 128,571 128,57

128,571 257,143 385,71

30,000 30,00 30,00 30,000 30,00 30,00 30,000

30,000 60,00 90,00 120,000 150,00 180,00 210,000 210,000 210,00



31/33

Latest Time Project Cost ScheduleID Task Name Fixed Cost Fixed Cost

Accrual

0 Reliable Construction 0 Prorated

1 Excavate 180,000 Prorated

2 Lay the foundation 320,000 Prorated

3 Put up the rough wall 620,000 Prorated

4 Put up the roof 260,000 Prorated

5 Install the exteriorplumbing

410,000 Prorated

6 Install the i nterior plumbing 180,000 Prorated

7 Put up the exter ior s id ing 900,000 Prorated

8 Do the ex te ri or pai nti ng 200, 000 Prorated

9 Do the electrical work 210,000 Prorated

10

Put up the wallboard 430,000 Prorated

11 Install the flooring 160,000 Prorated

12 Do the i nte ri or pai nti ng 250, 000 Prorated

13 Install the exterior f ixtures 100,000 Prorated

14 Install the interior f ixtures 330,000 Prorated

Details

CostCum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

CostCum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

CostCum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

Cost

Cum. Cost

25/04 02/05 09/05 16/05 23/05 30/05 06/06 13/06 20/06

May June

102,500 102,50 132,50 132,500 109,33 109,33 109,333 109,333 109,331,222,500 1,325,00 1,457,50 1,590,000 1,699,33 1,808,66 1,918,000 2,027,333 2,136,66

180,000 180,00 180,00 180,000 180,00 180,00 180,000 180,000 180,00

320,000 320,00 320,00 320,000 320,00 320,00 320,000 320,000 320,00

620,000 620,00 620,00 620,000 620,00 620,00 620,000 620,000 620,00

43,33 43,33 43,333 43,333 43,33

43,33 86,66 130,000 173,333 216,66

102,500 102,50 102,50 102,500102,500 205,00 307,50 410,000 410,00 410,00 410,000 410,000 410,00

36,00 36,00 36,000 36,000 36,00

36,00 72,00 108,000 144,000 180,00

30,00 30,000 30,00 30,00 30,000 30,000 30,00

30, 00 60, 000 90, 00 120, 00 150, 000 180, 000 210, 00



32/33

Cumulative Project

Costs

The top curve is the

schedule of cumulative

project costs when all

activities begin at their

earliest start times.

The bottom curve is theschedule of project costs

when all activities begin at

their latest start times.

The areas between the

two curves shows the onlyfeasible week by week

budgetthat will not delay

project completion. -

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

4,500,000

5,000,000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

ET project cost

schedule

LT project cost

schedule

Feasible region

for project costs



33/33

Budget and Cash Flow

Learning Points

How to schedule project costs;

Earliest and latest time project cost schedules, and

the feasible region for project costs;

Time-Cost trade-offs;

Which activities should be crashed?

Marginal cost analysis; Linear Programming to make crash decisions.


lecture 8. budget, cash flow, and uncertainty

Documents