Project Scheduling

Project SchedulingManajemen Sains Lanjut

Gantt Chart

Gantt Chart• Gantt Charts merupakan tool yang digunakan

untuk memonitor progress dari project yang dikerjakan.

• Gantt Chart menampilkan informasi antara lain:– Waktu (horizontal axis)– Aktivitas (vertical axis).

4

Immediate EstimatedActivity Predecessor Completion Time

A None 90B A 15C B 5D G 20E D 21F A 25G C,F 14H D 28I A 30J D,I 45

A90

90

B15

F25

I30

105

C5

115

G14

129

D20

149

E21

H28

J

45

194

194

5

A90

B15

F25

I30

C5

G14

D20

E21

H28

J

45

194

194

135

The shaded bars representcompleted work BY DAY 135.

Do not conclude that the project is behind schedule.

Activity “I” has a slack and therefore can be delayed!!!

6

Gantt Charts – Advantages and Disadvantages• Advantages.

– Easy to construct– Gives earliest completion date.– Provides a schedule of earliest possible start and finish times of

activities.

• Disadvantages– Gives only one possible schedule (earliest).– Does not show whether the project is behind schedule.– Does not demonstrate the effects of delays in any one activity on

the start of another activity, thus on the project completion time.

The Probability Approach to Project Scheduling

8

The Probability Approach to Project Scheduling• Activity completion times are seldom known with

100% accuracy.

• PERT is a technique that treats activity completion times as random variables.

• Completion time estimates are obtained by theThree Time Estimate approach

9

The Probability Approach – Three Time Estimates• The Three Time Estimate approach provides

completion time estimate for each activity.

a = an optimistic time to perform the activity.m = the most likely time to perform the

activity.b = a pessimistic time to perform the

activity.

10

The Distribution, Mean, and Standard Deviation of an Activity

= the mean completion time =a + 4m + b

6= the standard deviation =

b - a6

11

The Project Completion Time Distribution - Assumptions• Assumption 1

– A critical path can be determined by using the mean completion times for the activities.

– The project mean completion time is determined solely by the completion time of the activities on the critical path.

• Assumption 2– The time to complete one activity is independent of the time to

complete any other activity.

• Assumption 3– There are enough activities on the critical path so that the

distribution of the overall project completion time can be approximated by the normal distribution.

12

The Project Completion Time Distribution

The three assumptions imply that the overall project completion time is normally distributed, the following parameters:

Mean = Sum of mean completion times along the critical path.

Variance = Sum of completion time variance along the critical path.

Standard deviation = ÖVariance

13

The Probability Approach – KLONE COMPUTERS

Activity Optimistic Most Likely PessimisticA 76 86 120B 12 15 18C 4 5 6D 15 18 33E 18 21 24F 16 26 30G 10 13 22H 24 18 32I 22 27 50J 38 43 60

14

• Management at KLONE is interested in information regarding the completion time of the project.

• The probabilistic nature of the completion time must be considered.

The Probability Approach – KLONE COMPUTERS

15

A = [76+4(86)+120]/6 = 90A = (120 - 76)/6 = 7.33A

2 = (7.33)2 = 53.78

Activity A 90 7.33 53.78B 15 1.00 1.00C 5 0.33 0.11D 20 3.00 9.00E 21 1.00 1.00F 25 2.33 5.44G 14 2.00 4.00H 28 1.33 1.78I 30 4.67 21.78J 45 3.67 13.44

2

Finding mean and variance for the critical path – KLONE COMPUTERS

16

Finding mean and variance for the critical path – KLONE COMPUTERS

• Hasil perhitungan mean = Hasil dari CPM yang telah dikerjakan sebelumnya

• Critical path = A - F- G - D – J.

– Expected completion time = A +F +G +D +J=194.

– The project variance =A2 +F

2 +G2 +D

2 +J2 = 85.66

– The standard deviation = = 9.255 2

17

The Probability Approach – Probabilistic analysis• The probability of completion in 194 days =

5.0)0()9.255194-194P(Z=194)P(X ZP

194

18

The Probability Approach – Probabilistic analysis• The probability of completion in 180 days =

P(X < 180) = P(Z < -1.51) = 0.5 - 0.4345 = 0.0655

XZ

1940

180-1.51

0.0655

19

The Probability Approach – Probabilistic analysis• The probability that the completion time is longer

than 210 days =

0.0418=0.458-0.5=1.73)P(Z=210)P(X

XZ

1940

.4582

2101.73

?0.0418

20

The Probability Approach – Probabilistic analysis• Provide a completion time that has only 1%

chance to be exceeded.

XZ

1940

X0

2.33

0.01.49

P(XX0) = 0.01, or P(Z [(X0 – )/] = P(ZZ0) = .01P(Z 2.33) = 0.01; X0=+Z0 =194 + 2.33(9.255) = 215.56 days.

There is 99% chance that the projectis completed in 215.56 days.

21

The Probability Approach – Probabilistic analysis with a spreadsheet

NORMDIST(194, 194, 9.255, TRUE)

NORMINV(.025, 194, 9.255)NORMINV(.975, 194, 9.255)

NORMDIST(180, 194, 9.255, TRUE)

1 - NORMDIST(210, 194, 9.255, TRUE)

NORMINV(.99, 194, 9.255)

22

The Probability Approach – Critical path spreadsheet

MEAN 194STANDARD DEVIATION* 9.255629 * Assumes all critical activities are on one critical path

VARIANCE* 85.66667 If not, enter in gold box, the variance on one critical path of interest.

PROBABILITY COMPLETE BEFORE 180 = 0.065192

Acitivty Node Critical 2 ES EF LS LF SlackDesign A * 90 7.333333 53.77778 0 90 0 90 0Materials B 15 1 1 90 105 95 110 5Manufacture C 5 0.333333 0.111111 105 110 110 115 5Design Revision D * 20 3 9 129 149 129 149 0Production Run E 21 1 1 149 170 173 194 24Staff Training F * 25 2.333333 5.444444 90 115 90 115 0Staff Input G * 14 2 4 115 129 115 129 0Sales Training H 28 1.333333 1.777778 149 177 166 194 17Preprod. Advertise I 30 4.666667 21.77778 90 120 119 149 29Post. Advertise J * 45 3.666667 13.44444 149 194 149 194 0

CRITICAL PATH ANALYSIS

Cost Analysis Using the Expected Value Approach

24

Cost Analysis Using the Expected Value Approach• Menambahkan dana lebih dalam sebuah proyek

akan mempercepat proses pengerjaan proyek• Apakah operation cost digunakan secara efektif?• Pertanyaan itu akan kita jawab segera

25

KLONE COMPUTERS - Cost analysis using probabilities • Analysis indicated:

– Waktu penyelesaian dalam waktu 180 hari menghasilkan keuntungan tambahan sebesar $ 1 juta.

– Waktu penyelesaian antara 180 hari hingga 200 hari akan menghasilkan keuntungan $400.000

– Selebihnya akan dicapai dengan pelatihan tambahan

26

KLONE COMPUTERS - Cost analysis using probabilities

• 2 kemungkinan aktivitas yang berhubungan dengan pelatihan– Sales personnel training

• Cost = $200.000• Estimasi waktu yang baru yaitu a=19 , m=21, b= 23 hari

– Technical staff training• Cost $250.000• Estimasi waktu yang baru yaitu a=12, m=14, dan b=16

Which option should be pursued?

27

KLONE COMPUTERS - Cost analysis using probabilities• Evaluasi Jika membiayai sales personnel training

– Aktivitas (H) tidak critical– Berdasarkan asumsi bahwa waktu penyelesaian proyek adalah

ditentukan semata-mata oleh kegiatan kritis, pilihan ini tidak harus dipertimbangkan lebih lanjut.

• Evaluasi jika membiayai technical staff training– Aktivitas (F) termasuk critical– Pilihan yang akan dilakukan

• Menghitung ekpektasi keuntungan ketika TIDAK mebiayai sebesar $250.000

• Menghitung ekpektasi keuntungan ketika mebiayai sebesar $250.000• Memilih keputusan yang menawarkan keuntungan yang besar

28


– Case 1 : tidak membiayai sebesar $250.000 di pelatihan• X = waktu penyelesaian project• Keuntungan kotor yang diharapkan = E(GP)=P(X<180)($1 million) + P(180<X<200)($400,000) + P(X>200)(0).• Probabilities nya yaituP(X<180) = .065192; P(180<X<200) = .676398; P(X>200) =.25841• Keuntungan kotor yang didapatkan = .065192(1M)

+.676398(400K)+ .25841(0) = $335,751.20

29


– Case 2: membiayai sebesar $250.000 untuk trainingF= (12 + 4 (14) + 16)/6 = 14F= (16 -12)/6 =0.67F

2= 0(.67)2 =0.44

– Dengan menggunakan excel PERT-CPM template kita bisa menemukan critical path baru yaitu A-B-C-G-D-J dengan mean time = 189 days dan standard deviasi sebesar = 9.0185 hari

30


– Kembali menghitung probabilities of interestnya yaitu • P(X < 180) = .159152; • P(180 < X < 200) = .729561• P(X > 200) = .111287

• Sehingga ditemukan keuntungan kotornya yaitu P( X<180)(1M)+ P(180<X<200)(400K)+P(X>200)(0) = .159152(!M)+ .729561(400K)+ .111287(0) = $450,976.40

31


The expected net additional profit =

450,976-250,000 = $200,976 < $335,751

Expected additional net profit whenspending $250,000 on training

Expected profit withoutspending $250,000 on training

Conclusion: Jadi perusahaan tidak perlu menambahkan $250.000 untuk membiayai training

Cost Analyses Using The Critical Path Method

33

Cost Analyses Using The Critical Path Method• The critical path method (CPM) is a deterministic

approach to project planning.

• Completion time depends only on the amount of money allocated to activities.

• Reducing an activity’s completion time is called “crashing.”

34

Crash time/Crash cost• There are two crucial completion times to

consider for each activity.– Normal completion time (TN).– Crash completion time (TC), the minimum possible

completion time.

• The cost spent on an activity varies between– Normal cost (CN). The activity is completed in TN. – Crash cost (CC). The activity is completed in TC.

35

Crash time/Crash cost – The Linearity Assumption• The maximum crashing of activity completion

time is TC – TN.• This can be achieved when spending CN – CC.• Any percentage of the maximum extra cost

(CN – CC) spent to crash an activity, yields the same percentage reduction of the maximum time savings (TC – TN).

36

A demonstration of the Linearity AssumptionTime

Cost ($100)

2018161412108642

5 10 15 20 25 30 35 40 45

NormalCN = $2000TN = 20 days

Add to the normal cost...

…and save oncompletion time

Add more to the normal cost...

CrashingCC = $4400TC = 12 days

…and save more on completion time

Add 25% of the extra cost...

… to save 25% of the max. time reduction

Total Cost = $2600Job time = 18 days

37

Crash time/ Crash cost -The Linearity Assumption

Marginal Cost =Additional Cost to get Max. Time Reduction Maximum Time reduction= (4400 - 2000)/(20 - 12) = $300 per day

M = E R

38

Crashing activities – Meeting a Deadline at Minimum Cost• If the deadline to complete a project cannot be

met using normal times, additional resources must be spent on crashing activities.

• The objective is to meet the deadline at minimal additional cost.

39

Baja Burrito Restaurants – Meeting a Deadline at Minimum Cost• Baja Burrito (BB) is a chain of Mexican-style fast

food restaurants.• It is planning to open a new restaurant in 19

weeks.• Management wants to

– Study the feasibility of this plan,– Study suggestions in case the plan cannot be finished

by the deadline.

40

Baja Burrito Restaurants –

Without spending any extra money, the restaurant will open in 29 weeks at a normal cost of $200,000.

When all the activities are crashedto the maximum, the restaurantwill open in 17 weeks at crash costof $300,000.

Determined by the PERT.xls template

41

Baja Burrito Restaurants –Network presentation

A

D

C

B

E

F G

I

H

L

O

J NM

K

P

42

Baja Burrito Restaurants –Marginal costs

R = TN – TC = 5 – 3 = 2E = CC – CN = 36 – 25 = 11M = E/R = 11/2 = 5.5

43

Baja Burrito Restaurants –Linear Programming• Linear Programming Approach

– VariablesXj = start time for activity j.Yj = the amount of crash in activity j.

– Objective FunctionMinimize the total additional funds spent on crashing activities.

– Constraints• No activity can be reduced more than its Max. time reduction.• Start time of an activity takes place not before the finish time of

all its immediate predecessors. • The project must be completed by the deadline date D.

44

Baja Burrito Restaurants –Linear Programming

Min 5.5YA+10YB+2.67YC+4YD+2.8YE+6YF+6.67YG+10YH+5.33YI+12YJ+4YK+5.33YL+1.5YN+4YO+5.33YP

Minimize total crashing costs

45

Linear ProgrammingMin 5.5YA+10YB+2.67YC+4YD+2.8YE+6YF+6.67YG+10YH+

5.33YI+12YJ+4YK+5.33YL+1.5YN+4YO+5.33YP

Maximum time-reductionconstraints

H

F

E

D

C

B

A0.52.0

0.5

0.5

2.51.0

1.5

Y

YYYYYY

Y G 1.5

……..

19FINX )(

ST

Meet the deadline

46

Linear Programming

XA


Activity canstart only after all the Predecessors are completed.84

A

D

C

B

E

F G

I

H


L

O

J NM

K

P

XBXA+(5 – YA)

BXB

A

-YA

XA+5-YA

AXA+5

BXB

BXB

BXB

BXB

47

Linear Programming

84

A

D

C

B

E

F G

I

H


L

O

J NM

K

P

XBXA+(5 – YA)XCXA+(5 – YA)XDXA+(5 – YA)XeXA+(5 – YA)XFXA+(5 – YA)XBXB+(1 – YB)XFXC+(3 – YC)XGXF+(1 – YF)

X(FIN)XN+(3 – YN)X(FIN)XO+(4 – YO)X(FIN)XP+(4 – YP)


Activity canstart only afterall the predecessorsare completed.

……..

48

Baja Burrito Restaurants –Deadline Spreadsheet

TOTAL PROJECT COST 248.75 PROJECT NORMAL COST 200COMPLETION TIME 19 PROJECT CRASH COST 300

ACTIVITY NODECompletion

TimeStart Time

Finish Time

Amount Crashed

Cost of Crashing Total Cost

Revisions/Approvals A 3 0 3 2 11 36Grade Land B 1 3 4 0 0 10Purchase Materials C 1.5 3 4.5 1.5 4 22Order Equipment D 2 3 5 0 0 8Order Furniture E 4 12.5 16.5 0 0 8Concrete Floor F 0.5 4.5 5 0.5 3 15Erect Frame G 4 5 9 0 7.87637E-11 20Install Electrical H 2 9 11 0 0 12Install Plumbing I 2.5 9 11.5 1.5 8 21Install Drywall/Roof J 2 11.5 13.5 0 0 10Bathrooms K 2 13 15 0 0 8Install Equipment L 1.5 13.5 15 1.5 8 22Finish/Paint Inside M 1.5 15 16.5 1.5 8 18Tile Floors N 2.5 16.5 19 0.5 0.75 6.75Install Furniture O 2.5 16.5 19 1.5 6 14Finish/Paint Outside P 4 13.5 17.5 0 0 18

CRASHING ANALYSIS

49

Baja Burrito Restaurants –Operating within a fixed budget• Baja Burrito has the policy of not funding more

than 12.5% above the “normal cost” projection.

Crash budget = (12.5%)(200,000) = 25,000

• Management wants to minimize the project completion time under the budget constraint.

50

Baja Burrito Restaurants –Operating within a fixed budget

5.5YA + 10YB + 2.67YC + 4YD + 2.8YE + 6YF + 6.67YG + 10YH

+ 5.33YI + 12YJ + 4YK + 5.33Y L+ 1.5YN + 4YO + 5.33YP

25

The crash funds become a constraint Minimize

5.5YA + 10YB + 2.67YC + 4YD + 2.8YE + 6YF + 6.67YG + 10YH + 5.33YI + 12YJ + 4YK + 5.33Y L+ 1.5YN + 4YO + 5.33YPThe completion time becomes the objective function

X(FIN) 19

Minimize X(FIN)

The other constraints of the crashing model remain the same.

51

Baja Burrito Restaurants –Budget Spreadsheet

TOTAL PROJECT COST 225 PROJECT NORMAL COST 200COMPLETION TIME 23.3125 PROJECT CRASH COST 300

ACTIVITY NODECompletion

TimeStart Time

Finish Time

Amount Crashed

Cost of Crashing

Total Cost

Revisions/Approvals A 5 0 5 0 0 25Grade Land B 1 5 6 0 0 10Purchase Materials C 1.5 5 6.5 1.5 4 22Order Equipment D 2 5 7 0 0 8Order Furniture E 4 16.3125 20.3125 0 0 8Concrete Floor F 1 6.5 7.5 0 0 12Erect Frame G 4 7.5 11.5 0 0 20Install Electrical H 2 12 14 0 0 12Install Plumbing I 2.5 11.5 14 1.5 8 21Install Drywall/Roof J 2 14 16 0 0 10Bathrooms K 2 14 16 0 0 8Install Equipment L 1.5 16 17.5 1.5 8 22Finish/Paint Inside M 2.8125 17.5 20.3125 0.1875 1 11Tile Floors N 3 20.3125 23.3125 0 0 6Install Furniture O 3 20.3125 23.3125 1 4 12Finish/Paint Outside P 4 19.3125 23.3125 0 0 18

CRASHING ANALYSIS

PERT/COST

53

PERT/COST• PERT/Cost membantu manajemen mengukur

kemajuan terhadap jadwal waktu dan perkiraan biaya

• PERT/Cost didasarkan pada analisa segmentasi proses. Setiap segmen merupakan kumpulan dari paket pekerjaan PROJECT

Work Package 1Activity 1Activity 2



54

Work Package - Assumptions

• Begitu dimulai, paket pekerjaan dilakukan secara terus menerus sampai selesai

• Biaya yang berkaitan dengan paket pekerjaan yang tersebar merata di seluruh durasinya

55

Monitoring Project progress• Menentukan setiap paket pekerjaan :

– Work Package Forecasted Weekly cost =budgeted total cost for work package

expected completion time for work package (weeks)– Value of Work to date = p(budget for the work

package)• dimana p merupakan persentase estimasi paket pekerjaan

comleted.– Expected remaining completion time =

(1-p)(original expected completion time)

56

Monitoring Project progress• Analisas Waktu Penyelesaian

– Menggunakan perkiraan sisa waktu penyelesaian yang diharapkan, untuk merevisi waktu penyelesaian proyek.

• Analisa Pembengkakan Biaya / Kelebihan– Untuk menghitung setiap paket pekerjaan (selesai atau

sedang berlangsung)Cost overrun = [Actual Expenditures to Date] – [Value of Work to Date]

57

Monitoring Project Progress – Corrective Actions• Sebuah proyek dapat dikatakan melebihi jadwal,

atau mengalami pembengkakan biaya• Penyebabnya seperti :

– Kekeliruan terhadap waktu penyelesaian proyek dan perkiraan biaya

– Kekeliruan perkiraan penyelesaian paket pekerjaan dan perkiraan biaya

– Permasalahan yang terjadi pada departemen atau penundaan yang terjadi pada kontraktor

58

Monitoring Project Progress – Corrective Actions• Kemungkinan tindakan korektif yang harus

diambil ketika diperlukan :– Berfokus pada kegiatan yang belum selesai– Menentukan tindakan lain yangg akan digunakan – Dalam kasus biaya underrun, menyalurkan lebih banyak

sumner daya untuk kegiayan yang bermasalah– Mengurangi alokasi sumber daya untuk kegiayan non-

kritis

59

TOM LARKIN’s MAYORAL CAMPAIGN• Tom Larkin akan mencalonkan diri sebagai

walikota• 20 minggu sebelum pemilu berlangsung, sisa

kegiatan kampanye perlu dinilai.• Jika kampanye yang dilakukan tidak tepat sasaran

atau tidak sesuai dengan anggaran, maka diperlukan rekomendsi untuk tidakan perbaikan.

60

MAYORAL CAMPAIGN – Status Report

Work packages to focus on

Work Package Expenditures ($) StatusA Hire campaign staff 2,600 FinishB Prepare position paper 5,000 FinishC Recruit volunteers 3,000 FinishD Raise funds 5,000 FinishE File candidacy papers 700 FinishF Prepare campaign material 5,600 40% completeG Locate/staff headquarter 700 FinishH Run personal campaign 2,000 25% completeI Run media campaign 0 0% complete

61

MAYORAL CAMPAIGN – Completion Time Analysis

– The remaining network at the end of week 20.

I9

Finish

F7.8

H15

(1-p)(original expected completion time)=(1-0.25)(20)=15

20+15=35

20+7.8=27.8

27.8+9=36.8 .8

The remaining activities are expected to take 0.8 weeks longer than the deadline of 36 weeks.

62

MAYORAL CAMPAIGN –Project Cost Control

Budgeted ValuesWork Total Total Percent EstimatedActual CostPackage Time Cost Completed Value Value OcerrunA 4 2000 100% 2,000 2,600 600B 6 3,000 100% 3,000 5,000 2000C 4 4,500 100% 4,500 3,000 -1500D 6 2,500 100% 2,500 5,000 2,500E 2 500 100% 500 700 200F 13 13,000 40% 5200 5,600 400G 1 1,500 100% 1,500 700 -800H 20 6,000 25% 1,500 2,000 -500I 9 7,000 0% 0 0 0

Total 40,000 20,700 24,600 3,900

Estimated work value to date=(13,000)(0.40)=$5,200

Cost overrun = 5600 - 5200 = 400

63

MAYORAL CAMPAIGN –Results Summary• Proyek saat ini memiliki 8 minggu melebihi jadwal yang

ditentukan • Ada pembengkakan biaya sebesar $ 3.900• Waktu penyelesaian yang tersisa untuk paket pekerjaan yang

belum selesai adalah :– Paket pekerjaan F minggu 7,8– Paket pekerjaan H minggu 15– Paket pekerjaan I minggu 9

• Pembengkakan biaya terjadi pada :– Paket pekerjaan F $ 400– Paket pekerjaan H $ 500

Resource Leveling and Resource Allocation

Resource Leveling and Resource Allocation• It is desired that resources are evenly spread out

throughout the life of the project.

• Resource leveling methods (usually heuristics) are designed to: – Control resource requirements– Generate relatively similar usage of resources over

time.

Resource Leveling – A Heuristic• A heuristic approach to “level” expenditures

– Assumptions• Once an activity has started it is worked on continuously until it

is completed.• Costs can be allocated equally throughout an activity duration.

• Step 1: Consider the schedule that begins each activity at its ES.• Step 2: Determine which activity has slack at periods of peak

spending.• Step 3: Attempt to reschedule the non-critical activities performed

during these peak periods to periods of less spending, but within the time period between their ES and LF.

Resource Leveling –KLONE COMPUTERS, Inc. - continued• Management wishes to schedule the project such

that – Completion time is 194 days.– Daily expenditures are kept as constant as possible.

• To perform this analysis cost estimates for each activity will be needed.

67

68

Total Total CostCost Time per

Activity Description (x10000) (days) DayA Prototype model design 2250 90 25B Purchase of materials 180 15 12C Manufacture of prototype 90 5 18D Revision of design 300 20 15E Initial production run 231 21 11F Staff training 250 25 10G Staff input on prototype 70 14 5H Sales traini ng 392 28 14I Pre-production advertisement 510 30 17J Post-production advertisement 1350 45 30

Total cost = 5,623

Resource Leveling –KLONE COMPUTERS, Inc. – cost estimates

69

Cumulative Daily Expenditure –

Earliest Times vs. Latest Times55

50

45

40

35

30

25

201510 5

20 40 60 80 100 120 140 160 180 200

Level Budget

Earliest Start-Earliest FinishBudget

Latest Start-Latest FinishBudget

FeasibleBudgets

Time

70

55

50

45

40

35

30

25

201510 5

20 40 60 80 100 120 140 160 180 200

E

H

JJ

Cost Leveling

E

J

E

J

H

J

H

C

F A

B

F

I

I

H

27

15

44

30

Daily Expenditure of the ES Schedule55

I I I I I

25I

I39

45I

ES = 90I

LS = 110

22

32

I

I

I

F

G

D

71

G

55

50

45

40

35

30

25

201510 5

20 40 60 80 100 120 140 160 180 200

E

H

JJ

IE

J

E

J

H

JC

F A

B

F

I

I

H

25 27

22

15

44

3032

55

H

H

Cost Leveling

ID

I

F

Project Scheduling

Documents

Transcript of Project Scheduling