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PROJECT MANAGEMENT Network Analysis : Pert & CPM : 

PROJECT MANAGEMENT Network Analysis : Pert & CPM Made by: Bhala Manush Edited & cut-copy-paste by: Dr. Naval Asija

Introduction : 

Introduction Network analysis is one of the important tools for project management. Whether major or minor a project has to be completed in a definite time & at a definite cost. The necessary information of any information can be represented as a project network.

History : 

History Developed in 1950’s CPM by DuPont for chemical plants PERT by U.S. Navy for Polaris missile PERT was developed by the US Navy for the planning and control of the Polaris missile program and the emphasis was on completing the program in the shortest possible time. In addition PERT had the ability to cope with uncertain activity completion times (e.g. for a particular activity the most likely completion time is 4 weeks but it could be anywhere between 3 weeks and 8 weeks). CPM was developed by Du Pont and the emphasis was on the trade-off between the cost of the project and its overall completion time (e.g. for certain activities it may be possible to decrease their completion times by spending more money - how does this affect the overall completion time of the project?)

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Originated by H.L.Gantt in 1918 Gantt chart Advantages - Gantt charts are quite commonly used. They provide an easy graphical representation of when activities (might) take place. Limitations Do not clearly indicate details regarding the progress of activities Do not give a clear indication of interrelation ship between the separate activities

Methodology Involved in Network Analysis : 

Methodology Involved in Network Analysis Describing the Project Diagramming the network Estimating the time of completion Deterministic estimates Probabilistic estimates Monitoring the project progress

Key terminology : 

Key terminology Activity : All projects may be viewed as composed of activities. It is the smallest unit of work consuming both time& resources that project manager should schedule & control. An activity is represented by an arrow in network diagram The head of the arrow shows sequence of activities.

Classification of activities : 

Classification of activities Predecessor activity: Activities that must be completed immediately prior to the start of another activity are called predecessor activities. Successor activity : activities that cannot be started until one or more of other activities are completed but immediately succeed them are called successor activities. Concurrent activities: activities that can be accomplished together are known as concurrent activities. Dummy activity: An activity which does not consume any resource but merely depicts the dependence of one activity on other is called dummy activity.

Event : 

Event The beginning & end of an activities are called as events . Events are represented by numbered circles called nodes. i j Event start Event finish

Path & Network : 

Path & Network An unbroken chain of activity arrows connecting the initial event to some other event is called a path. A network is the graphical representation of logically & sequentially connected arrows & nodes representing activities & events of a project . It is a diagram depicting precedence relationships between different activities.

Application of network analysis : 

Application of network analysis Construction industry Manufacturing Research development Administration Marketing planning Inventory planning

Advantages : 

Advantages Planning & controlling projects Flexibility Designation of responsibilities Achievement of objective with least cost Better managerial control

Questions Answered by CPM & PERT : 

Questions Answered by CPM & PERT Completion date? On Schedule? Within Budget? Critical Activities? How can the project be finished early at the least cost?

Types of Events : 

Types of Events Merge event Burst event Merge & Burst Event

Guidelines for Network Construction : 

Guidelines for Network Construction A complete network diagram should have one stand point & one finish point. The flow of the diagram should be from left to right. Arrows should not be crossed unless it is completely unavoidable. Arrows should be kept straight & curved or bent. Angle between arrows should as large as possible. Each activity must have a tail or head event.. No two or more activities may have same tail & head events. Once the diagram is complete the nodes should be numbered from left to right. It should then be possible to address each activity uniquely by its tail & head event.

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Example 1 3 2 5 4 6 A B C D E F G

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Draw the network diagram for the following

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1 2 3 4 5 6 A B C D E F

Basic Terminologies : 

Basic Terminologies Earliest start time ( EI) : This is the earliest possible time that an activity can begin. All predecessor activities must be finished before an activity can began. Earliest finish time ( EJ) : This is the earliest possible time in which an activity can be finished. = earliest start time ( EI ) + Duration of the activity ( TIJ) Latest start time ( LI) : This is the latest time that an activity can began & not delay the completion time of overall project. = latest finish time ( LJ) – duration of the activity ( TIJ) Latest finish time ( LJ) : This is the latest time that an activity can be finished & not delay the completion time of the overall project

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Total project time : This is the shortest possible time in which the project is completed. Float : There are many activities where the maximum time available to finish the activity is more than the time required to complete the activity. The difference between the two times is known as float available for the activity. There are three types of float: Total float : It is the spare time available when all preceding activities occur at earliest possible times & all success ding activities occur at latest possible times. Total float = Latest start – Earliest finish.

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1 2 5 3 4 6 16 30 15 12 20 15 16 10 3 Network Diagram

Earliest Event Time : 

Earliest Event Time The total project time is the shortest time in which the project can be completed & this is determined by sequence of activities on the critical path. In order to calculate the total project time carry out the forward pass. Start from the left of the arrow of diagram Give the first event the time 0 Proceed to each event in order & compute the earliest possible time at which event can occur.

Forward pass Method : 

Forward pass Method Based on the fixed occurrence time of the initial network event , the forward pass method yields the earliest start time & earliest finish times for each activity & indirectly earliest expected occurrence of each event. The computation begins from the start node & move to the end node. To accomplish this , the forward pass computations start with an assumed earliest occurrence time of zero for the initial project event E1 = 0 Earliest start time for activity ( I,j) is the earliest event time of the tail end event ESIJ = EI Earliest finish time of the activity is the earliest start time of the activity plus the duration of the activity. EFij = ES ij+ tij Earliest occurrence time of the event j is the maximum of the earliest finish times of all the activities into that event.

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1/ 0 2/16 5/38 3/20 4/35 6/51 16 30 15 12 20 15 16 10 3 Calculation of earliest event time 0+16 0+20+10 0+20+15+3 0+16+15 Taking the maximum one 0+20+15 0+ 30 38+ 12 35+16 To the earliest time of each immediately preceding event add the duration of activity which connects it & selects the highest of the values obtained. Forward pass 0+ 20

Latest event time : 

Latest event time Latest event time : carry out the backward pass Start from right Give to this event its earliest time i.e is 51 in this case By subtracting the duration time for each corresponding job calculate the latest possible occurrence time for any event , assuming that final event is fixed.

Backward Pass Method : 

Backward Pass Method The latest occurrence time specifies the time by which all the activities entering into that event , must be completed without delaying the total project. These are computed by reversing the method of calculation used for earliest event times. Latest finish time of an activity is equal to the latest vent time j LFIJ= L J. Latest start time of an activity is given by latest completion time minus the activity time . LSIJ = LFIJ - tij Latest event time for event is the minimum of the latest start time of all activities originating from that event.

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1/ 0/0 2/16/24 5/38/39 3/20/20 4/35/35 6/51/51 16 30 15 12 20 15 16 10 3 Calculation of latest event time 24-16 39-10 39-15 Taking the minimum one 35-15 51-30 51-12 51-16 From the latest time of each immediately succeeding event , subtract the duration of the job which connects it & selects the lowest value obtained. Backward pass 39-3 20-20

Critical path : 

Critical path Those activities which contribute directly to the overall duration of the project constitute critical activities, the critical activities form a chain running through the network which is called critical path. Critical event : the slack of an event is the difference between the latest & earliest events time. The events with zero slack time are called as critical events. Critical activities : The difference between latest start time & earliest start time of an activity will indicate amount of time by which the activity can be delayed without affecting the total project duration. The difference is usually called total float. Activities with 0 total float are called as critical activities

Critical path : 

Critical path The critical path is the longest path in the network from the starting event to ending event & defines the minimum time required to complete the project. The critical path is denoted by darker or double lines.

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1/ 0/0 2/16/24 5/38/39 3/20/20 4/35/35 6/51/51 16 30 15 12 20 15 16 10 3 Critical Path The critical path lies along those jobs whose earliest & latest times for the start & finish events are same & whose duration times are equal to the difference between start & finish events time. Darker line is critical path

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Earliest start time : (2, 5) – earliest time of event 2 – 16 days Earliest finish time : ( 2, 5) – earliest start time + duration of activity EI + TIJ = 16 + 15 = 31days Latest finish time : ( 2, 5) – latest event time of finish event 39 days Latest start time : ( 2, 5) latest finish time – duration of activity LJ - TIJ 39 – 15 = 24 days Calculation of time estimates

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Time estimations Darker boxes indicate critical activities


PERT PERT is designed for scheduling complex projects that involve many inter-related tasks. it improves planning process because: It forms planner to define the projects various components activities. It provides a basis for normal time estimates & yet allows for some measure of optimism or pessimism in estimating the completion dates. It shows the effects of changes to overall plan s they contemplated. It provides built in means for ongoing evaluation of the plan.

PERT system of 3 time estimates : 

PERT system of 3 time estimates Optimistic time ( a or t0 ) : is that time estimate of an activity when everything is assumed to go as per plan. In other words it is the estimate of minimum possible time which an activity takes in completion under ideal conditions. Most likely time (m or tm ) : the time which the activity will take most frequently if repeated number of times. Pessimistic time ( b or t) : the unlikely but possible performance time if whatever could go wrong , goes wrong in series. In other words it is the longest time the can take.

Expected time (te ) : 

Expected time (te ) The a , m & b are combined statically to develop the expected time te . te = a + 4m +b 6 Standard deviation of the time of the time required to complete the project b- a 6

Steps in PERT : 

Steps in PERT Develop list of activities. A rough network for PERT is drawn. Events are numbered from left to right. Time estimates for each activity are obtained. Expected time for each activity is calculated : a + 4m +b / 6 Using these expected times calculate earliest & latest finish & start times of activities. Estimate the critical path. Calculate variance of each activity by : ( b –a)2 / 6 Using this estimate compute the probability of meeting a specified completion date by using the standard normal equation Z = Due date – expected date of completion project variance Where Z = number of standard deviations the due date lies from the mean or expected date.

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Using the information given below determine the following Expected task time & their variance The earliest & the latest expected times to reach each event The critical path The probability of an event occurring at proposed completion date if the original contract time of completing project is 48 days.

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1/0/0 2/8/8 4/20/20 6/26/38 3/12/15 5/20/20 7/26/26 8/26/29 9/34/34 10/44/44 Network Diagram & critical path 8 12 4 5 0 6 6 8 5 6 6 10

Slide 40: 

Te = 8 + 12 +0 +6 +8 +10 = 44 days σ2 = 1.78 + 1.78 + 0 + 1 + 1.78 + 4 = 10.34 σe = 3.216 Probability that project will be completed in 48 days Z = T - Te σe = 48 - 44 3.216 = 1.24 ( from normal distribution table ) 0.895 Therefore 89% is the probability that project will be completed on its due date.

Difference between PERT & CPM : 

Difference between PERT & CPM PERT A probability model with uncertainty in activity duration . The duration of each activity is computed from multiple time estimates with a view to take into account time uncertainty. It is applied widely for planning & scheduling research projects. PERT analysis does not usually consider costs. CPM A deterministic model with well known activity times based upon the past experience. It is used for construction projects & business problems. CPM deals with cost of project schedules & minimization.

Limitations of PERT /CPM : 

Limitations of PERT /CPM Network diagrams should have clear starting & ending points , which are independent of each other which may not be possible in real life. Another limitation is that it assumes that manager should focus on critical activities. Resources will be available when needed for completion for an an activity is again unreal.

Difficulties : 

Difficulties Difficulty in securing realistic time estimates. The planning & implementation of networks requires trained staff. Developing clear logical network is troublesome.

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Packages are available to determine the shortest path and other relevant information.

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Data entry window

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Output of the package

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