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Fall 2011 Master of Business Administration-MBA Semester 4 Project Management – PM0015 - 4 Credits (Book ID:) Assignment Set- 1 (60 Marks) Note: Each question carries 10 Marks. Answer all the questions. Q.1 Describe the process of setting up of a common resource. Answer:- The management of resources is a major feature of MS Project. It is possible to see how each one is being used and determine the times when they are under or over utilised. The system can adjust the project to eliminate over allocation of a resource. We can think of resource data being stored in a database, which is the partner to the task database. They system merges the data in the two databases to provide the facilities that are available. When a large pool of resources is built – for example, 200 employees – the best place to enter this information is in the Resource Sheet. If there are only a few resources working on the project, however, anybody might enter them “on the fly” using the Resource Assignment dialog box. Reviewing and Navigating the Resource Sheet .The Resource Sheet contains an array of required fields for entering resources. A Resource Sheet is illustrated below: Figure : Reviewing and Navigating the Resource Sheet Entering the Resources There are two separate stages in adding Resources to be managed by the system. They first must be entered in the Resource Sheet to identify them as being available. Secondly the available resources are associated with the respective tasks. Adding Resources to the Resource Sheet You add resources to the Resource Sheet in rows. The columns
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Fall 2011

Master of Business Administration-MBA Semester 4Project Management – PM0015 - 4 Credits

(Book ID:)Assignment Set- 1 (60 Marks)

Note: Each question carries 10 Marks. Answer all the questions. Q.1 Describe the process of setting up of a common resource.

Answer:-

The management of resources is a major feature of MS Project. It is possible to see how each one is being used and determine the times when they are under or over utilised. The system can adjust the project to eliminate over allocation of a resource. We can think of resource data being stored in a database, which is the partner to the task database. They system merges the data in the two databases to provide the facilities that are available.When a large pool of resources is built – for example, 200 employees – the best place to enter this information is in the Resource Sheet. If there are only a few resources working on the project, however, anybody might enter them “on the fly” using the Resource Assignment dialog box.

Reviewing and Navigating the Resource Sheet .The Resource Sheet contains an array of required fields for entering resources. A Resource Sheet is illustrated below:

Figure : Reviewing and Navigating the Resource Sheet

Entering the Resources There are two separate stages in adding Resources to be managed by the system. They first must be entered in the Resource Sheet to identify them as being available. Secondly the available resources are associated with the respective tasks.Adding Resources to the Resource SheetYou add resources to the Resource Sheet in rows. The columns identify the fields. The table below summarizes the information that you can store in the Resource Sheet.

Field DescriptionResource Name The name given to a resource. It can be the name of an individual or a type of group.Initials The abbreviated name for the resource.Group A resource can be placed in a group, which can beused by a filter to show only group members, it is also possible to use the group name to view all members of the group together.Max. Units The percentage (number) of resource units available. This is applicable only if using a type of resource. For example, you might have three technicians, but you can have only one Emma Cheesman.

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Std. Rate The standard cost of the resource per hour, week, or month.Ovt. Cost The overtime cost of the resource per hour, week, or month.Cost/Use The cost of the resource every time it is used.Accrue At This field identifies when the cost of the resource is added to the running total of the project. The options are at the “Start”, at the “End” or “Prorated” which means updated at the end of each time unit as the resource is used.BaseCalendar The base calendar to which you assign the resource.Code You can assign an alphanumeric code to each resource. The Code field can be used to associate an accounting code for use of the resource. This is an additional method of allocating the costs of the project as required and you have to use it for sorting, filtering, and reporting.

To add resources to the Resource Sheet:• From the View menu, choose Resource Sheet.• In the Resource Name cell, type the Resource Name.• Press TAB• Type the necessary information.• Repeat steps 3 and 4 until you have entered all the information needed for the resource.• Press ENTER• Press HOMERepeat steps 2 through 7 for each resource.A resource can be defined under the following headings:-

ID:Name:Initials:Group:Max Units:The next items relate to calculating the cost of the resource. They can be defined by setting a cost level for a specific period or a cost for each time the resource is used.Std. Rate:Ovt. Rate:Cost/Use:Accrue At:Code:Viewing the ResourcesWhere it is necessary to view all the resources, this is best done in the top part of the screen or a single pane view. Selecting Resource Sheet from the View pull down menu will show a complete list of the resources required by the tasks.

To add resources on the fly:•On the Standard toolbar, click the Resource Assignment button. •In the Resource Assignment dialog box, select a blank Name cell at the end of the resource list.•Type the name of the resource.•Press ENTER

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Q.2 Write a short note on MS projects and explain in brief some of the important terminologies used in MS Project. Answer:-MS Project is a tool to help you to plan projects, manage and update project information, and communicate the status once the project is under way. The details of the project tasks and associated resources are entered into the system as a new project. The system will then display the data in such a way that the relationships of the tasks and their time scales can clearly be seen and potential problem areas identified. Project data can be entered and/or viewed in a number of ways; the three principal formats are charts, forms, and sheets. Charts can be either Gantt Charts or Network Diagram Charts both of which are a diagrammatic representation of the project data. You can combine any two single-pane views on the screen to create a combination view. In a combination view, the information in the bottom relates only to the task or resources in the top view.The reason for having combination views is to make the job of entering and analysing information easier. At the heart of every project management system is a scheduling algorithm. An algorithm is a mathematical or logical equation that solves a complex problem by breaking down the problem into simple steps. When scheduling resources and parameters are entered into it, the scheduling algorithm produces a project schedule that would be impossible for you to produce manually. This Input/Output model is displayed below.

Figure 2: The Input/Output ModelIn Microsoft Project, even if your project is very complex, you can vary only information regarding the tasks or the resources. The information provided by you is fed into the “Black Box” or algorithm, in order to provide you with a schedule in the form of a Gantt chart, Network Diagram Chart, or Resource Graph. In summary, the seven or eight parameters that you enter result in output that is a schedule displayed on various views and forms. The project management industry uses specific language and terminology. Some of these terms are illustrated below.

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Figure 3: Clarification of Project Management TerminologiesIn the illustration above, two tasks have a relationship. Task A is the predecessor task, and Task B is the successor task. Both of these tasks are considered to be non-critical because they both have flexibility. Let‟s focus on Task A. EA marks the earliest possible time Task A can start. SS marks the scheduled start time for Task A. By default, all tasks are scheduled to start at the earliest possible time, unless you specify otherwise. In the example above, Task A is scheduled to start later and therefore has been delayed. SE marks the scheduled end time for Task A, and LE marks the latest possible time Task A can end. Both of these tasks have slack, the amount of time a task can slip before it affects another task‟s dates or the project finish date. Free slack is the amount of time Task A can be delayed before affecting the start time of Task B, and total slack is the amount of time that Task A can be delayed before affecting the finish date of the project. The summary task summarizes Tasks A and B.Critical tasks, not shown above, have no slack; therefore, delaying this type of task would mean delaying the project. A critical path is a series of critical tasks. All tasks on a critical path must be completed on time for the project to finish on time. If one task on a critical path is delayed, then the project is delayed. In Microsoft Project, a critical path is shown on the Gantt chart and the Network Diagram Chart in red. Some important terminologies in MS Projects Table 1: Some important terminologies in MS Projects and Project Management

Actual Usage A measure of the resource expended in completing or partially completing a task.

ALAP Refers to a task that should be started „As Late As Possible‟, using all the free-float time available.

ASAP Used to indicate a task that should be started „As Soon As Possible‟, taking into account the start date of the project and its predecessor tasks.

Baseline The original project plan, including the time schedule and resource and cost allocations. The baseline is used for comparing projected

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values to actuals, and facilitates the tracking and analysing of a project‟s progress.

Cost Variance A project tracking function recording the difference between the budgeted cost of the work performed and the actual cost. Values below the baseline show an overspend and positive values denote cost savings.

Critical Path The sequence of tasks or activities whose schedules and durations directly affect the date of overall project completion.

Earned Value This is a measure of a project‟s performance, and is calculated by multiplying a task‟s planned cost by the percentage of work completed.

Float (slack) The amount of time by which a non-critical task can be delayed before it affects another task‟s schedule.

Gantt chart A graphical representation of a project schedule showing each task as a bar, the length of which is proportional to its duration. Many project management packages use a spreadsheet section to the left of the Gantt chart to display additional information.

Hammock Task A task whose duration is calculated based on the time span between its predecessor and successor activities.

Histogram A bar chart that shows resource workloads over a time period. Lag The amount of time between the finish of a predecessor task and the

start of a successor task. Lead The amount of time that a task is permitted to start before its

predecessor is finished. Loading A measurement of resource usage on a task per unit of time. Different

methods of loading may be used depending on what‟s available in your project management application and what‟s applicable for your particular project.

Loading (back) A loading pattern that allocates resource usage as late in the task as possible.

Loading (contour) The contour-loading pattern assesses which resources are left over after allocation to the critical tasks and spreads these resources among the remainder.

Loading (fixed) When using fixed-loading algorithms, you specify the actual amount of resource allocated to the encompassing tasks.

Loading (front) Front loading systems will attempt to allocate resources as early in the task as possible.

Loading (uniform) This loading pattern allocates the resource usage on a by day basis in a task. This will usually be done without causing any one task to be over committed.

Milestone A project event that represents a checkpoint, a major accomplishment or a measurable goal.

Negative float Refers to an unscheduled delay before an actual task start time that must be recovered if the project is not to be delayed.

OBS codes Organisational Breakdown Structure codes are used to identify tasks by resource groups in a hierarchical format. OBS codes are often used to reflect departmental structure in a company or code of accounts, and can also be used for filtering tasks.

Network Diagram Project Evaluation and Resource Tracking charts, also called network diagrams. Network Diagrams are a graphical depiction of task dependencies, and resemble flow charts. Dependencies are shown by connecting lines or arrows indicating the work flow.

Predecessor In dependency relationships, the predecessor is the task that must be started or completed first.

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Project Management

Best defined as a body of knowledge, a set of principles, or techniques dealing with the planning and control of projects.

Resource Any person, group of people, item or equipment, service or material used in accomplishing a project task.

Resource Leveling The process of resolving resource conflicts. Most project management programs offer an automated resource levelling routine that delays tasks until the resources assigned to them are available.

Resource Driven Task durations determined by the program and based on the number of an allocation of resources, rather than the time available. Both individual tasks and entire projects can be resource-driven.

Sub-project A group of activities which are treated as a single task in a master project schedule. Subprojects are a way of working with multiple projects that keep all the data in one file rather than in independent files.

Successor In a dependency relationship between two tasks, the successor is the task that must await the start or completion of the other.

WBS codes Work Breakdown Structure codes are used to identify tasks in a hierarchy. Many project management applications associate these codes with an outline structure. WBS codes can be used to filter the project schedule for tracking and reporting purposes.

Q.3. Describe the time series forecasting with the help of autoregressive modeling. What do you understand by managing cash flow? Answer:-

Autoregressive Modelling for Trend-fitting and Forecasting

Another approach to the forecasting with annual time-series data is based on autoregressive

modelling. Frequently, the values of a series of data at particular points in time are highly

correlated with the values that precede and succeed them. A first-order autocorrelation refers to

the magnitude of the relationship between the values that are two periods apart. A p-th order

autocorrelation refers to the size of the correlation between values in a time-series that are p

periods apart. To obtain a better historical fit of the data and, at the same time, make useful

forecasts of their future behaviour, it is possible to take advantage of the autocorrelation inherent

in such data by considering autoregressive modelling methods.

The following equations describe a set of autoregressive models –

First Order Autoregressive Model

 (7.1)

Second Order Autoregressive Model

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 (7.2)

p-th Order Autoregressive Model

 (7.3)

where

Yi = the observed value of the series at time i

Yi-1 = the observed value of the series at time i-1

Yi-2 = the observed value of the series at time i-2

Yi-p = the observed value of the series at time i-p

A0 = fixed parameter to be estimated from least-squares regression analysis

A1, A2, …., Ap = Autoregression parameters to be estimated from the least-squares regression

analysis

= a non-auto-correlated random (error) component (with mean = 0 and constant variance)

The first-order autoregressive model is similar in the form to the linear regression model, the

second-order autoregressive model is similar to the multiple regression model with two

independent variables and the p-th order autoregressive model, is similar in the form to the

multiple regression model. In the regression models, the regression parameters are given by the

symbols  ,  ,  , …..,  , with corresponding estimates denoted by b0, b1, …., bk. In the

autoregressive models, the parameters are given by the symbols A0, A1, …. , Ap, with the

corresponding estimates denoted by a0, a1, ….., ap.

A first order autoregressive model is concerned only with the correlation between consecutive

values in a series. A second-order autoregressive model considers the effects of the relationship

between the consecutive values in a series and between values that are two periods apart. A p-th

order autoregressive model deals with the effects of the relationships between consecutive

values, values two periods apart, and so on – up to the values p periods apart.

The selection of an appropriate autoregressive model is a complex task. It is needed to weigh the

advantages that are due to simplicity against the concern of failing to take into account important

autocorrelation behaviour inherent in data. On the other hand, it is needed to be concerned with

the selection of a higher-order model requiring the estimation of numerous, unnecessary

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parameters – specially if n, the number of observations in the series, is not too large. The reasons

for this concern is that p out of n data values will be lost in obtaining an estimate of A p when

comparing each data value with another data value, which is p periods apart.

Managing Cash Flow

Managing cash flow in a project is an important task to be performed. Managing cash flow

involves making sure that sufficient payments are received from the customer in time so that one

has enough money to cover the costs of performing the project – employee payroll, charges for

materials, invoices from subcontractors, and travel expenses, for example.

The key to managing cash flow is to ensure that cash comes in faster than it goes out. If

sufficient cash isn’t available to meet expenses, money must be borrowed. Borrowing increases

project cost because any money borrowed must be paid back to the lender, along with a charge

for borrowing the money – the interest. The flow of cash coming in from the customer can be

controlled by the terms of payment in the contract. From the contractor’s point of view, it’s

desirable to receive payments from the customer early in the project rather than later. The

contractor might try to negotiate payment terms that require the customer to do one or more of

the following:

· Provide a down payment at the start of the project. This requirement is reasonable when the

contractor needs to purchase a significant amount of materials and supplies during the early

stages of the project.

· Make equal monthly payments based on the expected duration of the project. Cash outflow

usually is smaller in the early stages of a project. If more cash is coming in than is going out

during the early part of the project, the contractor may be able to invest some of the excess cash

and earn interest. The saved funds can then be withdrawn to meet the greater cash outflow

requirements later in the project.

· Provide frequent payments, such as weekly or monthly payments rather than quarterly

payments.

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The worst scenario from the contractor’s point of view is to have the customer make only one

payment at the end of the project. In this situation, the contractor will need to borrow money to

have cash available to meet expenses throughout the project.

Q.4. Describe how you can display data using Gantt chart and Network Diagram Chart

Network diagrams and Gantt ChartsAnswer:-

A Work breakdown Structure ( WBS) allows you to identify groups of activities that you need to accomplish in your project. However, the WBS does not show the dependencies or sequence between these activities. A network diagram will allow you to illustrate this. Once your network diagram is ready, only then can you realistically start determining your project’s schedule.

Here is a simplified network diagram for the “Build Shed” project:

 

 The above network diagram shows the relationships (arrows) between the main activities (rectangles) that are required to build a shed. You can flesh out the following information from the above diagram:

The Cut wood activity can be carried out in parallel to the Build shed base & Supervise cement hardening ones – this of course assumes that you have different teams working on each set of activities.

The dark arrows show what is known as the Critical Path (Buy materials->Build shed base->Supervise cement hardening->Assemble shed). The Critical Path is the sequence of activities that takes up the most time to complete your project. Any delay in this sequence

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of activities will impact the overall timeframe of your project. Therefore, you should monitor carefully monitor all activities on this path.

The Gantt chart

After you have finished working on your network diagram, you need to create your Gantt chart. A Gantt chart is a very useful project management tool that provides you with an overview of your schedule (something that the network diagram did not).

Here is the Gantt chart for the build shed project:

 A Gantt chart does not show the relationships between the activities of your project. However, a number of project management software packages allow you to show such relationships on a Gantt chart providing you with an overview of the schedule, and the critical path of your project.

Thanks to the WBS, network diagram and Gantt chart you now know what are the activities involved in a project, the sequence of these activities, and the overall schedule of the project. Include all of this information in your project plan.

Q.5. List the steps involved in Steps involved in Autoregressive Model Steps involved in Autoregressive Model

Answer:-

1. Choose a value for p, the highest-order parameter in the autoregressive model to be evaluated, realizing that the t-test for significance is based on n-2p-1 degrees of freedom.

2. Form a series of p “lagged predictor” variables such that the first variable lags by 1 time period, the second variable lags by 2 time periods, and so on and the last predictor variable lags by p time periods.

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3. Use Microsoft Excel to perform a least-squares analysis of the multiple regression model containing all p lagged predictor variables.

4. Test for the significance of Ap, the highest order autoregressive parameter in the model.(a) If the null hypothesis is rejected, the autoregressive model with all p predictors is selected for fitting (equation 7.5) and forecasting (equation 7.6)

(b) If the null hypothesis is not rejected, the p-th variable is discarded, steps 3 and 4 are repeated with an evaluation of the new highest-order parameter whose predictor variable lags by p-1 years. The test for the significance of the new highest order parameter is based on a t-distribution whose degrees of freedom are revised to correspond with the new number of predictors.

5. Repeat steps 3 and 4 until the highest order autoregressive parameter is statistically significant. The model is used for fitting (equation 7.5) and forecasting (equation 7.6)

Q.6. Write a short note on project crashing using network analysis. Answer:-

Network Analysis is a core technique available to the Project Managers for planning and controlling their projects. It has wide application in the architectural projects, transportations projects etc. Network analysis is a mathematical model of analyzing complex problems, as in transportation or project scheduling, by representing the problem as a network of lines and nodes. It can also be described as an analytic technique used during project planning to determine the sequence of activities and their interrelationship within the network of activities that will be required by the project. It involves breaking down a complex project’s data into its component parts (activities, events, durations, etc.) and plotting them to show their interdependencies and interrelationships. It real-life scenario, it can be used as a data processing method using topologically linked data such as street maps or river networks with the purpose of determining the routes between geographic locations, and other analyses requiring the consideration of path and direction.

Networks

A network is a set of points, called nodes, and a set of curves, called branches (or arcs or links), that connect certain pairs of nodes. In network analysis, only those networks are considered in which a given pair of nodes is joined by at most one branch. Nodes are usually denoted by the uppercase letters and branches are denoted by the nodes they use to connect.

The following figure shows a network with 5 nodes.

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Figure 2.1: Network

Figure 2.1 is a network consisting of five nodes, labeled A through E, and the six branches are defined by the curves AB, AC, AD, BC, CD and DE.

A branch is oriented if it has a direction associated with it. Schematically, directions are indicated by the arrows. The arrow of the branch AB in Figure 2.1 signifies that this branch is directed from A to B. Any movement along this branch must originate at A and it must end at B. Any movement in the direction B to A will not be permitted.

If the two branches have a common node, then these two branches are said to be connected. In figure 2.1, branches AB and AC are connected, but branches AB and CD are not connected. A path is a sequence of connected branches such that in the alternation of nodes and branches, no node is repeated. A network is said to be connected if for each pair of node in the network there exists at least one path joining the pair. If the path is unique for each pair of nodes, the connected network is called a tree. Equivalently, a tree is a connected network having one more node than branch.

In figure 2.1, {ED, DA, AB} is a path, but the sequence of connected branches {CA, AD, DC, CB} is not a path, as node C occurs in it twice. The network is connected, and remains connected even if branches DA and AB are deleted. However, in case of the deletion of the DE, the network would not remain connected, since there would not be a path linking D with E. Since D and C are joined by the three paths, the network is not a tree.

2.3 Minimum-Span Problems

A minimum-span problem involves a set of nodes and a set of proposed branches, none of them oriented. Each proposed branch has a nonnegative cost associated with it. The objective is to construct a connected network that contains all the nodes and is such that the sum of the costs associated with those branches actually used is minimum. It is to be assumed that there are enough proposed branches to ensure the existence of a solution. The minimum-span problem can be solved by a tree. If two nodes in a connected network are joined by two paths, one of these paths must contain a branch whose removal does not disconnect the network. Removing such a branch leads to the lowering of the total cost. A minimal spanning tree may be found by initially

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selecting any one node and determining which branch incident on the selected node has the smallest cost. This branch is accepted as part of the final network. The network is to be then completed iteratively. At each stage of the iterative process, the attention is to be focused on the nodes which are already linked together. All branches linking these nodes to the unconnected nodes are considered, and the cheapest such branch is identified. In case of the ties, the branches are to be chosen arbitrarily in order to break the tie. The branch is accepted as part of the final network. The iterative process is to be terminated when all the nodes have been linked. In case that all the costs are distinct, it can be proved that the minimal spanning tree is unique and is produced by the above algorithm for any choice of the starting node.

Example 1 – Solve the minimum-span problem for the network given in the figure below. The numbers on the branches represent the costs of including the branches in the final network.

Figure 2.2: Minimum-Span Problem Example

We arbitrarily choose A as our starting node and we consider all branches incident on it; they are AE, AB, AD and AC, with costs 10, 2, 1 and 4, respectively. Since AD is the cheapest, we add this branch to the solution, as shown in Figure 2.3 (a). Nodes A and D are connected.

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A shortest-route problem involves a connected network having a nonnegative cost associated with each branch. One node is designated as the source, and the other node is designated as the sink. These terms don’t imply an orientation of the branches. However, it suggests the direction in which the solution algorithm should be applied. In the shortest-route problem, the objective is to determine a path joining the source and the sink such that the sum of the costs associated with the branches in the path is minimum.

The following algorithm is to be used to solve the Shortest-route problems –

Step 1 – Construct a master list by tabulating under each node, in ascending order of cost, the branches incident on it. Each branch under a given node is written with that node as its first node.

Step 2 – Mark the source and assign it the value 0. Locate the cheapest branch incident on the source and encircle it. Next, mark the second node of this branch and assign this node a value equal to the cost of the branch. Delete from the master list all other branches that have the newly marked node as second node.

Step 3 – If the newly marked node is the sink, go to Step 5. If not, go to  Step 4.

Step 4 – Consider all marked nodes having un-circled branches under them in the current master list. For each one, add the value assigned to the node to the cost of the cheapest un-circled branch under it. Denote the smallest of these sums as M, and circle that branch whose cost contributed to M. Mark the second node of this branch and assign it the value M. Delete from the master list all other branches having this newly starred node as second node. Go to Step 3.

Step 5 – Z* is the value assigned to the sink. A minimum-cost path is obtained recursively, beginning with the sink, by including in the path each circled branch whose second node belongs to the path.

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Fall 2011

Master of Business Administration-MBA Semester 4Project Management – PM0015 - 4 Credits

(Book ID:)Assignment Set- 2 (60 Marks)

Note: Each question carries 10 Marks. Answer all the questions.

Q.1 Explain Relationship between PERT & CPM. Also describe the framework required for PERT & CPM Answer:-PERT and CPM are the project management techniques created for the need of the Western and Military Establishments to plan, schedule and control the complex projects. CPM/PERT developed along two parallel streams – one industrial and the other military. CPM was first introduced by M. R. Walker and J. E. Kelly. This computation was designed for the UNIVAC-I computer. The first test was made in 1958, when CPM was applied in the construction of a new chemical plant. In March 1959, the CPM was applied in the planned shutdown at the Du Pont works in Louisville, Kentucky. The introduction of CPM greatly reduced the unproductive time from the 125 hours to the 93 hours. PERT was introduced first for the POLARIS missile program by the Program Evaluation Branch of the Special Projects office of the U.S. Navy. The calculations were so arranged so that they could be performed in the IBM Naval Ordinance Research Computer (NORC) at Dahlgren, Virginia. Rather than giving technical benefits, it is found that PERT/CPM provides a focus around which managers could brain-storm and can put their ideas. PERT/CPM is a great communication medium by which thinkers and planners at one level can communicate their ideas, their doubts and fears for another level. Another important feature of the PERT/CPM is that it is a useful tool for evaluating the performance of the individuals and the teams. There are many variations of CPM/PERT which have been useful in planning costs, scheduling manpower and machine time. CPM/PERT can answer following important questions – How long will the entire project take to be completed? What are the risks involved in this? Which are the critical activities or tasks in the project which could delay the entire project if they were not completed on time? Is the project on schedule, behind schedule or ahead of schedule? If the project has to be finished earlier than the planned, what is the best way to do this at the least cost? The Framework for PERT and CPM There are six steps which are common to both the techniques. The procedure is as follows – 1. Define the Project and all of its significant activities or tasks. The project (made up of several tasks) should have only a single start activity and a single finish activity. 2. Develop the relationships among the activities. Decide which activities must precede and which must follow others. 3. Draw the ‘Network’ connecting all the activities. Each activity should have unique event numbers. Dummy arrows are used where required to avoid giving the same numbering to two activities. 4. Assign time and/or estimates to each activity. 5. Compute the longest time path through the network. This is called the critical path.

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6. Use the network to help plan, schedule, monitor and control the project.

The key concept used by both in PERT as well as CPM is that a small set of activities, which make up the longest path through the activity network control the entire project. If these ‘critical’ activities could be identified and assigned to the responsible persons, management resources could be optimally used by concentrating on the few activities which determine the fate of the entire project. The non-critical activities can be re-planned, rescheduled and resources for them can be reallocated flexibly, without affecting the whole project. The five important questions that should be asked before the preparation of an activity network are the following –

Is this a Start Activity? Is this a Finish Activity? What activity precedes this? What activity follows this? What activity is concurrent with this?

Some activities are serially linked. The second activity can begin only after the first activity is completed. In the certain cases, the activities are concurrent, because they are independent of each other and can start simultaneously. This is essentially the case in organizations which have supervisory resources so that work can be delegated to various departments that will be responsible for the activities to be performed and their completion as per the planning.

Q.2 Describe Time-Cost optimization Algorithm. Answer:-Time-Cost Optimization Algorithm The process of shortening a project is called crashing and is usually achieved by adding extra resources to an activity. The steps involved in the project crashing are the following – Step 1 – Schedule a project with all its activities at their normal duration as well as identify the critical path and critical activities Step 2 – Calculate the cost slope for the different activities and rank the activities in the ascending order of the cost slope Step 3 – Crash the activities on the critical path as per the ranking, i.e., activity having lower cost slope would be crashed first to the maximum extent possible Step 4 – As the critical path duration is reduced by crashing in Step 3, other paths may also become critical, i.e., we get parallel critical paths. This means that the project duration can be reduced duly by simultaneous crashing of activities in the parallel critical paths Step 5 – Crashing as per Steps 3 and 4, one reaches a point when further crashing is either not possible or does not result in the reduction of crashing of project duration Step 6 – Compute the total project cost by adding corresponding fixed cost to the direct cost, which is obtained by adding the crashing cost cumulatively to the normal cost

Q.3 Explain the importance of business forecasting. List & explain the steps in the PERT planning process. Ans: Because of the variation of the economic and business conditions over time, managers must find ways to keep abreast of the effects that such changes will have on their organizations. One technique which is very much useful in planning for the future needs is the forecasting. Although numerous forecasting methods have been devised, they all have one common goal – to make

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predictions of the future events so that the projections can then be incorporated into the planning and strategy process. The need for forecasting encompasses the modern society. Forecasting is highly essential in our modern society to take necessary precautionary action. For example, officials in government must be able to forecast such things as unemployment, inflation, industrial production, and expected revenues from personal and corporate income taxes in order to formulate policies. Marketing executives of a large retailing corporation must be able to forecast product demand, sales revenues, consumer preferences, inventory and so on, in order to make timely decisions regarding current and future operations and to assist in strategic planning activities. The directors of an airline must be able to fill equipment and personnel needs based on forecasts of the number of passengers and revenues. Administrators of a college or university must make forecasts of student enrolments and consider the trends in curricula that are based on technological developments in order to plan for the construction of dormitories and other academic facilities, plan for student and faculty recruitment, and make assessments of other needs. There are two common approaches to forecasting – qualitative and quantitative. Qualitative forecasting methods are especially important when historical data are unavailable. Qualitative forecasting methods are considered to be highly subjective and judgmental. Quantitative forecasting methods make use of historical data. The goal of these methods is to study what has happened in the past in order to better understand the underlying structure of the data and thereby provide a way of predicting future values. Quantitative forecasting methods can be subdivided into two types – time-series and casual. Time-series forecasting methods involve the projection of future values of a variable based entirely on the past and present observations of that variable. For example, the daily closing prices of a particular stock on the New York Stock Exchange constitute a time series. Other examples of economic or business time series are the monthly publication of the Consumer Price Index, the quarterly statements of gross domestic product (GDP), and the annually recorded total sales revenues of a particular company. Casual forecasting methods involve the determination of factors that relate to the variable to be predicted. These include multiple regression analysis with lagged variables, econometric modelling, leading indicator analysis, diffusion indexes, and other economic barometers. Steps in the PERT Planning Process PERT planning involves the following steps – 1. Identification of the specific activities and the milestones

2. Determination of the proper sequence of the activities 3. Construction of a network diagram 4. Estimation of the time required for each activity 5. Determination of the critical path 6. Updating of the PERT chart as the project progresses 1. Identification of the Specific Activities and Milestones The activities are the tasks that are required to be completed in the project. The milestones include 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 the sequence and duration. 2. Determination of the Activity Sequence This step may be combined with the activity in the identification step since the activity sequence is evident for some tasks. Other tasks may require more analysis in order to determine the exact order in which they must be performed.

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3. Construction of the Network Diagram Using the activity sequence information, a network diagram can be drawn showing the sequence of the serial and parallel activities. For the original activity-on-arc model, the activities are depicted by arrowed lines and milestones are depicted by circles of ‘bubbles’. Manual drawings may require several drafts for correct portrayal of the relationships among the activities. Software packages simplify the step by automatically converting the tabular information into a network diagram. 4. Estimation of the Activity Times Weeks or days are 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 times. For each activity, the model usually includes three time estimates – Optimistic time – Generally optimistic time represents the shortest time in which the activity can be completed. It is the common practice to specify optimistic times to be three standard deviations from the mean so that there is approximately a 1% chance that the activity will be completed within the optimistic time. Most likely time – Most likely time is the completion time having the highest probability. This time is different from the expected time. Pessimistic time – The pessimistic time is the longest time that an activity might require. Three standard deviations from the mean are commonly used for the pessimistic time. PERT assumes a beta probability distribution for the time estimates. For the beta distribution, the expected time for each activity can be approximated using the following weighted average – Expected time = (Optimistic + 4 X Most likely + Pessimistic) / 6 This expected time may be displayed on the network diagram. To calculate the variance for each activity completion time, if three standard deviation times were selected for the optimistic and pessimistic times, then there are six standard deviations between them, so the variance is given by – [(Pessimistic – Optimistic)/6]2. 5. Determination of 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. If activities outside the critical path speed up or slow down (within limits), the total project time does not change. The amount of time that a non-critical path activity can be delayed without delaying the project is referred to as slack time. If the critical path is not immediately obvious, it may be helpful to determine the following four quantities for each activity –

ES – Earliest Start Time EF – Earliest Finish Time LS – Latest Start Time LF – Latest Finish Time

These times are calculated using the expected time for the relevant activities. The earliest start and finish times of each activity are determined by working forward through the network and determining the earliest time at which an activity can start and finish considering its predecessor activities. The latest start and finish times are the latest times that an activity can start and finish without delaying the project. LS and LF are found by working backward through the network. The difference in the latest and earliest finish of each activity’s slack. The critical path then is the path through the network in which none of the activities have slack. The variance in the project

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completion time can be calculated by summing the variances in the completion times of the activities in the critical path. Given this variance, one can calculate the probability that the project will be completed by a certain date assuming a normal probability distribution for the critical path. The normal distribution assumption holds if the number of activities in the path is large enough for the central limit theory to be applied. Since the critical path determines the completion date of the project, the project can be accelerated by adding the resources required to decrease the time for the activities in the critical path. Such a shortening of the project sometimes is referred to as project crashing. 6. Updating of the PERT chart as the Project Progresses Adjustments in the PERT chart are to be made as the project progresses. As the project unfolds, the estimated times can be replaced with the actual times. In cases where there are delays, additional resources may be needed to stay on schedule and the PERT chart may be modified to reflect the new situation.

Q.4 What do you understand by a decision tree. Write a short note on project crashing using network analysis. Ans: A Decision tree (or tree diagram) is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs and utility. Decision trees have vast applications in operations research and decision analysis for identifying a strategy most likely to reach a specific goal. It is widely used for project policy decision making. Another use of decision tree is as a descriptive means for calculating conditional probabilities. A decision tree analysis is a specific technique in which a diagram (decision tree) is used for the purposes of assisting the project leader and the project team in making a difficult decision. The decision tree is a diagram that presents the decision under consideration and, along different branches, the implications that may arise from choosing one path or another. The decision tree analysis is often conducted when a number of future outcomes of scenarios remains uncertain, and is a form of brainstorming which, when decision making, can help to assure all factors are given proper consideration. A decision tree is a logical model represented as a binary (two-way split) tree that shows how the value of a target variable can be predicted by using the values of a set of predictor variables. It can be described as an algorithm or a formal step-wise process used in coming to a conclusion or making a judgment. An example of the decision tree is shown below –

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Figure 1: Decision Tree on choosing between two productsFigure 1 describes a decision tree for choosing between two products X and Y. A company has to decide upon development of two products X and Y. They can develop only one product at a time. For developing the product X, they have to make an initial investment of INR 2 Lakh, whereas for developing the product Y, they have to make an initial investment of INR 3 Lakh. Now as per the decision tree, in case of opting the product X, there is probability of 0.7 that the return in one year will be INR 1 Lakh and there is probability of 0.3 that the return will be INR 3 Lakh. Now, if the product Y is opted, there is probability of 0.4 that the return will be INR 2 Lakh after a year and there is probability of 0.6 that the return will be INR 3 Lakh after a year. Now, after analyzing the decision tree, it is possible to get an insight of the future prospects (expected returns) of both the products and accordingly it is possible for the company to choose the most profitable product for development. Project Crashing as in question 6 of assignment set 1

Q.5 Describe in brief the various pages of the task information form in the MS Project software.Answer:- Task entry is the main activity in setting up a new project. The tasks which have been identified at the Design Stage must be entered in this stage. The system will hold task information in a task database, which we cannot access directly but is used by the system whenever we view task data. This is one of the two databases the system uses and the other is the resource database. It is important to understand that the system checks the data that it holds and where the data does not cross check then the system will generally update the database to make it right. It is important to keep an eye on this process; this will be discussed in a later section. As each entry is made, the system will update the appropriate data and views to reflect the entries. The order of entry should be in the logical progression but this is not essential as it can be changed. Normal Task entry will be by using the standard Task Sheet. The Gantt View shows the Gantt Chart in the right part of the window with the Task Sheet in the left part.

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Figure 2: Task Information Box / Task Sheet (General Section) The task sheet is a view of the selected task with information shown in the columns as follows: ID: The Task Identification number. Name: The Name of the Task. Duration: The time the Task will take including the time

units. Start Date: This is the current Scheduled Start date for the

Task. Not the Planned or Actual Start. Finish Date: The Scheduled Finish date. Predecessors: The ID numbers for the preceding Tasks that

are linked to this Task. Resources: The names of the resources performing or used

in the Task. Table 1: Information in the Task Sheet

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Figure 3: Task Information Sheet (Predecessors Section)Task Entry Form One can select the Task Entry view to see the Gantt Chart in the upper pane and the Task Form in the lower pane. To do this, you have to choose View, More Views, Task Entry. From the Task Sheet the following entries can be made. ID: The Task Identification number. Task Name: The Name of the Task. Duration: The time the Task will take including the time units. As the entries are made, the Gantt Chart will automatically be updated to display the tasks. If someone is using the Task Form, it is possible for him/her to enter and/or view the following: Name: The name of the task Duration: The length of time the task will take and the units of time. Fixed: A check box to specify the start date to be fixed. Start: The scheduled start date, if this is not entered the system will calculate it from the data entered and the relationships defined. Finish: The scheduled finish date, entered or calculated as above. % Complete: A measure of the completion of the Task if it has been started. Tables and Descriptions Resource Table ID: The identification number of the Resource Resource Name: The name of the resource. Units The number of units available for the resource.

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Work The amount of work currently assigned to the resource. Predecessor Table ID The identification number of the Predecessor. Predecessor Name: The name of the Predecessor. If this is not entered the system will look it up using the ID number. Type: The relationship with the current Task which will be FS, or SS, or FF. Lag The time delay between the end of the Predecessor the start of the Successor. Completion of all the fields at entry time is not necessary as more information is added so the system will update the boxes. It is only necessary to enter the data that has been determined in the design stage. In order to enter task descriptions and durations one cell at a time:

In the Task Name column, select the first available cell and type the name of the task. Press TAB In the Duration column, type the value of the duration. If the duration is anything other

than days, type m for minutes, h for hours, or w for weeks. Press ENTER Press LEFT ARROW to return to the Task Name column and repeat steps 1 through 4 as

required.

Entering task descriptions and durations by selecting a range:

Select the first cell (the numbered cell) of the desired range. Drag the mouse through the range of cells you want to include. In the first cell, type the desired information. Press TAB In the Duration column, type the appropriate information. Repeat steps 4 and 5 as required.

It is possible to move to the previous cell without deselecting the range through pressing SHIFT+TAB. Clicking the mouse inside or outside the range will deselect the range.

Q.6. Describe how you can change the duration of a project task

Answer:-

Changing Duration The default duration is 1day. To change this one can simply overtype with the new value.

Change the durations for each Module to 2d. When the Wizard appears READ THE INFORMATION then click on the OK button. Select all the remaining tasks. Open the Task information box. Set the duration to 1.5d