Network Planning Methods Example PERT & CPM

Terms Used in Project Management Activity : A certain amount of work or task required in the project Activity duration: In CPM the best estimate of time to complete an activity . In PERT the expected time or average time to complete an activity Critical activity : An activity that has no room for schedule slippages : if it slips the entire the entire project completion will slip. An activity with zero slack

Critical path: The chain of critical activities for the project Critical path: The chain of critical activities for the project .The longest path through the network Dummy activity :An activity that consumes no time but shows precedence among activities Earliest finish (EF): The earliest that an activity can finish from the beginning of the project Earliest start ( ES): The earliest that an activity can start from the beginning of the project

Event :A beginning , a completion point ,or a milestone accomplishment within the project . An activity begins and ends with events Latest finish (LF) : The latest that an activity can finish from the beginning of the project Latest start (LS) :The latest that an activity can start from the beginning of the project Most likely time ( t m) : The time for completing the activity that is is the consensus best estimate, used in PERT

Optimistic Time (to): The time for completing an activity if all goes well : used in PERT Pessimistic Time (tp): The time for completing an activity if bad luck is encountered : used in PERT Predecessor activity : An activity that must occur before another activity . Slack : The amount of time that an activity or group of activities can slip without causing a delay in the completion of the project Successor activity : An activity that must occur after another activity

Conventions used in drawing network diagrams (Arrows & Circles ) Activity on Arrow (AOA) : The activities are denoted by Arrows and events are denoted by circles Activity on Node(AON) : Activities are denoted by circles(or nodes) and the precedence relation ships between activities are indicated by arrows

AOA Project Network for House 3 2 1 4 6 7 5 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house AON Project Network for House 1 3 2 4 5 6 7 Start Design house and obtain financing Order and receive materials Select paint Select carpet Lay foundations Build house Finish work

Situations in network diagram B C A must finish before either B or C can start A B C both A and B must finish before C can start D C B A both A and C must finish before either of B or D can start A C B D Dummy A must finish before B can start both A and C must finish before D can start

Backward Pass Forward Pass EF= ES + t Latest Start Time (LS) Earliest Start Time (ES) earliest time an activity can start ES = maximum EF of immediate predecessors Earliest finish time (EF) earliest time an activity can finish earliest start time plus activity time EF= ES + t Backward Pass Latest Start Time (LS) Latest time an activity can start without delaying critical path time LS= LF - t Latest finish time (LF) latest time an activity can be completed without delaying critical path time LS = minimum LS of immediate predecessors

CPM analysis Draw the CPM network Analyze the paths through the network Determine the float for each activity Compute the activity’s float float = LS - ES = LF - EF Float is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project Find the critical path is that the sequence of activities and events where there is no “slack” i.e.. Zero slack Longest path through a network Find the project duration is minimum project completion time

PERT / CPM Network planning methods that generate: Relationship between activities Project duration Critical path Slack for non – critical activities Crashing (cost / time trade-offs) Resource usage

St. Paul’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. B Select site and do site survey. C Select equipment. D Prepare final construction plans and layout. E Bring utilities to the site. F Interview applicants and fill positions in nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. H Construct the hospital. I Develop an information system. J Install the equipment. K Train nurses and support staff. — A B C D E,G,H F,I,J

St. Paul’s Hospital Immediate Activity Description Predecessor(s) AON Network Finish Start A B C D E F G H I J K A Select administrative and medical staff. B Select site and do site survey. C Select equipment. D Prepare final construction plans and layout. E Bring utilities to the site. F Interview applicants and fill positions in nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. H Construct the hospital. I Develop an information system. J Install the equipment. K Train nurses and support staff. — A B C D E,G,H F,I,J

St. Paul’s Hospital Completion Time Immediate Finish Start K 9 I 15 F 10 C D E 24 G 35 H 40 J 4 A 12 B Immediate Activity Description Predecessor(s) A Select administrative and medical staff. B Select site and do site survey. C Select equipment. D Prepare final construction plans and layout. E Bring utilities to the site. F Interview applicants and fill positions in nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. H Construct the hospital. I Develop an information system. J Install the equipment. K Train nurses and support staff. — A B C D E,G,H F,I,J

St. Paul’s Hospital Path Expected Time (wks) A-I-K 36 A-F-K 31 A-C-G-J-K 70 B-D-H-J-K 72 B-E-J-K 46 St. Paul’s Hospital Critical Path Completion Time Finish Start K 9 I 15 F 10 C D E 24 G 35 H 40 J 4 A 12 B Immediate Activity Description Predecessor(s) A Select administrative and medical staff. B Select site and do site survey. C Select equipment. D Prepare final construction plans and layout. E Bring utilities to the site. F Interview applicants and fill positions in nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. H Construct the hospital. I Develop an information system. J Install the equipment. K Train nurses and support staff. — A B C D E,G,H F,I,J

Critical Path The longest path in the network Defines the shortest time project can be completed Critical path activity delay project delay

Earliest Start and Earliest Finish Begin at starting event and work forward ES is earliest start ES = 0 for starting activities ES = Maximum EF of all predecessors for non-starting activities EF is earliest finish EF = ES + Activity time ES LS EF LF Activity Name Activity Duration

Earliest Start / Earliest Finish 15 A 12 F 10 K 9 C 10 G 35 Start Finish B 9 D 10 H 40 J 4 E 24

Earliest Start / Earliest Finish 15 12 27 Earliest finish time Earliest start time A 12 F 10 K 9 0 12 12 22 63 72 C 10 G 35 12 22 22 57 Start Finish Critical path B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 E 24 9 33

Latest Start and Latest Finish Begin at ending event and work backward LF is latest finish LF = Maximum EF for ending activities LF = Minimum LS of all successors for non-ending activities LS is latest start LS = LF – Activity time Activity Name ES EF LS LF Activity Duration

Latest Start / Latest Finish 15 12 27 Latest start time 48 63 Latest finish time A 12 F 10 K 9 0 12 12 22 63 72 2 14 53 63 63 72 C 10 G 35 12 22 22 57 Start Finish Critical path 14 24 24 59 B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 What do you notice about ES/LS & EF/LF? E 24 9 33 35 59

What do you notice about ES/LS & EF/LF? For Activity A ES = 0 LS = 2 Meaning: Due to some reason of if activity A is not started at 0 weeks but 1, 2 or 3 weeks, even then completion of project is not delayed For Activity B LS = 0 Meaning Any delay in start would delay project completion.

Activity Slack Analysis 15 12 27 Slack = LS – ES or Slack = LF – EF Latest start time 48 63 Latest finish time A 12 F 10 K 9 0 12 12 22 63 72 2 14 53 63 63 72 C 10 G 35 12 22 22 57 SlackK = 63 – 63 = 0 or SlackK = 72 – 72 = 0 Start Finish Critical path 14 24 24 59 B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 E 24 9 33 35 59

Activity Slack Analysis 15 12 27 Node Duration ES LS Slack A 12 0 2 2 B 9 0 0 0 C 10 12 14 2 D 10 9 9 0 E 24 9 35 26 F 10 12 53 41 G 35 22 24 2 H 40 19 19 0 I 15 12 48 36 J 4 59 59 0 K 6 63 63 0 Latest start time 48 63 Latest finish time A 12 F 10 K 9 0 12 12 22 63 72 2 14 53 63 63 72 C 10 G 35 12 22 22 57 Start Finish Critical path 14 24 24 59 B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 Activity slack = maximum delay time Critical path activities have zero slack E 24 9 33 35 59

Activity Slack How much would we like to reduce the time for activity B? C 15 5 20 10 25 A 5 0 5 Finish Start B 20 5 25 D 10 25 35

PERT tp + 4 tm + to tp - to 6 Mean (expected time): te = PERT is based on the assumption that an activity’s duration follows a probability distribution instead of being a single value Three time estimates are required to compute the parameters of an activity’s duration distribution: pessimistic time (tp ) - the time the activity would take if things did not go well most likely time (tm ) - the consensus best estimate of the activity’s duration optimistic time (to ) - the time the activity would take if things did go well Mean (expected time): te = tp + 4 tm + to 6 Variance: Vt =2 = tp - to 2

PERT analysis Draw the network. Analyze the paths through the network and find the critical path. The length of the critical path is the mean of the project duration probability distribution which is assumed to be normal The standard deviation of the project duration probability distribution is computed by adding the variances of the critical activities (all of the activities that make up the critical path) and taking the square root of that sum Probability computations can now be made using the normal distribution table.

Probability computation Determine probability that project is completed within specified time Z = x -   where  = tp = project mean time  = project standard mean time x = (proposed ) specified time

Normal Distribution of Project Time  = tp Time x Z Probability

PERT Example Immed. Optimistic Most Likely Pessimistic Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A -- 4 6 8 B -- 1 4.5 5 C A 3 3 3 D A 4 5 6 E A 0.5 1 1.5 F B,C 3 4 5 G B,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7

PERT Example PERT Network D A E H J C B I K F G

Activity Expected Time Variance PERT Example Activity Expected Time Variance A 6 4/9 B 4 4/9 C 3 0 D 5 1/9 E 1 1/36 F 4 1/9 G 2 4/9 H 6 1/9 I 5 1 J 3 1/9 K 5 4/9

PERT Example Activity ES EF LS LF Slack A 0 6 0 6 0 *critical B 0 4 5 9 5 C 6 9 6 9 0 * D 6 11 15 20 9 E 6 7 12 13 6 F 9 13 9 13 0 * G 9 11 16 18 7 H 13 19 14 20 1 I 13 18 13 18 0 * J 19 22 20 23 1 K 18 23 18 23 0 *

PERT Example Vpath = VA + VC + VF + VI + VK = 4/9 + 0 + 1/9 + 1 + 4/9 = 2 path = 1.414 z = (24 - 23)/(24-23)/1.414 = .71 From the Standard Normal Distribution table: P(z < .71) = .5 + .2612 = .7612

PROJECT COST

Cost consideration in project Project managers may have the option or requirement to crash the project, or accelerate the completion of the project. This is accomplished by reducing the length of the critical path(s). The length of the critical path is reduced by reducing the duration of the activities on the critical path. If each activity requires the expenditure of an amount of money to reduce its duration by one unit of time, then the project manager selects the least cost critical activity, reduces it by one time unit, and traces that change through the remainder of the network. When there is more than one critical path, each of the critical paths must be reduced. If the length of the project needs to be reduced further, the process is repeated.

Project Crashing Crashing reducing project time by expending additional resources Reduction in activity duration by any change in its resources, resource use, method or material is referred to as crashing of the activity Crash time an amount of time an activity is reduced Crash cost cost of reducing activity time Goal reduce project duration at minimum cost

Activity crashing Crash cost Crashing activity Activity cost Activity time Crashing activity Crash time Crash cost Slope = crash cost per unit time Normal Activity Normal time Normal cost

Time-Cost Relationship Crashing costs increase as project duration decreases Indirect costs increase as project duration increases Reduce project length as long as crashing costs are less than indirect costs Time-Cost Tradeoff cost time Min total cost = optimal project time Direct cost Total project cost Indirect cost

Project Crashing example 1 12 2 8 4 3 5 6 7

Time Cost data Activity Normal time Normal cost Rs Crash time Crash cost Rs Allowable crash time slope 1 2 3 4 5 6 7 12 8 3000 2000 4000 50000 500 1500 9 2800 3500 6000 71000 1100 21000 400 700 8000 7000 75000

Project duration = 36 From….. To….. Project duration = 31 12 2 8 3 4 5 6 7 Project duration = 36 From….. 1 7 2 8 3 4 5 6 R400 12 Project duration = 31 Additional cost = R2000 To…..

GANTT CHART

Gantt Chart Gantt Chart was developed by… Henry Laurence Gantt (1861-1919) was a mechanical engineer and management consultant who is most famous for developing the ‘Gantt chart’ in the 1910s. These Gantt charts were employed on major infrastructure projects including the Hoover Dam and Interstate highway system. He refined production control and cost control techniques.

Example of Gantt Chart Month 0 2 4 6 8 10 | | | | | 1 3 5 7 9 Activity | | | | | Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work 0 2 4 6 8 10 Month 1 3 5 7 9

Gantt Chart Activities in Buy a House