Answer:

PERT and CPM:

In order to keep track of the different activities of a project, the following project evaluation tools have to be used. The most predominantly used techniques are PERT and CPM. It is used in project planning and coordination as well.

Program evaluation and review technique (PERT) is used to plan, schedule and control different projects such as construction works, design and installation of systems, maintenance work, and research and development processes. It is useful for planning for large and complicated projects.

Consider the following data showing optimistic, most probable and pessimistic time estimates for different activities:

a) Project network and Expected duration:

Determine the critical activities of the project by the following steps as shown below:

Step 1 : Determine the expected (estimated) time for activity using the below mentioned formula:

…… (1)

Here,

refers to the optimistic time estimate

refers to the most likely time estimate

refers to the pessimistic time estimate.

Calculate expected time in the excel spread sheet with the help of the above formula as shown below:

Step 2: Draw a network diagram for the data using the expected time of each activity as shown below:

Step 3: Now, calculate the length of each path by adding the expected time required for completion of each activity present in a path.

The path having the maximum completion time is considered as the critical path. From the above calculation it is clear that path B-E-H has the maximum completion time i.e. 16 months.

Therefore, path B-E-H is considered to be the critical path and the critical activities are B, E, and H.

To identify the critical path of the project, the longest path has to be selected and the path should have no slack. In order to do this, the following diagram is presented. Each circle or node represents an event. An activity occurs between two events. The network diagram is drawn accordingly keeping the predecessors and successors of each activity in mind. Each activity is denoted by an arrow and the number in the brackets is the time taken by each activity. The legend of the diagram is given as follows:

Each node is then divided into three parts. The upper half of the node denotes the activity and the time taken to complete the event is in brackets. The lower half is sub-divided into two parts. The left hand side of the lower half of the node is the Earliest Start Time ( ES ) and the right hand side is the Latest Finish Time ( LF ). The calculation of ES for all the activities is done from left to right of the network diagram. This is known as Forward Pass. In this, the time taken by each activity is added to the Earliest Start time of each activity. The Earliest Start time from start is considered to be zero. The time taken by activity A is 6 months so the Earliest Start time for activity A is 6 months (i.e.

). In this manner, the Earliest Start Time is calculated for all the events. In case of multiple predecessors in forward pass, the highest value has to be considered as the Earliest Start time of the event. For example, in activity H, the Earliest Start Time can be

(or)

or

. The highest value should be considered i.e. 16 months.

On reaching the last event, the calculation of the Latest Finish time of each event has to be done. This is done from right to left. This is known as backward pass. The Earliest Start time of the last event is equal to the Latest Finish time of the last event. The Latest Finish time is then calculated by subtracting the time taken by each activity. For activity B, the Latest Finish time is either

(or)

. In backward pass, in case of multiple predecessors, the lowest value has to be taken. Therefore, activity B will take 2 months. In this way, the calculation should be done from activity J to start. The Earliest Start time and the Latest Finish time should be equal to each other at the beginning and end of the network diagram, respectively.

The critical path is shown by blue arrows as follows:

The scheduling time for each activity is calculated as follows:

Step 1: List down the different activities in column A, time taken in each activity in column B and the immediate predecessor for each activity in column C.

Step 2 : In the column D, write the Earliest Start Time ( ES) of each activity. If an activity has multiple predecessors, then

. The Earliest Start time for the subsequent activities will be the Earliest Finish time of the preceding activity. In case there are too many preceding activities, use the finish time of the activity which ends after all the others.

Step 3 : In column E, add the time taken in each activity with ES to get the Earliest Finish Time ( EF). The formula used is

Step 4 : In column G, write the Latest Finish Time of each activity ( LF). If an activity has multiple successors,

. In case of multiple successors, use the smallest late start time from among all of the activities, as the latest finish time.

Step 5 : In column F, subtract the time taken in each activity from LF of each activity and obtain LS. The formula used is

Step 6: In column H, subtract ES from LS and obtain the Total Slack value ( TS ). The formula used is

From the scheduling time for each activity also it can be observed that the activities which have slack time as zero are B, D, E and H. Thus, from this also it can be justified that the critical path will have the activities B, E and H.

c) Determine the probability for completion of the project within 2 years:

Step 1: Determine the variance for activity by using the formula as shown below:

Calculate Variance using the above formula in the excel spread sheet as shown below:

Step 2: Now, calculate the activity variance along critical path by adding the variance of each activity present in the path.

Variance is

Step 3: Determine the standard deviation of the expected time for each path by substituting variance in the formula as shown below:

Standard deviation is

Step 4: Calculate the probability for completion of the project before 2 years by substituting the values of standard deviation, specified time and path mean in the formulas shown below:

Substituting the values in the formula:

Step 5: Now, determine the probability for z value using NORMSDIST (4.5756) formula in an excel spread sheet as shown below:

Therefore, the probability for completing the project i.e. P (z) before 2years or 24 months is

(or)

Answer:

Project:

The project is an organized approach that is undertaken to plan and achieve a particular aim. These are a set of activities that have a definite beginning and end. They have a well-defined scope and utilize resources. A project is unique in nature and it has a specific set of operations designed for achieving the goal.

A project cannot be carried out individually. There is requirement of a number of people for carrying out the different activities of the project. So, there is a need for project team.

Four stages of Team building:

In order to achieve the objective of a project, the members of the project will have to come together and work as a team. The four stages of team building as given by B.W. Tuckman are: Forming, Storming, Norming and Performing.

Forming: In this stage the team members get introduced to each other. They are excited about the project but are not clear about their role in the project. The team is given instructions by the project manager and the objective, scope and schedule of the work has to be prepared accordingly.

Storming: This stage is characterized by some dissatisfaction in the minds of the team members. This is due to the project constraints and the dependence on the instructions given by the project manager. The project manager has to be able to handle and resolve the conflict as well as provide a good environment for the project work to progress.

Norming: This stage begins with the development of cohesion in the team members of the company. The decision making power of the project shifts from the project manager to the project team. The work performance and the productivity of the firm will improve due to the good and friendly environment at workplace. The project manager now plays only a supportive role.

Performing: This stage is the final stage in the project team development. The project team collaborates with each member of the team and accomplishes the goal. The project manager only monitors the performance of the team and its progress with respect to the time, cost, and plan of the project. If the project fails then the manager undertakes corrective emasures that should be implemented.

Answer:

PERT and CPM:

In order to keep track of the different activities of a project, the following project evaluation tools have to be used. The most predominantly used techniques are PERT and CPM. It is used in project planning and coordination as well.

Program evaluation and review technique (PERT) is used to plan, schedule and control different projects such as construction works, design and installation of systems, maintenance work, and research and development processes. It is useful for planning for large and complicated projects.

Consider the following data showing optimistic, most probable and pessimistic time estimates for different activities:

a) Project network and Expected duration :

Determine the critical activities of the project by the following steps as shown below:

Step 1 : Determine the expected (estimated) time for activity using the below mentioned formula:

…… (1)

Here,

refers to the optimistic time estimate

refers to the most likely time estimate

refers to the pessimistic time estimate.

Calculate expected time in the excel spread sheet with the help of the above formula as shown below:

Step 2: Draw a network diagram for the data using the expected time of each activity as shown below:

b) Critical Path and Expected completion time:

Step 1: Calculate the length of each path by adding the expected time required for completion of each activity present in a path.

The path having the maximum completion time is considered as the critical path. From the above calculation it is clear that path A-C-E-H-J has the maximum completion time i.e. 37 days. Therefore, path A-C-E-H-J is considered to be the critical path and the critical activities are A, C, E, H and J.

To identify the critical path of the project, the longest path has to be selected and the path should have no slack. In order to do this, the following diagram is presented. Each circle or node represents an event. An activity occurs between two events. The network diagram is drawn accordingly keeping the predecessors and successors of each activity in mind. Each activity is denoted by an arrow and the number in the brackets is the time taken by each activity. The legend of the diagram is given as follows:

Each node is then divided into three parts. The upper half of the node denotes the activity and the time taken to complete the event is in brackets. The lower half is sub-divided into two parts. The left hand side of the lower half of the node is the Earliest Start Time ( ES ) and the right hand side is the Latest Finish Time ( LF ). The calculation of ES for all the activities is done from left to right of the network diagram. This is known as Forward Pass. In this, the time taken by each activity is added to the Earliest Start time of each activity. The Earliest Start time from start is considered to be zero. The time taken by activity A is 6 months so the Earliest Start time for activity A is 7 days (i.e.

). In this manner, the Earliest Start Time is calculated for all the events. In case of multiple predecessors in forward pass, the highest value has to be considered as the Earliest Start time of the event. For example, in activity H, the Earliest Start Time can be

(or)

. The highest value should be considered i.e. 36 days.

On reaching the last event, the calculation of the Latest Finish time of each event has to be done. This is done from right to left. This is known as backward pass. The Earliest Start time of the last

event is equal to the Latest Finish time of the last event. The Latest Finish time is then calculated by subtracting the time taken by each activity. In backward pass, in case of multiple predecessors, the lowest value has to be taken. Therefore, activity B will take 2 months. In this way, the calculation should be done from activity J to start. The Earliest Start time and the Latest Finish time should be equal to each other at the beginning and end of the network diagram, respectively.

The critical path is shown in blue arrows as follows:

The scheduling time for each activity is calculated as follows:

Step 1 : List down the different activities in column A, time taken in each activity in column B and the immediate predecessor for each activity in column C.

Step 2 : In the column D, write the Earliest Start Time ( ES) of each activity. If an activity has multiple predecessors, then

. The Earliest Start time for the subsequent activities will be the Earliest Finish time of the preceding activity. In case there are too many preceding activities, use the finish time of the activity which ends after all the others.

Step 3 : In column E, add the time taken in each activity with ES to get the Earliest Finish Time ( EF). The formula used is

Step 4 : In column G, write the Latest Finish Time of each activity ( LF). If an activity has multiple successors,

. In case of multiple successors, use the smallest late start time from among all of the activities, as the latest finish time.

Step 5 : In column F, subtract the time taken in each activity from LF of each activity and obtain LS. The formula used is

Step 6: In column H, subtract ES from LS and obtain the Total Slack value ( TS ). The formula used is

From the scheduling time for each activity also it can be observed that the activities which have slack time as zero are A, C, E, H and J. Thus, from this also it can be justified that the critical path will have the activities A, C, E, H and J. The expected project time is 37 days on the critical path.

c) Determine the probability for completion of the project within 41days or less:

Step 1: Determine the variance for activity by using the formula as shown below:

Calculate Variance using the above formula in the excel spread sheet as shown below:

Step 2: Now, calculate the activity variance along critical path by adding the variance of each activity present in the path.

Variance is

Step 3: Determine the standard deviation of the expected time for each path by substituting variance in the formula as shown below:

Standard deviation is

Step 4: Calculate the probability for completion of the project before 41 days by substituting the values of standard deviation, specified time and path mean in the formulas shown below:

Substituting the values in the formula:

Step 5: Now, determine the probability for z value using NORMSDIST (0.8) formula in an excel spread sheet as shown below:

Therefore, the probability for completing the project i.e. P (z) before 41 days is

(or)