PM0015 - Quantitative Methods - Set1

8/3/2019 PM0015 - Quantitative Methods - Set1

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Master of Business Administration-MBA Semester 4Project ManagementPM0015 - 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.Ans. It is very much essential to use some common resources for multiple numbers of projects. When we have

several projects running using a common pool of staff, it is essential that the user is aware of any conflict

arising due to a staff member being assigned to conflicting tasks or unavailable due to other commitments in

some other project.

MS Project allows us to set up our project so that we share resources and can be warned of any such conflict.

One of the easiest ways is to set up a Staff project and add non-project tasks to this. Any new project created

will use the resources of this and show over assignments if these occur.

Setting up of a Resource Project

Set up a new project entering only items which are notrelevant to any of your main projects. For example,Training Course etc.

Save as Staff.MPP. Open project CDEV.MPP. Select Tools, resources, Share Resources.

Setting up of a Resource Project

Select Staff.MPP as the file.

Check for any resource over allocations.Addition of Sub ProjectsWhen you have very a large project to manage, it may be useful to have some parts split into one or more sub

projects. These can be inserted into the main project at the appropriate point. This will reduce the effort of

managing the whole project to a considerable extent.This can also be used where some steps in the project are repeated.

Inserting projects into MS Projects

By inserting individual project files into an existing project, it is possible to view, print, or change information

for the projects for which someone is working with as though they were a single project.

View Bar, click Gantt Chart .

be

inserted at any level of the outline.

you cannot find the project in the folder list, you can search for it.


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-click the inserted project as if it was a task. Now change the inserted project options youwant.

Inserting Project in MS Project

Link to

Project check box. By default, this option is selected.

the Read

Only check box. By default, this option is cleared.

Hide

Subtasks check box. By default, this option is selected. You can also choose to hide or show tasks after you've

inserted the project.

CTRL as you click each project.

After a project has been inserted, it is possible to quickly show an inserted projects hidden subtask by clickingthe summary tasks outline symbol. Outline symbols indicate whether a summary task has subtasks displayedor does not have subtasks displayed.

Creating and Adding a Sub Project

CD Sub Project_1.MPP.

insert CD Sub Project.MPP_1 as a sub project.

Q.2 Write a short note on MS projects and explain in brief some of the important terminologies used in

MS Project.9.3 Basics of MS Project


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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.

Chart Views Gantt Chart

Network Diagram

Resource Graph

Forms contain the data relevant to a single specific task or resource.

Form Views Task View

Resource Form

Sheets are a table of all the Tasks or all the Resources that are part of the Project.

Sheet Views Task Sheet

Resource Sheet

The above can be displayed separately or in any combination of two, for example,

Combinations View Task Entry View

Top Half Gantt Chart

Bottom Half Task Form

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.

The Input/Output Model

In 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 provideyou with a schedule in the form of a Gantt chart, Network Diagram Chart, or Resource Graph. In summary, the


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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.

Clarification of Project Management Terminologies

In 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 sfocus 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. Inthe 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 tasks dates or the project finish date. Free slackis theamount of time Task A can be delayed before affecting the start time of Task B, and total slackis the amount of

time that Task A can be delayed before affecting the finish date of the project. The summary tasksummarizes

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

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-floattime available.

ASAP Used to indicate a task that should be started As Soon As Possible, taking intoaccount 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 values to actuals, and

facilitates the tracking and analysing of a projects 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 projects performance, and is calculated by multiplying a tasksplanned 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 tasks 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 aspreadsheet section to the left of the Gantt chart to display additional information.


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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 whats available in your project management

application and whats 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.

Project

Manage-ment

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

Levelling

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.


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Q.3. Describe the time series forecasting with the help of autoregressive modeling. What do you

understand by managing cash flow?Autoregressive modeling is another approach in forecasting with the annual time-series data. 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.

After the model is selected and the least-squares regression methods are used to obtain estimates of the

parameters, the next step is to determine the appropriateness of this model. Either it is possible to select a

particular p-th order autoregressive model based on previous experiences with similar data, or as a starting

point, it is also possible to choose a model with several parameters and then to eliminate the parameters that do

not contribute significantly. In the latter approach, a t-test for the significance of Ap, the highest orderautoregressive parameter in the current model under consideration, is used. The null and the alternative

hypothesis are as followsH0: Ap = 0

H1: Ap 0The test statistic of t-Test for Significance of the Highest-order Autoregressive Parameter Ap is the following -

Where

Ap = hypothesized value of the highest-order parameter Ap in the regression model

ap = the estimate of the highest-order parameter Ap in the regression model

= the standard deviation of ap paS

And the test statistic t follows a t-distribution having n-2p-1 degrees of freedom.

8.6 Managing Cash FlowManaging 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, andtravel expenses, for example.

The key to managing cash flow is to ensure that cash comes in faster than it goes out. If sufficient cash isntavailable 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 moneythe interest. The flowof cash coming in from the customer can be controlled by the terms of payment in the contract. From the

contractors point ofview, its 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 thefollowing:

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.

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.

The worst scenario from the contractors point of view is to have the customer make only one payment at theend of the project. In this situation, the contractor will need to borrow money to have cash available to meet

expenses throughout the project.


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

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.

12.2 Displaying of DataThere are several ways for displaying the data. Gantt Chart as well as Network Diagram Chart are two

important tools by which it is possible to display project data.

Gantt ChartThe Gantt Chart is a horizontal bar chart that represents each task in the time scale of the project. Each task

entered in the project will be shown.

The Gantt Chart can be used to visually keep track of the tasks and also may be used to identify importantpoints about each task. Those tasks that together control the completion date are known as the critical Path and

are shown differently to highlight that fact.

Gantt Charts can be printed and therefore these form the significant part of a regular report which shows the

current progress, comparison with the original plan, and the new projected completion data.

Changing the split between chart and tableWhen the Gantt Chart view or the Task Entry view is selected, the Gantt Chart area has part of a table on the left

and the bars on the right.

It is possible to move the dividing line between these two areas with the mouse pointer. When the pointer is on

the dividing line, it changes to two vertical lines with left and right arrows. If the left button is held down then

the dividing line can be moved to the left or right as required.

Changing Time ScaleIt is possible to change the time scale on the right side of the chart directly by using the View, Zoom command

or with the Format, Timescale command.

Where the latter is chosen, the dialog box will provide the ability to change both the major and minor time

scales and within each of these it will be possible to alter the units, the label, the alignment, and the count of the

interval between the unit labels.

Changing the PaletteThe Palette can be accessed from the Format, Bar command or by double clicking on the Gantt Chart.

Using the dialog box, it is possible to maximise the information provided by the format of the bars on the Gantt

Chart. The appearance of the existing bars can be changed and additional bars can be used. The full use of

colour is also possible.


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Figure 12.1: Format BarFor example it is possible to show the planned, actual and scheduled times for each task.

Editing TasksOne method of editing tasks is changing them on the Gantt Chart using the mouse and dragging the changes

into place.

Positioning the pointer at the beginning of a bar will change the pointer to a % sign and if the left button is

pressed and the symbol dragged to the right a box will appear showing the amount of "percentage complete"

that has been added. This information will then be updated throughout the system.

If the pointer is placed in the centre of the bar it will change to a four-way arrow pointer. If the left button is

held down it is then possible to drag the bar to the left or right in time, the changing dates options will be shown

in a dialog box (see below) and, on clicking OK, the files will be updated with the new information.

Figure 12.2: Planning WizardThe third possibility is that the duration of the task can be changed by changing the length of the bar. If the

pointer is positioned at the right end of the bar it will change into a right pointing arrow. If the left button is held

down it is then possible to change the length of the bar and the respective change in duration is shown in a box.

Viewing the Gantt Chart

Gantt Chart from the View menu.

left or right.


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Format menu, select Timescale. Try changing the major and minor scales as view thechanges at the bottom of the box.

View menu, choose Zoom. Try out the various changes that can be made to the amount

seen.

Network Diagram ChartThe term Network Diagram is derived from Programme Evaluation and Review Technique which was

invented for the management of Projects by paper based systems. The Network Diagram chart is a

diagrammatic view of the tasks where the position of the task and the lines linking them together represent the

detailed steps that comprise the project. It is possible to modify the project in the Network Diagram by adding

extra tasks or nodes and creating the links. Each task on the chart is known as a node and within the node is a

selection of the data that is relevant to the task. The Nodes can have different boarders which represent the task

type.

Using the Format, Box Styles commandWithin this command box (shown below) there are many different types of Task, each of which can be given a

combination of line style and colour to provide visual identification, for example the critical tasks can have

thick red borders.

The Network Diagram view must be active in order to see the Box Styles as an option in the Format menu.


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Figure 12.3: Changing styles of Network Diagram Chart

Changing the contents of a NodeThe Data Template command in the Box Styles dialog allows change to the data that the node displays.

Figure 12.4: Changing data template of Network Diagram Chart

Setting the following is possible:

- on or off.

selection of the size of the Node - Small, Medium or Large.

Modifying the layout of the ChartThe Format, Layout command gives the ability to select how the interconnecting lines between the nodes will

be shown.


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Figure 12.5: Changing Layout of Network Diagram Chart

View the Network Diagram Chart

Network Diagram Chart from the View menu.

View, menu, select Zoom and change the size of the Nodes

Format menu, select Box Styles and examine the different style of borders that are

available to show different types of tasks.Boxes Tab.

Format menu, select Layout and examine the different ways the lines can be displayed.

Zoom to 50% or Entire Project you will find it

easier.

Zooming In and OutZooming in can be useful when you want to focus on a particular Network Diagram box or group of Network

Diagram boxes. Alternatively, zooming out can be helpful when you want to see as much of the project as

possible on one screen. The more you zoom out, the more clear the paths become and the more unclear the text

becomes.

To zoom in:

To zoom out:

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


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Steps involved in Autoregressive Model1. 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, thesecond variable lags by 2 time periods, and so on and the last predictor variable lags by p time periods.

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)

Pg140(133)/Pg 141(134)

Q.6. Write a short note on project crashing using network analysis.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 projectsometimes is referred to as project crashing.

4.3 Time-Cost Optimization AlgorithmThe 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 followingStep 1Schedule a project with all its activities at their normal duration as well as identify the critical path and

critical activities

Step 2Calculate the cost slope for the different activities and rank the activities in the ascending order of thecost slope

Step 3Crash the activities on the critical path as per the ranking, i.e., activity having lower cost slope wouldbe crashed first to the maximum extent possible

Step 4As 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 simultaneouscrashing of activities in the parallel critical paths

Step 5Crashing as per Steps 3 and 4, one reaches a point when further crashing is either not possible or doesnot result in the reduction of crashing of project duration

Step 6Compute the total project cost by adding corresponding fixed cost to the direct cost, which is obtainedby adding the crashing cost cumulatively to the normal cost

The following examples will be helpful to understand the time-cost optimization algorithm.

Example 1The following table gives data on normal time-cost and crash time-cost for a project

Table 4.1: Normal time-cost and Crash time-cost for a Project Example 1

Activity Normal Crash

Time (Days) Cost (`) Time (Days) Cost (`)

1 - 2 6 600 4 1000

1 - 3 4 600 2 2000

2 - 4 5 500 3 1500

2 - 5 3 450 1 650

3 - 4 6 900 4 2000

4 - 6 8 800 4 3000

5 - 6 4 400 2 1000

6 - 7 3 450 2 800

The indirect cost per day is INR 100.

i) Draw the network and identify the critical path.

ii) What are the normal project duration and associated cost?


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iii) Crash the relevant activities systematically and determine the optimum project completion timeand cost.

SolutionUsing the normal time distributioni) Resulting network with earliest and latest occurrence times at various nodes are as shown in Figure

4.4.

Figure 4.4: Example 1 Problem DiagramAs per the Critical Path Method

ii) The normal project duration is 22 days. The associated total cost will be as follows

Direct Cost = ` (600 + 600 + 500 + 450 + 900 + 800 + 400 + 450) = ` 4700

Indirect Cost = ` 100 X 22 = ` 2200

Total Cost = ` 6900

iii) For the optimum cost schedule, we first compute the cost slope (incremental cost of crashing) as

follows

Critical Activity Crash Cost Slope

1 -- 2 (1000-600)/(6-4) = 200

2 -- 4 (1500-500)/(5-3) = 500

4 -- 6 (3000-800)/(8-4) = 550

6 -- 7 (800-450)/(3-2) = 350

Table 4.2: Critical Activity and Crash Cost Slope Example 1Crashing of Activities - Since the activities lying on the critical path control the project duration, we crash the

activities lying on the critical path.

Step 1Activity (1, 2) on the critical path gives the lowest cost-slope. Therefore, we shall crash this activity byone day at an additional cost of ` 100 X 1 = ` 100

Figure 4.5: Example 1 Problem DiagramWith crashing activity 12, the total project cost corresponding to 21 days = ` 4700 + ` 200 X 1 + ` 100 X 21= ` 7000.

Step 2In the network given in Figure 4.5, there are two parallel critical paths, namely,

Figure 4.5: Example 1 Problem DiagramWith crashing activity 12, the total project cost corresponding to 21 days = ` 4700 + ` 200 X 1 + ` 100 X 21= ` 7000.

Step 2In the network given in Figure 4.5, there are two parallel critical paths, namely,


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Now the least cost slope is for activity 67, therefore we shall crash this activity by one day and then crashactivity (4, 6) by four days. The additional cost will be` 350 X 1 + ` 550 X 4, i.e., ` 2550

Figure 4.6: Example 1 Problem DiagramWith crashing of activities 46 and 67, the total project cost corresponding to 16 days will be equal to` 7000 + ` 2550` 100 X 5 = ` 9050.Step 3We now crash activities 12 and 34 by one day each at additional cost of ` 550 1 + ` 200 1, i.e.,` 750. Next, we crash activities 24 and 34 by one day each at additional cost of ` 500 1 + ` 550 1, i.e.,

` 1050.

Figure 4.7: Example 1 Problem DiagramIn the network in Figure 4.7, after crashing the activities (1, 2) by one day, (2, 4) by one day and (3, 4) by two

days, the total project cost corresponding to 14 days is equal to

` 9050 + ` 750 + ` 1050` 100 2 = ` 10650.Step 4Next we crash activities (1, 3) and (2, 4) by one day each at additional cost of 700 1 + 500 1, i.e.,

` 1200.

Figure 4.8: Example 1 Problem diagramAfter crashing activities (1, 3) and (2, 4), the total project cost corresponding to 13 days = ` 10650 + ` 1200`

100 1 = ` 11750.

Figure 4.8 shows the three critical paths:


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Also, no further crashing being possible, the minimum duration of the project is 13 days with associated cost of

` 11750.

Documents

PM0015 - Quantitative Methods - Set1