Project management

Project is a temporary ,complex and connected activities having a single goal or purpose that must be completed with in the time and cost and according to the specification

Project management is the process of application of skills , knowledge ,tools that must be used to complete the project objectives ,with in the time and cost and according to the specification

What is a network?

Any system of interconnected linear features

What is network analysis?

• General name given to certain specific techniques which can be used for the planning, management and control of projects.
• Solving problems involving networks
• Goal is efficiency – Saving time and money

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Network Diagram

Network diagram is a graphical / pictorial representation of a series or a sequence of activities in the logical order of their performance, such that we establish the inter relation and interdependence of one activity on all other activities of the project.

Network Diagram comprises of two basic elements:

1. Activity
2. Event (Node)

Elements of Network Diagram

1. Activity: An activity is denoted by an arrow

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It signifies the deployment of finite resources over a finite period of time. The tail of the arrow signifies the commencement of the activity and the head signifies the completion of the activity.

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2. Events or Nodes: An event is denoted by a circle

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It signifies the status of the project at a point of time. It indicates the start & completion of an activity.

i

Tail

Head

where, i={1,2,3,4…. and so on}

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A-O-A Convention (i-j convention)

i

j

A

t_ij

i < j

Activity A or Activity i-j

Tail event signifies commencement status of the activity.

Head Event signifies completion status of the activity

Arrow signifies deployment of finite resources over a finite period of time.

t_ij is the duration of the activity

Tail Event

Head Event

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Good practices of drawing a Network Diagram

1. Drawing a network diagram is a trial and error procedure
2. The starting event is always one event, irrespective of the number of starting activities. This event signifies the commencement status of the project
3. The completion event is always one event, irrespective of the number of final activities. This event signifies the completion status of the project.
4. The length of the arrow is the convenience of drawing the network diagram. It is no indication of the duration of activity.
5. The arrows must be drawn in the forward direction. Avoid crossing of arrows.
6. The numbering of events starts with the first event and progressively moves from the left to the right of the network diagram
7. There is no uniqueness in the final picture of the network diagram.

Slide 9

• All the activities must be filled into the network so that danglers should be avoided
• Dummy activities can be used to maintain precedence relationships only when actually required. Their use should be minimized in the network diagram.

Types of events

Event

• Represents project such as the start or completion of an activity, and occur at a particular time has been some specific part of project is complete.

• An event is represented as a node.
• Each node is represented by a circle and numbered. Following steps are involved in the numbering of the nodes:
• The initial event, which has all outgoing arrows and no incoming arrow, is numbered as 1.
• Delete all the arrows coming out from the node just numbered (i.e. 1). This step will create some more nodes (at least one) into initial events. Number these events in ascending order (i.e. 2, 3 ­etc.).
• Continue the process until the final or terminal node which has all arrows coming in, with no arrow going out, is numbered.

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• Events can be of two types:
• Merge Event: Many activities lead to a single event

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• Burst Event: Many activities are initiated due to a single event

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Activity

• Represents project operation or the task to be conducted as such.
• All activities (except dummy activity) consume time and resource.
• Represented as an arrow.
• Activities can be of three types:
• Predecessor Activity: This activity must be completed before other activities.
• Successor Activity: This activity must be immediately initiated after the completion of one or more activities.
• Dummy Activity: This activity is a fictitious activity with zero activity time used to represent precedence or used whenever two or more activities have the same starting and ending nodes. It is represented by a dashed arrow.

Draw network diagram from the following data

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Draw network diagram from the following data

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G

Draw network diagram from the following data

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D

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Draw network diagram from the following data

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CPM

• The objective of critical path analysis is to estimate the total project duration and to assign starting and finishing times to all activities involved in the project
• This helps in checking actual progress against the scheduled duration of the project

CPM BASIC TERMINOLOGY

• Critical path: critical path is that path which consumes the maximum amount of time or resources

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• Slack: it means the time taken to delay a particular event without affecting the project completion time. If a path has zero slack that means it is the critical path

slack = LFT-EFT

• Earliest start time (EST): it is the earliest possible time at which an activity can start. And is calculated by moving from first to last event in the network diagram.
• Earliest finish time (EFT):it is the earliest possible time at which an activity can finish

EFT= EST+ Duration of activity

• Latest start time(LST): it is the latest possible time by which an activity can start with out delaying the date of completion of the projectf
• LST= LFT-Duration of activity

Latest finish time (LFT): It is latest time by which

The activity must be completed .so that the scheduled date for the completion of the project may not delayed .it is calculated by moving backwards.

Float and types of float

• Float: floats in the network analysis represent the difference between the maximum time available to finish the activity and the time required to complete it
• The basic difference between slack and float time is a slack is used with reference to event, float is use with reference to activity

Type of float

• Total float
• Free float
• Independent float
• Total float: it is additional time which a non-critical activity can consume without increasing the project duration. However total float may affect the floats in previous and subsequent activities
• Total float= LST-EST OR LFT-EFT

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• FREE FLOAT:
• Free float refers to the time by which an activity can expand without affecting succeeding activities
• Free float= EST of Head event –EST of tail event-activity duration

• Independent float
• This the time by which activity may be delayed or extended without affecting the preceding or succeeding activates in any away

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• Independent float= EST of Head event- LFT of tail event- Activity duration

The following are the activities identified in a small project with time days

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Draw the network diagram,

Identify the critical path

Calculate project duration

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3

2

6

5

4

7

8

A(2)

B(5)

D(3)

C(1)

E(6)

H(4)

F(1)

G(1)

I(2)

E1=0

L1=0

L3=7

E3 =7

E2=2

L8=20

E8=20

L6=17

E6=15

L5=14

E5=14

L4=8

E4=8

L2=2

E7=18

L7=18

Critical path :

Critical path 1 is

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2

3

4

7

5

8

A(2)

B(5)

C(1)

E(6)

H(4)

I(2)

Duration of the project is =2+5+1+6+4+2 =20 days

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2

8

7

5

4

A(2)

D(3)

E(6)

H(4)

I(2)

Duration of the project is =2+3+6+4+2 =17 days

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Critical path 2 is

Original critical path is

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Duration of the project is 2o days

A small engineering project consists of 6 activities namely ABCDE & F with duration of 4, 6, 5, 4, 3 and 3 days respectively. Draw the network diagram and calculate EST, LST, EFT, LFT and floats. Mark the critical path and find total project duration.

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Note: LST = LFT – activity duration

EFT = EST + activity duration

Total float = LST – EST or LFT – EFT

Free float = EST of Head Event – EST of Trail Event – Activity duration Independent float = EST of Head event – LFT of Trail event – Activity duration

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• PERT was developed in the late 1950 in the US the Polaris submarine missile programme. It has the potential to reduce both the time & cost require to complete a project.
• Programme evaluation and review technique (PERT) is a tool to evaluate a given Programme and review the progress made in it from time to time. A Programme is also called a project. A project is defined as a set of activities with a specific goal occupying a specific period. It may be a small or big project, such as construction of a college building, roads, marriage, picnics etc.

PERT: It is concerned with estimating the time for different stages in such a Programme or a project and find out what the critical path is, which consumes a maximum resources

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PERT planning involve the following steps:

Determine the proper sequence of the activities

Construct a network diagram

Estimate the time require for each activity

Determine the critical path

Identity the specific activity & events

IDENTIFY THE SPECIFIC ACTIVITIES AND MILESTONES. The activities are the tasks required to complete a project. The milestones are the events marking the beginning and the end of one or more activities. It is helpful to list the tasks in a table that in later steps can be expanded to include information on sequence and duration.

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DETERMINE THE PROPER SEQUENCE OF THE ACTIVITIES  This step may be combined with the activity identification step since the activity sequence is evident for some tasks. Other tasks may require more analysis to determine the exact order in which they must be performed.

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CONSTRUCT A NETWORK DIAGRAM. Using the activity sequence information, a network diagram can be drawn showing the sequence of the serial and parallel activities.

 Each activity represents a node in the network, and the arrows represent the relation between activities.

 Software packages simplify this step by automatically converting tabular activity information into a network diagram.

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ESTIMATE THE TIME REQUIRED FOR EACH ACTIVITY  Weeks are a commonly used unit of time for activity completion, but any consistent unit of time can be used. A distinguishing feature of PERT is its ability to deal with uncertainty in activity completion time.  For each activity, the model usually includes four time estimates:  Optimistic time  Most likely time  Pessimistic time  Expected time

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TIMES

 Optimistic time  It is generally the shortest time in which the activity can be completed.

 Most likely time – the completion time having the highest probability. Note that this time is different from the expected time.

 Pessimistic time – the longest time that an activity might require.

 Expected time = (Optimistic + 4 x Most likely + Pessimistic) / 6

 This expected time may be displayed on the network diagram.

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DETERMINE THE CRITICAL PATH.  The critical path is determined by adding the times for the activities in each sequence and determining the longest path in the project.

 The critical path determines the total calendar time required for the project.

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Normal Deviate If Ts is the schedules time of completionIf Ts is the schedules time of completion & Te is the expected time of completion& Te is the expected time of completion Z = Ts-Te/sigmaZ = Ts-Te/sigma Sigma = (Sum of variances along critical path)Sigma = (Sum of variances along critical path)0.50.5 Variance = (tp-to/6)Variance = (tp-to/6)22

A small engineering project consists of six activities. The three time estimates in number days for each activity are given below.

Activity to tm tp

1-2 2 5 8

2-3 1 1 1

3-5 0 6 18

5-6 7 7 7

1-4 3 3 3

4-5 2 8 14

Find out:

• Calculate the values of expected time (t_e), S.D and variance of each activity
• Draw the network diagram and mark t_e on each activity
• Calculate EST and LFT and mark them on the net work diagram
• Calculate total slack for each activity
• Identify the critical path and mark on the net work diagram
• Probability of completing project in 25 days.

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From the table value (z = 1.31) = 0.90490 =90.5%

Probability for completing project in 25 days

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Z = Ts-Te/sigma

Z = Ts-Te/sigma

Sigma = square root of (Sum of variances along critical path)

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Ts = 25 days , Te = 20 days

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Standard deviation ( sigma ) = square root of (1 +0+9+0) = 3.16

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Z = 25-20

3.18

Z = 5/3.18 = 1.31

Project crashing

• It is common in project management that additional resources are used to either speed up some activities to get the project back on schedule or to reduce the project completion time.
• Crashing an activity refers to the speeding up or shortening of the duration of an activity by using additional resources. These include overtime, hiring temporary staff, renting more efficient equipment, and other measures.

• Project crashing refers to the process of shortening the duration of the project by crashing the duration of a number of activities.
• Since it generally results in an increase of the overall project costs, the challenge faced by the project manager is to identify the activities to crash and the duration reduction for each activity such that as the project crashing is done in the least expensive manner possible.

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a) Direct cost: These costs are those, which are directly proportional to the number of activities involved in the project Ex: Raw material cost

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b) Indirect cost: In direct cost are those costs that are determined per day. Some of examples for indirect costs are supervisory personnel salary, supplies, rent, interest an borrowings, ads, depreciation. These costs are directly proportional to the number of days of the duration of the project. If the project duration is reduced the indirect cost also comes down.

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Normal cost (Nc): It is the lowest cost of completing an activity in the minimum time, employing normal means i.e. not using overtime or other special resource.

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Normal time (NT): It is the minimum time required to achieve the normal cost Crash cost (CC): It is the least cost of completing an activity by employing all possible means like overtime, additional machinery, proper materials etc.

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Crash time (CT): It is the absolute minimum time associated with the crash cost.

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The crash time refers to the shortest possible time to complete an activity with additional resources.

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The crashing cost refers to the activity cost under the crashing activity time. This relationship is assumed to be linear. Hence, for each activity a crash cost per period (e.g. per week) can be derived as follows:

crash cost per period = (Crash cost - Normal Cost)/ (Normal time - Crash time)

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Crashing of Network: After identifying the critical path, it is necessary to identify the priority to crash the activities by calculating the cost slope.

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For reducing the duration extra expenditure to be incurred, but to save resources, organizations keep this extra expenditure at a minimum.

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When the direct cost (A) decrease with an increase in time, as the project duration increase, the indirect cost (B) like overheads, depreciation, insurance etc. increases. The total cost (A+B) curve is a flat U-shaped curve, with implies that only up to a particular point (O) the crashing is economical, not beyond. The time duration, which involves the least total cost, is the optimum duration at optimum cost. Crashing the duration of a project may not be possible beyond a particular point.

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Steps involved in project crashing

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Step 1: Determine the normal project completion time and associated critical path using normal time

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Step 2: Identify the critical activates and calculated the cost slope for each of these by using the relationship

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Note : The values of cost slope for critical activities indicate the direct cost extra cost required to execute an activity per unit

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Step 3: Compare the cost slope with given indirect cost

If cost slope is zero or greater than indirect cost or is equal to indirect cost , don’t crash (reduce ) activities

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If cost slope is less than indirect cost ,crash the relevant acitivites

Step 4 : calculate the associated cost and time and critical path

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Note : Accept the new critical path along with the existed critical path , if new one arrives Never neglect the original critical path

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Step 5 :

Repeat the steps from 2 to 5 until the optimal solution is reached

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Associated cost :

Total normal cost +total indirect cost + total crashed cost

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Crashing the activities under critical path to reduce the project duration .Identify the critical path for the following network .show how far the project can be crashed also show the extent of increase in normal costs with every stage of crashing

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Here it is assumed that normal cost is includes overheads

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3

2

4

A(6)

B(4)

D(3)

C(7)

E(5)

0

0

6

6

18

18

13

13

Critical path is 1-2-3-4 = 6+7+5 = 18 days

Total cost = total normal cost +total indirect cost =27000 +0 = 27000

Calculation of cost slope

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A(6)

B(4)

D(3)

C(6)

E(5)

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12

12

Critical path is 1-2-3-4 = 6+6+5 = 17 days

Total cost = total normal cost +total indirect cost =27000 +0+1*300 = 27300

To start with let us crash activity 2-3 by reducing one day

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A(4)

B(4)

D(3)

C(6)

E(5)

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10

10

Critical path is 1-2-3-4 = 4+6+5 = 15 days

Total cost = total normal cost +total indirect cost =27000 +0+1*300+2*600 =28500

crash activity 1-2 by reducing two day

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2

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A(4)

B(4)

D(3)

C(6)

E(3)

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4

13

13

10

10

Critical path is 1-2-3-4 = 4+6+3 = 13 days

Total cost = total normal cost +total indirect cost + total crashed cost

=27000 +0+(1*300)+(2*600)+(2*750) =30000

crash activity 3-4 by reducing two day

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The project duration at every stage of crashing and increase in normal costs can be summarized as below

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Hence the optimum duration of the project is 13 days and cost of the project is 30000

From the following particulars

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• Draw a network diagram
• Calculate the earliest expected time , latest allowable time and identify the critical path
• determine cost slope
• Prepare a statement showing the different stages of crashing and corresponding cost estimates, assuming that the project has fixed overhead cost rs 600
• Find out the optimum duration and cost of the project

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3

2

4

(3)

(6)

(7)

(9)

(3)

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15

15

12

12

Critical path is 1-2-3-4 = 3+9+3 = 15 days

Total cost = total normal cost +total indirect cost =33000+15*600 = 42000

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(3)

(6)

(7)

(9)

(2)

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14

14

12

12

Critical path is 1-2-3-4 = 3+9+2 = 14 days

Total cost = total normal cost +total indirect cost+ total crashed cost =33000+14*600+1*400 = 41800

Crashing of 3-4 activity by reducing one day

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(3)

(6)

(7)

(3)

(2)

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3

10

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8

Critical path is 1-2-4 = 3+7 = 10 days

Crashing of 2-3 activity by reducing 6 days its impact on the original critical path then you don’t crash the activity

Crashing of 2-3 activity by reducing 6 day

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(3)

(6)

(7)

(5)

(2)

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3

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8

Critical path is 1-2-3-4 = 3+5+2 = 10 days

Total cost = total normal cost +total indirect cost+ total crashed cost =33000+10*600+(1*400)+(4*500)

= 41400

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Crashing of 2-3 activity by reducing 4 day

The project duration at every stage of crashing

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Hence the optimum duration of the project is 10 days and cost of the project is 41400