#### 1 INTRODUCTION

1.1 Background:

A project is a set of tasks, arranged in a defined sequence or relationship, that produce a pre-defined output or effect. A project always has a start, middle and an end. When "projects" are big, important and costly, limited time and resources are available to accomplish goals. Sometimes the projects are risky. This is where Project Management comes in. Project Management can help guide efforts and provide effective outcomes. Project Management tools and techniques, enable to function with speed, affordability and complexity.

1.2 Motivation:

Project Management is a set of principles, methods, tools and techniques for planning, organizing, staffing, directing and controlling of related activities to achieve an objective with time, cost and performance constraints.

Project Management function primarily involves Planning, Monitoring and Controlling. These involve estimating, scheduling, tracking progress and implementing corrective action wherever needed. Effective project management reduces the risk of failure and increases the probability of success. An efficient Project Management software provides the Project Managers, the ability of interfacing with management and giving them a proper appreciation of the state of the project and ensuring that they can make appropriate resource allocation decisions that involve time, people and money.

Hence as learners of Industrial and Production and Mechanical Engineering we find it challenging and interesting field to work in and contribute.

1.3 Challenges:

There are no hard and fast rules or techniques evolved that can be used to tackle all the problems in this area. Different organizations may have conflictive objectives therefore unique solutions are required for each individual organization. It is also a dynamic system involving uncertainties and inter-dependencies of time and cost parameters for various activities in a Project, making it difficult to determine the most effective strategy.

1.4 Scope of the Project:

This project aims at reviewing the major decisions in the life cycle of a project - from project identification, to appraisal, to selection, to planning and finally implementation. A software project module has been developed for many of the major decisions in the project life cycle.

The purpose of developing these modules is to

· provide convenient computational packages to handle the routinely encountered problems in project management.

· assist in laboratory experimentation with varying project parameters to gain insights into solutions and algorithms.

· solve a real life case study with actual data which might be difficult to handle manually.

The software has been developed for a genre of projects where the user is able to provide input in the form of precedence relationships, time, cost and resource requirements of the activities for the project.

2 PROBLEM FORMULATION

2.1 Problem statement:

The project undertaken here is to develop different modules and integrate them into a software package that can assist various Project Management activities and operations. This involves analyzing different models and solutions available for operations such as Project Appraisal, Project Selection, Scheduling, Cost Analysis and Resource Allocation that are involved in various stages of Project Management. Learning and applying the techniques such as SAW, TOPSIS, PERT, CPM and other Project Management tools used for analyzing and decision making. Developing programs that can be used as Laboratory exercises for better understanding of the subject. Finally, validating the developed software with Industry examples and Case Studies.

As follows the title of the project is “Project Management: Software Development and Applications”.

2.2 Outline of the approach adopted

The project life-cycle which typically consists of the following stages was used to identify and select problems for the contemplated Project Management software.

· Project Identification and Screening

· Project Appraisal

· Project Selection

· Basic Scheduling

· Monitoring and Control

· Resource Scheduling

· Project Implementation

#### 3 LITERATURE REVIEW

3.1 Project Management

Project Management is a set of principles, methods, tools, and techniques for the planning, organizing, staffing, directing and controlling of related activities to achieve an objective with time, cost and performance constraints. Project Management function primarily involves Planning, Monitoring and Controlling. These involve estimating, scheduling, tracking progress and implementing corrective action wherever needed.

3.2 Project Life Cycle

The project planning process consists of the following:

i. Setting the project start date.

ii. Setting the project completion date.

iii. Selecting the project methodology or project life cycle to be used.

iv. Determining the scope of the project in terms of the phases of the selected project methodology or project life cycle.

v. Identifying or selecting the project review methods to be used.

vi. Identifying any predetermined interim milestone or other critical dates which must be met.

vii. Listing tasks, by project phase, in the order in which they might be accomplished.

viii. Estimating the personnel necessary to accomplish each task.

ix. Estimating the personnel available to accomplish each task.

x. Determining skill level necessary to perform each task.

xi. Determining task dependencies

1. Which tasks can be done in parallel?

2. Which tasks require the completion of other tasks before they can start?

xii. Project control or review points.

xiii. Performing project cost estimation and cost-benefit analysis.

3.3 Network Definitions

Before studying the development of network, it is essential to have an idea about the basic concepts and terms involved in the technique as explained below:

3.3.1 Project: It is a task with defined objective.

3.3.2 Network: A network is a graphic representation of all activities and events that must be completed to reach the end objective of a project, showing the planned sequence of their accomplishments, their precedence relationships and interdependencies. Thus the basic components of a network are events and activities.

3.3.3 Event: An event is a specific accomplishment, physical or mental, in a project. The main characteristics of an event are.

- It is recognizable at a particular instant of time, which is a point in time and not a passage of time.
- It does not, therefore, consume time or resources.
- It is represented on a network by a geometrical figure such as a circle.
- It expresses a state of being, such as: contract awarded, project approved, plant commissioned etc.

3.3.4 Activity: An activity represents a job or a project element to be completed. It is a relationship between two events and usually devotes the efforts required to perform a task measured in terms of elapsed time. The characteristics of an activity are:

- It usually consumes time and resources.
- It is represented on the network by an arrow, the direction of arrow indicating the sequence in which the events are to occur.
- It must be independent i.e. each arrow is used to represent exactly one, and only one, operation of segment of an overall programme.
- It indicates works, such as: preparation of decision, scrutiny of tenders, etc.

3.3.5 Predecessor Event: An event which restricts or precedes another. It establishes the starting point of an activity.

3.3.6 Successor Event: An event which succeeds another. It establishes the termination point of an activity.

3.3.7 Objective Event: An event which has no successor event. It is the goal of the project and usually has a committed date.

3.3.8 Activity Duration: The time required to perform an activity on a network is termed as activity duration. It is the time estimated for performing that activity. It is desirable that the time estimates of an activity should be :

- made by personnel most familiar with the individual activities and responsible for their accomplishments
- based on normally available and expected resources, and
- expressed in suitable times such as days/weeks.

3.4 Constructing the Network

The first step is to determine the end objective. Next, the major areas of endeavor that will contribute to the accomplishment of the plan must be determined.

The major activities that lead to the end activity are then identified and listed. After this the following procedure is adopted.

· Write the description of the end objective near the right margin of a large piece of paper, centered vertically.

· Determine which major activities must be completed just prior to the completion of the objective, and write them to the left of the last activity.

· Indicate, by drawing a line, the work to be done between the events.

· Determine which activities must be completed prior to the accomplishment of each of the activities listed and record them and their associated activities, another step to the left.

· Report the process till the first activity is reached. Layout the network so that all activity lines flow from left to right. They may cross one another as long as they can be followed easily.

· When the network has been laid out, assign even number starting with the beginning event in the order in which they must be completed.

3.5 Rules for Network Development

· No event can occur until all the activities leading into that event have been completed.

· An activity succeeding an event cannot be started until that event has occurred.

· There should not be any close loop in the network, that is, an event cannot occur more than once.

· Activity lines cannot be drawn from the middle of other activity. If it is necessary to start an activity from the middle, one must define the exact point at which the second activity starts. An event is placed at this point, and this event may initiate the desired activity.

· All activity heads should be marked with an arrow to indicate the direction of flow.

· All events should be numbered and so this number should be unique, as to give an activity reference.

· All activities should have unique reference number, i.e. between two events there should be only one activity.

· In a network, flows are from left to right, that is , activity lines with arrow heads that point to the left should be avoided.

· There should be only one initiating event and one objective event, thus every activity on the networks should be completed to reach the end objective work. Hanging activities are not permissible.

3.6 Dummy Activities

Dummy activities are activities which consume no resource or time. They are used:

i. To maintain the logic in the network diagram.

ii. To show interdependencies between events, and

iii. To give a unique number or activity reference to an activity.

Dummies are also often used to tie the completion of several activities to the beginning of a single activity or vice versa.

3.7 Topological Ordering

The activities of the project are ordered in such a manner that no activity appears in the list before all its predecessor activities have been considered. Hence activities are ordered according to the lower preceding node number first.

3.8 Scheduling Computation

The basic scheduling computation consists of three distinct sequences:

i. The forward pass through the network,

ii. The backward pass through the network,

iii. Calculation of slack or float and determination of critical path.

3.9 Forward Pass Computation

The forward pass through the network is made by computing the earliest expected occurrence dates for every other event and the earliest completion dates for the activities. In case there is more than one activity merging at a point, the maximum of the completion times is taken as the earliest completion time. Starts should be chosen as it fulfills the condition that no activity can begin until all its constraining activities are complete. The forward pass procedure proceeds event to event along each node of the network until the end event has been reached. The expected duration time will be longest sequence of activities through the network i.e. the earliest completion time of the last event.

3.10 Backward Pass Computation

The planner establishes the latest allowable occurrence date for each event (TL) and latest allowable start at completion date for the event. In the backward pass the planner employs the path tracing procedure characteristic of the forward path in reverse starting with the last event and proceeding backwards along each path to the baseline or the beginning event.

In the backward pass a latest allowable occurrence time is set for the end event corresponding to the scheduled or expected completion date for the project. In the absence of a scheduled end later the earliest expected completion date is automatically set as the latest allowable date.

3.11 Slack Computation

Slack is defined as the difference between an earliest possible occurrence time for an event and its latest allowable occurrence time. This difference expressed in time units indicates how the occurrence of the event can be delayed without delaying the end event in the network.

3.12 Identification of Critical Path

Once we have determined the slack values attached to various events and activities in the network, the critical path is identified. Critical path can be defined as the longest sequence of activities leading to the end objective. It is the path with the lowest slack value. When a network contains negative slack, the path with the most negative slack is identified as the critical path.

There are many types of slack defined in literature but the two most important ones are Total Slack and Free Slack.

Total Slack: It is the amount of time an activity could be delayed without affecting the overall project duration.

Free Slack: It is the amount of time an activity could be delayed without delaying subsequent activities. It is equal to the difference between the earliest start time of the successor activity and the early finish time of the activity in question.

3.13 The Problem of Uncertainty

The project network is the basis of both the PERT and the CPM technique. The notions of the critical path and activity slack are common to each. But these models were developed independently and in somewhat distinct problem settings.

PERT was developed for and has been used most frequently research and development types of programmes. The technologies are rapidly changing and their products are nonstandard. CPM on the other hand, has most frequently been applied to construction projects. The activities in these projects use standard materials whose properties are well known. They employ long-developed and well-seasoned components, and they are based on a more or less stable technology. The PERT technique assumes that the activities and their network relationships have been well defined, but it allows for uncertainties in the activity times.

3.14 Work breakdown Structures

The development of a project plan is predicated on having a clear and detailed understanding of both the tasks involved, the estimated length of time each task will take, the dependencies between those tasks, and the sequence in which those tasks have to be performed. Additionally, resource availability must be determined in order to assign each task or group of tasks to the appropriate worker.

One method used to develop the list of tasks is to create what is known as a work breakdown structure.

A work breakdown structure (WBS) is a hierarchic decomposition or breakdown of a project or major activity into successive levels, in which each level is a finer breakdown of the preceding one. In final form a WBS is very similar in structure and layout to a document outline. Each item at a specific level of a WBS is numbered consecutively (e.g., 10, 10, 30, 40, 50). Each item at the next level is numbered within the number of its parent item (e.g., 10.1, 10.2, 10.3, 10.4).

The WBS may be drawn in a diagrammatic form (if automated tools are available) or in a chart resembling an outline.

The WBS begins with a single overall task representing the totality of work to be performed on the project. This becomes the name of the project plan WBS. Using a methodology or system life cycle (analysis, design and implementation) steps as a guide, the project is divided into its major steps. The first phase is project initiation; the second major phase is analysis, followed by design, construction, testing, implementation, and post-implementation follow-up. Each of these phases must be broken in their next level of detail, and each of those, into still finer levels of detail, until a manageable task size is arrived at.

The first WBS level for the life cycle would be as shown in Table 3.1

WBS number | Task Description
1.0 | Project initiation
1.1 | Draft project plan
2.0 | Analysis phase
2.1 | Plan user interviews
2.2 | Schedule users interviews
3.0 | Examination and test
4.0 | Design
5.0 | Test
6.0 | Implementation
7.0 | Post implementation review

Table 3.1 First WBS level for life cycle

Tasks at each successively finer level of detail are numbered to reflect the task from which they were derived. Thus, the first level of tasks would be numbered 1.0, 2.0, 3.0, and so forth. Each of their subtasks would have a two part number: the first part reflecting the parent task and the second part, the subtask number itself, such as 1.1, 1.2, or 1.3. As each of these, in turn, decomposed or broken down into its component tasks, each component receives a number comprised of its parent number plus a unique number of its own.

A manageable task is one in which the expected results can be easily identified; success, failure, or completion of the task can be easily ascertained; the time to complete the task can be easily estimated; ant the resource requirements of the task can be easily determined

3.15 Program Evaluation and Review Technique (PERT)

Program evaluation and review technique (PERT) charts depict task, duration, and dependency information. Each chart starts with an initiation node from which the first task, or tasks, originates. If multiple tasks begin at the same time, they are all started from the node or branch, or fork out from the starting point. Each task is represented by a line which states its name or other identifier, its duration, the number of people assigned to it, and in some cases the initials of the personnel assigned. The other end of the task line is terminated by another node which identifies the start of another task, or the beginning of any slack time, that is, waiting time between tasks.

Each task is connected to its successor tasks in this manner forming a network of nodes and connecting lines. The chart is complete when all final tasks come together at the completion node. When slack time exists between the end of one task and the start of another, the usual method is to draw a broken or dotted line between the end of the first task and the start of the next dependent task.

A PERT chart may have multiple parallel or interconnecting networks of tasks. If the scheduled project has milestones, checkpoints, or review points (all of which are highly recommended in any project schedule), the PERT chart will note that all tasks up to that point terminate at the review node. It should be noted at this point that the project review, approvals, user reviews, and so forth all take time. This time can never be underestimated when drawing up the project plan. It is not unusual for a review to take 1 or 2 weeks. Obtaining management and user approvals may take even longer.

When drawing up the plan, it has to be made sure to include tasks for documentation writing, documentation editing, project report writing and editing, and report reproduction as these tasks are usually time-consuming.

PERT charts are usually drawn on ruled paper with the horizontal axis indicating time period divisions in days, weeks, months, and so on. Although it is possible to draw a PERT chart for an entire project, the usual practice is to break the plans into smaller, more meaningful parts. This is very helpful if the chart has to be redrawn for any reason, such as skipped or incorrectly estimated tasks.

Many PERT charts terminate at the major review points, such as at the end of the analysis. Many organizations include funding reviews in the projects life cycle. Where this is the case, each chart terminates in the funding review node.

Funding reviews can affect a project in that they may either increase funding, in which case more people have to be made available, or they may decrease funding, in which case fewer people may be available. Obviously more or less people will affect the length of time it takes to complete the project.

3.16 PERT chart

A PERT chart is a project management tool used to schedule, organize, and coordinate tasks within a project. PERT stands for Program Evaluation Review Technique, a methodology developed by the U.S. Navy in the 1950s to manage the Polaris submarine missile program. A similar methodology, the Critical Path Method (CPM), which was developed for project management in the private sector at about the same time, has become synonymous with PERT, so that the technique is known by any variation on the names: PERT, CPM, or PERT/CPM.

Fig 3.1 PERT chart

A PERT chart presents a graphic illustration of a project as a network diagram consisting of numbered nodes (either circles or rectangles) representing events, or milestones in the project linked by labeled vectors (directional lines) representing tasks in the project. The direction of the arrows on the lines indicates the sequence of tasks. In Figure 3.1 the tasks between nodes 1, 2, 4, 8, and 10 must be completed in sequence. These are called dependent or serial tasks. The tasks between nodes 1 and 2 and nodes 1 and 3 are not dependent on the completion of one to start the other and can be undertaken simultaneously. These tasks are called parallel or concurrent tasks. Tasks that must be completed in sequence but that don't require resources or completion time are considered to have event dependency. These are represented by dotted lines with arrows and are called dummy activities. For example, the dashed arrow linking nodes 6 and 9 indicates that the system files must be converted before the user test can take place, but that the resources and time required to prepare for the user test (writing the user manual and user training) are on another path. Numbers on the opposite sides of the vectors indicate the time allotted for the task.

The PERT chart is sometimes preferred over the Gantt chart, another popular project management charting method, because it clearly illustrates task dependencies. On the other hand, the PERT chart can be much more difficult to interpret, especially on complex projects. Frequently, project managers use both techniques.

3.17 Critical Path Method (CPM)

Critical Path Method (CPM) charts are similar to PERT charts and are sometimes known as PERT/CPM. In a CPM chart, the critical path is indicated. A critical path consists of that set of dependent tasks (each dependent on the preceding one) which together take the longest time to complete. Although it is not normally done, a CPM chart can define multiple, equally critical paths. Tasks which fall on the critical path should be noted in some way, so that they may be given special attention. One way is to draw critical path tasks with a double line instead of a single line.

Tasks which fall on the critical path should receive special attention by both the project manager and the personnel assigned to them. The critical path for any given method may shift as the project progresses; this can happen when tasks are completed either behind or ahead of schedule, causing other tasks which may still be on schedule to fall on the new critical path.

3.18 Gantt charts

A Gantt chart is a matrix which lists on the vertical axis all the tasks to be performed. Each row contains a single task identification which usually consists of a number and name. The horizontal axis is headed by columns indicating estimated task duration, skill level needed to perform the task, and the name of the person assigned to the task, followed by one column for each period in the project's duration. Each period may be expressed in hours, days, weeks, months, and other time units. In some cases it may be necessary to label the period columns as period 1, period 2, and so on.

The graphics portion of the Gantt chart consists of a horizontal bar for each task connecting the period start and period ending columns. A set of markers is usually used to indicate estimated and actual start and end. Each bar on a separate line, and the name of each person assigned to the task is on a separate line. In many cases when this type of project plan is used, a blank row is left between tasks. When the project is under way, this row is used to indicate progress, indicated by a second bar which starts in the period column when the task is actually started and continues until the task is actually completed. Comparison between estimated start and end and actual start and end should indicate project status on a task-by-task basis.

Variants of this method include a lower chart which shows personnel allocations on a person-by-person basis. For this section the vertical axis contains the number of people assigned to the project, and the columns indicating task duration are left blank, as is the column indicating person assigned. The graphics consists of the same bar notation as in the upper chart indicates that the person is working on a task. The value of this lower chart is evident when it shows slack time for the project personnel, that is, times when they are not actually working on any project.

3.19 Expected Times for Activities

For each activity in the project network, not only is an estimate made of the most probable time required to complete the activity, but some measure of uncertainty is also noted in the estimate. The pessimistic estimate and optimistic estimate is also made to have an idea of the approximate maximum and minimum completion times respectively for the activity.

PERT calculates the expected value of activity duration (te) as a weighted average of the three time estimates. The expected time is the best estimate that we can make of the time required for a single occurrence of an activity.

3.20 Variability of Activity Times

One measure of variability of possible activity times is given by the standard deviation of their probability distribution. Standard deviation and variance are commonly used as measures of variability among numbers. The variance (Vt) is simply the average squared difference of all the numbers from the mean value. The standard deviation (St) is the square root of the variance.

3.21 The Expected Length of a Critical Path

The expected length of a sequence of independent activities is simply the sum of their separate expected lengths. We calculate a te for every activity in the project network and use these te s to identify the critical path. We obtain an expected length of the project (Te) by summing the expected activity durations along the critical path.

Similarly, the variance (VT) of a sum of independent activities is equal to the sum of their individual variances and the standard deviation of the project length (ST) is the square root of VT.

3.22 Effects of Near-Critical Path

We calculate Te by adding the te s of the critical path activities. But it might not always be the best estimate of project length because under some combination of activity times and variances, a near-critical path may exist with a higher variance than the "main" critical path. Thus, where the possibility of uncertain activity times is admitted, the possibility of alternate critical paths is implied and the simple estimating procedures tend to yield overly optimistic results.

3.23 Simulation of a Network

The normal PERT procedure which bases the estimates of Te and ST on a single critical path can grossly overstate the probabilities of completing a project by a given date, especially if there are one or more parallel paths through the network which are nearly critical, and/or which have relatively large variances. By use of Monte Carlo sampling technique, activity times are randomly selected for each activity from some appropriate frequency distribution. The project length and critical path data are then calculated in the normal way, based on these times. This procedure is repeated several thousand times and finally an average project length and standard deviation are calculated on the basis of simulated data. In the simulation procedure no single path is identified as the critical, but the probability of each activity's being on a critical path is estimated. Thus, this procedure helps the planner in identifying the critical activities which may not lie on the same path.

3.24 The Cost Consideration

The CPM was developed to solve the scheduling problems in an industrial setting. It was more concerned with the costs of scheduling and how to minimize them. Most jobs can be reduced in duration if extra resources are assigned to them. If the other advantages outweigh the additional cost, then the job should be expedited or crashed. But it is not necessary to crash all jobs to get a project done faster; only the critical jobs need be expedited. The CPM attempts to solve the problems of finding such jobs and how to crash them.

3.25 Schedule-Related Project Costs

The cost of a project is due to the direct costs associated with individual activities and the indirect expenses such as managerial services, indirect supplies, equipment rentals etc. Normally the direct costs related to an activity will increase if we crash that activity. On the other hand, the indirect costs decrease if the activity is shortened.

The relationship can be expressed by a straight line on a graph plotting job duration versus cost. The steeper the slope of this line, the higher the cost of expediting the activity. A horizontal line, then, indicates that crashing the job would result in no decreased efficiency shortening is possible (either because the job duration cannot be reduced further or because some other job has become critical on a parallel path). If there are parallel critical paths, then one job in each of them must be chosen for crashing. The improvements are made in a stepwise fashion and the new schedules are continued as long as the jobs can be crashed with a net reduction in total costs.

3.26 Basic Concepts of Network Cost Systems

The basic concept of PERT and CPM cost systems is different from that of most cost accounting systems. In essence it is: Costs are to be measured and controlled primarily on a project basis rather than according to the functional organization of a firm. The rationale of the system is the entirely logical notion that responsibility for expenditures should coincide with responsibility for managing that which gives rise to the expenditures. Under a PERT or CPM management system, project managers and submanagers are ordinarily chosen for supervising individual activities and they should be responsible for controllable costs associated with the activities.

A project-oriented cost accounting system does not necessarily replace existing systems based on organizational structure. If the costs are identified with the proper degree of detail, cost summaries can readily be generated on either basis.

3.27 Cost Accounting by Work Packages

If a project has been broken down into activities small enough to be used for purposes of detailed planning and scheduling, many such activities would be too small to be used and, therefore no added cost. If a job cannot be shortened regardless of extra resources applied to it, the line would be vertical. All the three possibilities are represented in figure 3.2.

There is probably a minimum duration which cannot be reduced no matter what the expenditure of resources (vertical portion of line). Similarly, slowing the job will decrease the costs only upto a certain point; beyond this no additional savings are obtained (horizontal portion of line).

Figure 3.2 Time-Cost Trade-off Relationship for a Typical Job

3.28 The Lowest-Cost schedule

The CPM model specifies a method for finding the optimum point representing the lowest-cost schedule. A preliminary schedule is generated in which all jobs are assigned at their early start times and with normal resources. The length of this maximum duration schedule can be reduced only by expediting one or more of the critical path activities at an extra cost.

At each step of the process, the cost-time slope of each critical job is examined, and the job with least slope is determined. This job is expedited upto the point where no further conveniently for cost-control purposes. If so, several related activities may be grouped together into larger "work packages". These represent particular units of work for which responsibility can be clearly defined and which are still small enough to be manageable for planning and control purposes. The work packages formed at the lowest level of breakdown, then, constitute the basic unit in the PERT cost system by which actual costs are (1) collected and (2) compared with estimates for purposes of cost control.

3.29 Forecast of Project Costs

For planning and budgeting purposes, it is useful for a manager to know the time pattern of the expenditures. If costs are estimated for each work package then a projection of costs can easily be made. To do this, the assumption is usually made that expenditures for an activity are incurred at a constant rate over the duration of the activity. If this assumption is not valid for certain activities, they should be divided into a sequence of two or more activities, each having a constant expenditure rate.

A schedule graph, in which the network is plotted on a time scale and in which the horizontal length and placement of activity arrows indicate activity duration and schedule, facilitates cost calculation. When cumulative costs are plotted versus time, the graph illustrates the budget implications of early start and early finish times. The area between these two curves represents a range of budgets which are feasible from a technological viewpoint.

3.30 Analysis and Control of Project Costs

The first step in the control procedure is the measurement and recording of costs which are incurred as the project progresses. At the same time that costs are reported, an estimate should be made of the percentage of work accomplished. With the cost and time data collected from period to period as the project progresses, some very useful graphic reports are produced that help the managers to answer such questions as :

- Is the project on schedule?
- How far over budget are the present costs?
- What are the sources of delay and overruns?

3.31 Accounting Problems with PERT/Cost

The managerial benefits from the PERT/Cost system derive largely from the increased detail with which the costs are categorized and reported. Although this detail permits closer control of project performance and costs, it is also the cause of some accounting problems. More specific of them include the following:

· Indirect Costs: Some project costs are not easily identifiable with end items or specific work packages. Conventionally, such items are considered to be a part of the overhead.

· Overhead Control: Since overhead is a sizable expense, and since overruns may result from indirect as well as direct costs, it seems desirable to provide some means of exerting better control over overhead.

· Material Costs: Because of long lead time between release of material requirements and their eventual use, actual costs of materials are often incurred long before the work packages are scheduled to begin.

3.32 Resource Scheduling

After the objective of a project has been explicitly specified, one of the important constraints to be considered is the means or resource by which it is to be attained. A resource is a physical variable, such as labour, finance, equipment and space, which will impose a limitation on time for the project. When the resources are limited and conflicting demands are made for the same type of resource, a systematic method for the allocation of resources becomes essential. Resource scheduling usually incurs a compromise and the choice of this compromise depends on the judgment of managers.

There are basically two approaches in solving such a problem, resource leveling and resource allocation. In resource leveling, the total project duration is maintained to the minimum level, but the activities having floats are shifted so that a uniform demand on the resources is achieved. In other words, the constraint in the case of resource leveling operation would be the project duration time. In resource allocation, the main constraint would be on the resources. If the maximum demand on any resource is not to exceed a certain limit, the activities will then have to be rescheduled so that the total demand on the resource at any time will be within the limit. The project duration time consequently is exceeded.

3.33 Complexity of Network Scheduling with Limited Resources

Problems of resource scheduling vary in kind and severity, depending upon the project and the organizational setting. The problem of scheduling activities so that none of the resource availabilities are exceeded and none of the precedence relationships are violated is an exceedingly difficult task. Scheduling projects with limited resources is a large combinatorial problem. That is, there are a very large number of combinations of activity start times – each combination representing a different schedule - too large to enumerate even with a computer.

3.34 Heuristic Programs

In recent years a good deal of work has been done in the development of heuristic programs for solving large combinatorial problems. Heuristic programs for resource scheduling may take one of the following two forms:

i. Resource Leveling Programs. These attempt to reduce peak resource requirements and smooth out period-to-period assignments, within a constraint on project duration.

ii. Resource Allocation Programs: These allocate available resources to project activities in an attempt to find the shortest project schedule consistent with fixed resource limits.

#### 4 DEVELOPMENT OF SOFTWARE

#### A software package, MANAGE XP, has been developed to assist in various decision making stages of a Project. MANAGE XP finds its utility suited for a variety of projects where the user is able to provide input in the form of precedence relationships, time, cost and resource requirements of the activities. MANAGE XP consists of various program modules mutually incorporated to form an integrated software package utility. The integrated software package has a flexibility of application as per the requirement of the case under consideration. A specific module can be used independently to assist in decision making for a particular problem associated to one of the stages in the life-cycle of a project, or an integrated utility of the software can be used for a broader application. The results provided by different modules are obtained by calculations based on only some of the important methods available. This package can be further integrated with related modules to obtain parallel solutions, based on a wider range of methods and techniques, to solve more complex real life problems from various fields.

#### The modules which are incorporated in MANAGE XP are:

· Project Selection

· Financial Appraisal

· Network Development and Scheduling

· Project Monitoring and Control

· Resource Scheduling

5 PROJECT SELECTION AND APPRAISAL

##### 5.1 Project Selection Program

This program can make calculations based on the techniques of SAW, TOPSIS and ELECTRE. Special provision has been given for appreciating the differences between cost criteria and benefit criteria.

We have a common window for entering data into decision matrix. At present it supports analysis of five projects with six criteria at a time. Selection of project selection module, opens a data entering window which is shown is Fig 5.1

Fig 5.1 Data input window for Project Selection

Here the module has been tested on the following problem.

Problem: A country decided to purchase a fleet of jet fighters from the U.S. The Pentagon officials offered the characteristic information of four models which may be sold to that country. The Air Force analyst team of that country agreed that six characteristics (attributes) should be considered. They are: maximum speed (x1), ferry range (x2), maximum payload (x3), purchasing cost (x4), reliability (x5) and maneuverability (x6). The values of the six attributes for each model (alternative) are given in Table 5.1.

Alternatives | Attributes
(Pi) | Maximum speed (Mach) | Ferry range (NM) | Maximum Payload (pounds) | Acquisition cost ($ x 10^6) | Reliability (high-low) | Maneuverability (high-low)
P#1 | 2 | 1500 | 20000 | 5.5 | average | very high
P#2 | 2.5 | 2700 | 18000 | 6.5 | low | average
P#3 | 1.8 | 2000 | 21000 | 4.5 | high | High
P#4 | 2.2 | 1800 | 20000 | 5 | average | average

Table 5.1 Data for Project Selection

Fig 5.2 Result of SAW analysis

The data shown in Table 5.1 is entered in the module as shown in Fig 5.1, and the result of the SAW analysis for this is displayed as shown in Fig.5.2

Fig 5.3 Result of TOPSIS analysis

For the data entered in Fig 5.1, the result of the TOPSIS analysis is displayed as shown in Fig 5.3 and Fig 5.4

Fig 5.4 Result of TOPSIS analysis

Thus the module gives following results after successfully performing SAW and TOPSIS analysis.

SAW analysis: Aircraft 3 (maximum points)

TOPSIS analysis: Aircraft 1 (maximum closeness to ideal solution)

5.2 Program for Financial Appraisal

This program can make calculations for NPV, IRR and Payback period and subsequently show graphical representations of the results. Options are available to choose probabilistic and deterministic model.

This module calculates NPV and Payback period for deterministic data and probabilistic data. It can calculate NPV and payback period for returns upto 20 years.

Here the module has been tested on the following problem.

Problem: An entrepreneur is considering investing in a project to manufacture a new brand of soap with an initial investment of Rs10,00,000. Expected returns are given in Table 5.2.

Year | 1 | 2 | 3 | 4 | 5
Total returns expected (in Rs) | deterministic model | 250000 | 420000 | 600000 | 600000 | 720000
probabilistic model | optimistic
pessimistic | 200000 | 300000 | 500000 | 550000 | 600000

Table 5.2 Data for Financial Appraisal

Calculate the NPV, Internal Rate of Return and Payback Period if the minimum expected rate of return is

1. 18% ( for deterministic model)

2. 13% (for probabilistic model)

Fig 5.5 Data input window for deterministic model

NPV and payback calculation can be done for a deterministic model and probabilistic model. The data provided in Table 5.2 in entered in the Data entry windows for deterministic model and probabilistic model are shown in Fig 5.5 and Fig 5.6

Fig 5.6 Data input window for probabilistic model

Fig 5.7 NPV and IRR calculation (deterministic model)

Fig 5.8 Payback period calculation (deterministic model)

Fig 5.7 shows NPV and IRR calculation for deterministic model and Fig 5.8 shows payback period calculation for deterministic model. Input values are shown in Fig 5.5.

blue curve

red curve

Fig 5.9 Result for probabilistic model

Fig 5.9 shows NPV and IRR calculation for probabilistic model. Input values are shown in Fig 5.6. The two curves are for optimistic values and pessimistic values. The red curve indicates the pessimistic and blue curve indicates the optimistic calculations.

6 PROJECT SCHEDULING AND MONITORING

6.1 Program for Scheduling and A-O-N representation of project network

This program assists in scheduling of activities of a project and representation based on A-O-N method. The program is able to identify various nodes in a project network and arrange the corresponding activities in topological order.

Fig 6.1 Data input window for Project representation

Data input window for the Project representation is shown in Fig 6.1. Data required regarding the precedence relationship, duration and cost of activities is entered here.

The module has been tested on the project details provided in Table 6.1

Activity | Predecessor(s) | Duration (months) | Cost (Rs) | Resource Requirement
A | none | 3 | 60,000 | 5
B | none | 2 | 40,000 | 3
C | A | 4 | 12,000 | 5
D | B | 1 | 20,000 | 8
E | C, D | 6 | 60,000 | 4
F | C, D | 4 | 16,000 | 6
G | E | 3 | 20,000 | 6
H | F, G | 2 | 15,000 | 5

Table 6.1 Data for Project Scheduling

Fig 6.2 Project representation based on A-O-N method

The data from Table 6.1 is entered in the input window shown in Fig 6.1, and a network representation of the project activities is generated as shown in Fig 6.2

Fig 6.3 Project representation on a Gantt chart

A Gantt chart for representation of the project activities is generated as shown in Fig 6.3. Different shaded regions show the Early Start and Late Start of activities.

Figure 6.4

Figure 6.4 shows calculations of various floats for the project represented in Figure 6.2 and Figure 6.3.

6.2 Program for Project Monitoring and Control

This program assists in Project Monitoring and Control based on PERT/COST techniques and Time-Cost Trade Off. For the data entered in the input window shown in Fig 6.1, cost calculations are made for each period.

Fig 6.4 Graphical representation of cost calculations

Cost calculations made with 0% rate of interest are shown in Fig 6.4 and Fig 6.5. Tabulated results can also be generated from the graphical representation window.

Re-calculation can be performed with modified rate of interest on the same data, from the same window.

Fig 6.5 Tabular representation of cost calculation

Tabular representation of cost calculations made with 0% rate of interest is shown in Fig 6.5

Fig 6.6 Graphical representation of modified cost calculations

Cost calculations made with modified rate of interest are shown in Fig 6.6. Tabulated results can be generated from the graphical representation window. Figure 6.7 shows a representation of the cumulative cost calculations.

Fig 6.7 Graphical representation of cumulative cost calculations

Figure 6.7 shows a representation of the cumulative cost calculations for the project data provided in the Table 6.1.

7 RESOURCE SCHEDULING

7.1 Program for Resource Leveling

This module helps in resource leveling. It is combination of both heuristic and simulation approach. In this module user can manually shift non-critical activities according to the float available and activity relationship. The program calculates resource for each time period and displays sum of squares of resource for each period. Lower the sum of squares of resource for each period, more leveled is resource profile.

Basically we try to minimize this sum of squares of resource. In simulation random numbers are generated. It performs following

· Randomly pick up non-critical activity

· Randomly set itself to move right or left.

· Move activities by random number.

· After running simulation user can manually shift activities to get most suitable/optimal result.

Simulation considerably reduces time of leveling through heuristic approach. The resource leveling module window is shown in Figure 7.1. The data from Table 6.1 has been used to test the application of the module. The program is able to optimize resources allocation based on precedence constraints and resource requirement of scheduled activities as specified in the preceding modules.

Fig 7.1 Resource leveling program (Display before simulation)

When program loads it initializes and arranges all activities in early start schedule as shown in fig 7.1.

Fig 7.2 Resource leveling program window (after simulation)

After the simulation, program re-arranges activities such that the peaks are reduced and hence resource smoothing takes place, as shown in Figure 7.2. This may not be the optimal result, it is just a simulated result. Now we can apply heuristic method. For this reason we can say that this program is combination of both heuristic and simulation methods. Earlier, simulation activities were arranged according to early start schedule as shown in Fig 7.1, and its corresponding resource profile is shown in Fig 7.3.

Fig 7.3 Resource profile before simulation

The maximum peak is as high as 10.2 resources per unit time. After simulation peak comes down to 6.4 resources per unit time as shown in Fig 7.4.

Fig 7.4 Resource profile after simulation

7.2 Program for Resource Allocation

This module provides limited resource allocation, for a case with constraint on number of resources. The objective is to create the most efficient schedule possible that minimizes the project duration and maximizes the utilization of limited resources available. The module provides a choice of priority rules that assign priority rankings to the project activities based on heuristic techniques obtained from the critical path calculations.

The module has been tested on the data provided in Table 6.1, with a constraint on the availability of resources to be 8 resources at maximum.

Figure 7.5 Limited Resource Allocation (least unit resource priority rule)

Figure 7.5 shows the allocation of resources based on the least unit resource priority rule. Figure 7.6 shows corresponding calculations for the same constraint using maximum unit resource priority rule. The tabular representations of these allocations have been shown in Figure 7.7 and Figure 7.8 respectively.

Figure 7.6 Limited Resource Allocation (maximum unit resource priority rule)

Figure 7.7 Tabular Representation (least unit resource priority rule)

Figure 7.8 Tabular Representation (maximum unit resource priority rule)

8 A REAL LIFE CASE STUDY

8.1 Validation of the developed software with industrial examples and case studies

We have used the developed modules to study different sets of problems associated to various stages in the life cycle of a project. We will now be working on a real life case study where each of the modules can be used independently as well as their integrated application can be tested and verified with actual data from industry.

8.2 About L&T

Larsen & Toubro Limited is India’s largest engineering and construction organization with leading edge capabilities in fields related to infrastructure and basic industries. L&T is engaged in four principal business segments, and enjoys market dominance in all of them - engineering and construction, cement, electrical and electronics and construction equipment.

8.2.1 L&T in Power Plant Construction

L&T have extensive experience in construction of power plants - thermal, gas-based open/combined cycle, diesel, co-generation, solar and other non-conventional plants; L&T offers

· Turnkey construction of power plants including civil, mechanical, electric instrumentation works

· Associated detailed engineering, procurement and other related services. Deals with fossil fuel stations - coal, liquid, gas and non-conventional.

Construction and erection services include:

· Survey and soil investigation

· Site development works

· Equipment foundations

· Powerhouse building

· River/seawater intake works, CW system, plant reservoirs and pump houses

· Erection of SG, TG, GTG, HRSG and all other main equipment

· Installation of electrical equipment

· Cabling work

· Assistance in testing and commissioning

· Plant and non-plant buildings

· Piping and ducting - fabrication and erection, including insulation

Turnkey services are offered for natural and induced draft cooling towers, chimneys, coal- and ash-handling systems, water and effluent treatment systems, compressed air/fire protection/HV AC systems, complete plant electrification, instrumentation, switchyards and transmission lines.

8.3 Project from L&T, ECC

8.3.1 Description of Project

The project taken for study and implementation of the procedures is the Boiler Erection of a 190 MW thermal power plant. Power plant erection is reasonably complex, though the construction methods that are in use are routine. The schedules generally are reused from one project to another.

In power plant construction, boiler erection is possibly the most critical activity for timely completion of construction of a power plant. So optimizing erection schedules is very important. Boiler erection includes the installation of large, heavy custom-made mechanical equipment. This requires expensive lifting equipment, complex rigging procedures, and highly skilled personnel. Identifying these as part of the scheduling process, before construction starts, is a key to success.

Power plant projects are capital intensive. Because time value of the money, it is important that the project duration be kept short. Many power plants are therefore developed on a fast track schedule. Components with a long lead-time must be procured early and their arrival on site often drives the schedule of other work.

8.3.2 Data Collection

The data for this case study has been taken from the M. Tech Project submitted on ‘Project Crashing and Monitoring: A Case Study’ by Mr. Vadavalli N V Stayandra (Construction Technology and Management) in December 2002. The data was originally collected from the project site of a thermal power plant of L&T ECC during the period 15th May 2002 to 25th June 2002 and again during the period 13th Nov 2002 to 20th Nov 2002.

Data collected:

· Construction schedules

· Labor and P&M requirements and schedules

· Quantities of various components of work involved

· cost details of resources

· projects direct and indirect costs

· job status

8.4 Data Analysis

8.4.1 Nature of Work

Erection, testing, commissioning and handing over of boiler 195 MW Thermal Power Station.

8.4.2 Important Dates

Scheduled date of commencement of work: 12 December 2001

Scheduled date of completion of work: 11 October 2003

8.4.3 Value Distribution of the project

Total sales price : 100.00%

Labour and material cost : 68.24%

Overheads : 14.04%

Plant cost ECC : 6.23%

Plant Cost (client) : 2.26%

Regional office overheads : 3.25%

Tax : 2.10%

Net earnings : 3.87%

The direct costs cover LMP i.e. labor, material and plant.

The overheads cover Miscellaneous labor, staff expenses, conveyance, site office, furniture etc.

8.5 Project Data

Data is collected and compiled in the format as required as input to the program.

The data collected is compiled and is tabulated. A network diagram is constructed based on the activity precedence relationships. The start and end are given for each activity based on the project network. The relationships are taken care of by the provision of relation activities and dummy activities to meet the precedence conditions. The complete data necessary to implement on software package to investigate the working of modules is shown in Table 8.1

Activity | Predecessor | Duration | Cost
A1 (Issue of LOI) | None | 1 | 0
A2 | A1 | 20 | 100000
A3 | A2 | 113 | 3856320
A4 | A49 | 350 | 3675555
A5 | A3 | 5 | 45000
A6 (Boiler Drum Lifting) | A5 | 1 | 522210
A7 | A6 | 150 | 1140828
A8 | A6 | 65 | 212901
A9 | A50 | 95 | 1060488
A10 | A6 | 160 | 903825
A11 | A8 | 95 | 658788
A12 | A9 | 30 | 28119
A13 | A6 | 105 | 289224
A14 | A51 | 85 | 1630902
A15 | A6 | 125 | 522210
A16 | A6 | 85 | 68289
A17 | A16 | 35 | 461955
A18 | A52 | 25 | 88374
A19 | A6 | 95 | 1148862
A20 | A50 | 80 | 237003
A21 | A18 | 25 | 48204
A22 | A19 | 15 | 16068
A23 | A22 | 20 | 44187
A24 | A20 | 25 | 232986
A25 | A7, A10, A11, A12, A14, A15, A17, A23, A24, A56, A57 | 8 | 4017
A26 (Hydro Test) | A25 | 1 | 75000
A27 | A26 | 40 | 293241
A28 | A26 | 30 | 24102
A29 | A28 | 65 | 301275
A30 | A26 | 35 | 28119
A31 | A30 | 220 | 984165
A32 | A13 | 65 | 498108
A33 | A53 | 30 | 92391
A34 | A54 | 30 | 8034
A35 | A21 | 130 | 1076556
A36 | A6 | 175 | 2297724
A37 | A26 | 65 | 188799
A38 | A37 | 25 | 124527
A39 | A29 | 25 | 44187
A40 | A55 | 15 | 24102
A41 | A19 | 180 | 1900041
A42 | A55 | 165 | 6970002
A43 | A34 | 60 | 610584
A44 (Light Up) | A27, A32, A33, A35, A36, A38, A39, A40, A41, A43 | 10 | 70000
A45 | A44 | 10 | 55000
A46 | A45 | 15 | 120000
A47 | A4, A31, A42, A46 | 15 | 80000
A48 (Handing Over) | A47 | 1 | 50000
A49 | A2 | 15 | 0
A50 | A6 | 25 |
A51 | A6 | 20 |
A52 | A6 | 10 |
A53 | A26 | 5 |
A54 | A53 | 10 |
A55 | A26 | 15 |

Table 8.1 Project Data

8.6 Data Analysis

The data shown in the Table 8.1 has been analyzed using the developed software package MANAGE XP. The results of the analysis are shown in the following Figures.

Figure 8.1 shows an AON scheduling of the project using the scheduling module.

Figure 8.1 A-O-N scheduling

Figure 8.2a Gantt Chart

Figure 8.2 (a, b and c) show the gantt chart representation of the project activities as per the schedule obtained in Figure 8.1.

Figure 8.2b Gantt Chart

Figure 8.2c Gantt Chart

Figure 8.3a Floats

Figure 8.3 b Floats

Figure 8.3 c Floats

Figure 8.3 (a, b and c) show the calculation of various floats for the scheduled activities.

Figure 8.4 a Resource Leveling

Figure 8.4 (a, b and c) show the application of the resource leveling module for the project.

Figure 8.4 b Resource Leveling

Figure 8.4 c Resource Leveling

Figure 8.5 Resource Profile (before simulation)

Figure 8.6 Resource Profile (after simulation)

The resource profile before and after simulation using the resource leveling module have been shown in Figure 8.5 and Figure 8.6 respectively.

Figure 8.7 Cumulative Cost

Figure 8.7 is a graphical representation of the cumulative cost calculations for the project.

9 CONCLUSION

#### 9.1 Highlights of work done

####

#### In this Project major decisions over the entire life-cycle of a project have been considered and suitable software modules have been developed for the following specific problems

· Project Identification and Screening

· Project Appraisal

· Project Selection

· Basic Scheduling

· Monitoring and Control

· Resource Scheduling

· Project Implementation

####

#### These modules have been tested on different set of problems to remove possible errors. The integrated software package of the developed program modules has a flexibility of application as per the requirement of the case under consideration. A specific module can be used independently to assist in decision making for a particular problem related to one of the stages in the life-cycle of a project, or an integrated utility of the software can be used for a broader application.

#### 9.2 Limitations and scope for future work

####

#### Presently the developed software has been designed to cater to a limited set of problems associated with Project Management. The results provided by different modules are obtained by calculations based on only some of the important methods available. The program is not capable of making calculations based on PERT. This package can be further integrated with related modules to obtain parallel solutions, based on a wider range of methods and techniques, to solve more complex real life problems from various fields.

#### REFERENCES

[1] Wiest J.D. and F.K. Levy,“ A Management Guide to PERT/CPM with GERT / PDM /DCPM and other Networks”, Prentice-Hall of India, New Delhi, Second Edition, sixteenth reprint, 2002.

[2] Hwang C.L., and Kwangsun Yoon,“ Lecture notes in Economics and Mathematical Systems, 186”, Multiple Attribute Decision Making, Methods and Applications, Springer-Verlag, Berlin/ Heidelberg/ New York, 1981.

[3] Elmaghraby S.E., Activity Networks, Wiley, NY, 1977.

[4] Moder J.J., C.R. Phillips and E.W. Davis, Project Management with CPM, PERT and Precedence Diagramming, Third Edition, Tata McGraw Hill, N. Delhi, 2002.

[5] Chandra P, Projects: Preparation, Appraisal Budgeting and Implementation, Fifth Edition, Tata Mc Graw Hill, N. Delhi, 2002.

[6] Wysocki Robert K, Robert Beck Jr. and David B. Crane, Effective Project Management, Second Edition, John Wiley & Sons, 2002.

[7] Ghattas R.G. and Sandra L. McKee, Practical Project Management, Pearson Education Asia, 2001.

[8] Nicholas, John M., Project Management for Business and Technology: Principles and Practice, Second Edition, Prentice Hall of India Pvt Ltd, EEE, 2002.

[9] L.S. Srinath, “PERT and CPM, Principles and Applications”, Affiliated East-West Press Private Limited, 1975.

[10] Stayandra Vadavalli N V, “Project Crashing and Monitoring: A Case Study”, Department of Civil Engineering, IIT Delhi, December 2002.

# APPENDIX A

ALGORITHMS USED

1. Algorithm for SAW analysis

xij = the numerical outcome of the ith alternative with respect to the jth criterion

xij is element of decision matrix

1. Calculate weighted decision matrix.

A* = {Ai / max j=1Σn Wj xij / j=1Σn Wj}

2. Calculate sum for each alternative.

sumj = j=1Σn A*ij

3. Rank the preference order, according to sumj.

2. Algorithm for TOPSIS analysis

xij = the numerical outcome of the ith alternative with respect to the jth criterion

xij is element of decision matrix

1. Calculate rij (normalized decision matrix).

rij = xij / √(j=1Σm x2ij)

where, m = number of alternatives

2. Calculate weighted normalized decision matrix.

Calculate by multiplying each column of the matrix R with its associated weight wj

for all j=1Σnwj = 1

Vij = i=1Σm wi rij

3. Determine ideal & negative - ideal solution

A* = {(max Vij / j Є J), (min Vij / j = J') / i = 1, 2, … m}

= {V1*, V2*, … Vn*}

A‾ = {(min Vij / j Є J), (max Vij / j Є J') / i = 1, 2, … m}

= V1‾, V2‾, … Vn‾

where J = {j = 1, 2, … n / j associated with benefit criteria}

J' = {j = 1, 2, … n / j associated with cost criteria}

4. Calculate the separation measure;

separation from ideal solution

Si* = √{j=1Σn (Vij – Vj*)2}, i = 1, 2, … m

separation from non ideal solution

Si‾ = √{j=1Σn (Vij – Vj‾)2}, i = 1, 2, … m

5. calculate the relative closeness to the ideal solution

Ci* = Si‾ / (Si* + Si‾), 0 < Ci* < 1

i = 1, 2, … m

6. rank the preference order.

3. Algorithm for limited resource allocation

1. Read activity, time, resource and precedence relationship data from file.

2. Select activities with pid = nil.

pid = activity ID of predecessors

3. Schedule these activities on day 1.

day = 1

4. Arrange the activities in order of priority (according to the chosen priority rule).

5. Pick priority activity

6. If (activity resource < available resource)

schedule the activity

else

priority = priority – 1

go to step 5.

7. day = day + 1

8. Select activities which can be scheduled on

day = day

9. Have all activities been scheduled.

If yes

then go to step 11

10. If no activity can be scheduled on given day

then

go to step 7

else

go to step 5

11. Plot resource profile.

12. End.

4. Algorithm for resource leveling simulation

1. Pick activity, time, resource and precedence relationship data from file.

2. Calculate Early Start of activities.

3. Plot gantt chart.

4. Calculate project duration and total resource requirement.

5. Average resource = total resource / project duration.

6. Generate random numbers a, b and c.

(0 < a, b < 1), (1 ≤ c ≤ maxactivity)

maxactivity = maximum no. of activities

7. Calculate left slack and right slack.

right slack = Late Finish – end of activity

left slack = start of activity – Early start

8. pick cth activity,

if a < 0.5, then Move Left = b × (Left Slack)

else Move Right = c × (right slack)

9. calculate error square

error square = i=1Σmaxtime (average resource – resource of ith day)

10. if error square < error, then

set new start time of activity

set new finish time activity

11. repeat step 6 to 10.