Quantitative Methods in Project Management

PM 0015

Name: Aju K Panicker

Roll number: 530911171

Learning centre: 2542

Assignment No.: Set 1

Date of submission at learning centre: 10/ 07/2011

Q.1 Describe the process of setting up of a common resource.

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.

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

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

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

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

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

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, however complex your project may be, you can vary only information

regarding tasks or resources. The information you provide is fed into the “Black Box” or

algorithm, 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.

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’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

slackis 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

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

ALAPRefers to a task that should be started ‘As Late As Possible’, using all the free-float time available.

ASAPUsed 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 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 PathThe sequence of tasks or activities whose schedules and durations directly affect the date of overall project completion.

Earned ValueThis 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 TaskA 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.

LagThe amount of time between the finish of a predecessor task and the start of a successor task.

LeadThe 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.

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

Negative floatRefers 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.

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

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

ResourceAny 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.

SuccessorIn 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.

1. 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

 (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

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.

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 Charts

A Workbreakdown 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 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 Autoregressive Model

Steps involved in Autoregressive Model

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.

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.

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.

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 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.

Figure 2.3 (a): Minimum-Span Problem Example 1

Figure 2.3 (b): Minimum-Span Problem Example 1

Figure 2.3 (c): Minimum-Span Problem Example 1

Figure 2.3 (d): Minimum-Span Problem Example 1

Figure 2.3 (e): Minimum-Span Problem Example 1

 Shortest-Route Problems

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.