Project Evaluation And Review Technique

Published Date: 02 Nov 2017

The research project is a systematic set of procedures to be followed from the original conception of new research, through the specification, modelling, testing, acceptance, presentation and evolution of that research. It includes techniques to assist in the critical tasks of specification, documentation, design, building, testing, analysis and managing the research products. It also includes management procedures to control the research process and the deployment of technical methods.

The purpose of project management is to establish procedures, organization and plans to deal with constraints on the utilization of resources. Information on which decisions can be based should be available; procedures should be set up to ensure the timely detection of errors and their correction so that the timescale and budget are controlled, technical risks are minimized and quality is established.

Each phase in the project is defined in terms of the outputs produced during the phase. The completion of a phase is determined by the satisfactory review of the defined products of that phase and these form the baseline for the work in the next phase.That is, the products of the succeeding phase are measured and validated to ensure conformance to the requirements of the preceding baseline before themselves forming a new baseline. These review points form natural milestones in the development of the project.

Separate phases can be identified although the designation and number of phases may vary with the type of research. The endpoint of each phase is a product or products, and the prescribed output build up to form the research report. Several phases may run in parallel and provide slack for the management of critical tasks.

While there is a need to proceed in an orderly manner, allowance should be made for some reworking of the previous phase in the light of subsequent work. In addition, exploratory work on a future phase is usually required before an earlier one has been completed. The project should anticipate these.

Errors should be kept to a minimum and eliminated early, at the same time ensuring completion within planned cost and timescale. As the project develops the cost of changing the research escalates. This is so whether the need for modification arises from an incorrect specification, changes in the specification, errors in the modelling, or analysis mistakes.

Of prime importance is the user. The researcher should ensure that a sound model design is completed and shown to satisfy user needs before any attempt is made at implementation. The user is inevitably involved in the evaluation of the products before the next phase can be commenced.

Careful selection of research techniques, however, does not in itself guarantee success. Success or failure is primarily determined by the approach to project management. No matter how sophisticated the design and implementation techniques, a systematic approach to project management is essential.

A vital element of project management is the monitoring of project progress and, where there is a deviation from the plan, the application of corrective action. In order to assess the progress, regular reports should show:

� Completed activities.

� Duration remaining on started activities.

� An assessment of movement on milestones.

The establishment of the project environment, obtaining the personnel and dealing with perturbations is the responsibility of the project manager � usually the researcher. The responsibility also includes the research methodology used on the project with precise definition of the details of its application. The methods selected should be matched to the characteristics of the research, the imposed schedules and other operational considerations. Once selected, the methods should be implemented and controlled.

The aim of this chapter is to help students answer questions such as:

� When will the project be finished?

� When is each individual part of the project scheduled to start and finish?

� Of the many parts of the project, which ones must be finished on time to avoid being late?

� Is it possible to shift resources to critical parts of the project from non-critical parts of the project without affecting the overall completion time of the project?

� Where should management concentrate its efforts at any time?

The objective is for the student to be able to:

� Define the different phases of the project.

� Identify milestone products.

� Set up a network of separate tasks to be completed.

� Estimate time, money and other resources needed for each task.

� Determine critical tasks and balance resources.

� Manage the project to ensure completion of the research on time and within budget.

10.1 Project Management

The research project management procedure requires the project manager to plan and schedule, in proper sequence, the many details needed to predict when tasks or activities involved in the project can be expected to occur and to complete the project. The project manager should have overall control of the project. The project manager is the one with imagination, experiences, resources and responsibility for getting the project accomplished in the best possible time for the best possible cost. In most cases the project manager is also the researcher, as the researcher should be familiar with the activities involved in research.

Project management consists basically of three phases: planning, scheduling and control/monitoring. The planning of the project should be completed before a schedule can be produced, but the schedule is subject to revision during the control/monitoring phase.

Planning is the most important, and most time-consuming phase. It is here that all necessary activities are defined as an integral part of the feasibility study and allow the project manager to obtain intimate and early knowledge of the project and insight into details or anticipated problem areas.

In scheduling, the planning information is used to produce a schedule for the activities in the project. Only simple arithmetic is needed to prepare a schedule, and it can be done manually. There is no substitute, however, for a critical path schedule for organizing a project. Such a network shows who waits for what, who is on the critical path, and how much an activity can slip before it moves into the critical path.

Preparation of the critical path chart is the most valuable part of its use. Laying out the network, identifying the dependencies, and estimating the durations all force a great deal of very specific planning early in the project. The first chart is always the worst, and as the project proceeds it gives confidence in the progress of the project.

The first step in controlling a project is to have a schedule which can be adjusted as unforseen difficulties are encountered. Each person responsible for an activity is responsible for reporting the progress of that activity to the project manager.

Successful project control and monitoring is best conducted with a proper management program. The project manager can keep the schedule up-to-date manually, but a project management and control program reduces the effort involved, and allows easy production of status reports. In this case, one can expect that planning would require perhaps 60% of the project management effort, scheduling 10%, and monitoring and control 30%.

10.1.1 Project Network

Many research projects are extremely complex. Therefore the quality of the research is better guaranteed by an appropriate research project process.

The formal description of the research project process produces the model. It describes all the phases and activities to be performed. For each activity all the necessary inputs and results are specified. Results produced in one activity are in turn used as input for subsequent activities. Therefore, the complete process as described by the model appears as a network structure.

In practice, an arrow diagram is normally drawn to identify the individual activities or tasks, and their durations between events. An activity depends upon and cannot begin until the completion of all preceding activities. All activities that start with the same event depend upon and cannot begin until the completion of all activities that end with that event.

The project network forms the basis of the Project Manual, and is easily translated into a suitable form for an appropriate project management program.

10.1.2 Phases

Research is constructed in phases which are made up of activities. Activities are subdivided into tasks. The phases are structured to follow the fundamental management principles that each phase should have a clearly defined starting point, a clearly defined endpoint, and tangible products to which quality assurance techniques can be applied to assess quality, completeness, and hence progress.

Phases are represented in this document as bold upper-case letters. Each activity within the phase is represented in bold lowercase letters. For example:

PLANNING PHASE

Develop initial plan

Complete alternative plans

Decide best approach

SCHEDULING PHASE

Produce schedules

Allocate resources

CONTROL/MONITOR PHASE

Report progress

Consider alternatives

Change requirements

The endpoint of each phase is marked by a milestone. For choosing the milestones there is only one relevant rule. Milestones should be specific, measurable events, clearly defined. Milestones are 100 per cent completed events. For example, Feasibility Report complete. Model complete. Research Report complete.

The milestones provide formal quality assurance checkpoints to ensure that customization does not distort the development procedure and lose any of its inherent strengths. The project should contain a structured, planned way of working, with techniques that cross-check each other and therefore test the assumptions of the research.

10.1.3 Activities and tasks

The total resource and work content of these critical phases of research is broken down into discrete, manageable portions. This is essential for purposes of estimation and subsequent project control.

The activities define what is to be done, what must already have been done, and the resources needed. The project describes a logical sequence but in practice this logical sequence may need altering as the project proceeds. Some work for an activity may well be done in earlier activities, and work done in later activities may cause reworking of those already done. The project provides a framework on which information can be hung, and this should be reported as the information is obtained.

Activities are subdivided into tasks represented here in a standard format, preceded by a box (?) and followed by resource estimates in brackets [resource estimates can be included with experience]. This is followed by a brief description of what is involved and techniques used in the task. For example:

Develop initial plan

? Produce Arrow Diagram [resources]

Define the activities in the project and their relationship to one another.

? Estimate Activity Duration [resources]

Establish the amount of time expected for completion of each activity.

? Estimate Activity Cost [resources]

Determine costs where relevant.

? Estimate Resource Requirements per Activity [resources]

Estimate other resources.

Produce schedules

? Produce Project Schedules [resources]

� The earliest date upon which work related to the activity can start.

� The earliest date upon which all work related to the activity will be completed.

� The deadline date by which time the activity must be started if the project is to avoid delay.

� The deadline date by which time the activity must be completed if project delay is to be avoided.

� The amount of extra time available for the activity.

? Predict Cash Flow [resources]

How much money will be expended as a result of the scheduled activity completion.

? Analyse Resource Requirements [resources]

How many of each kind of resource will be required to accomplish the project.

Report Progress

? Activity actual start [resources]

Report start for historical record.

? Activity actual finish [resources]

Notification of finish for records.

? Activity percent complete [resources]

An indication of what portion of the time, cost and resource usage to completion.

? Additions to the arrow diagram [resources]

New activities caused by changes to the project.

? Deletions from the arrow diagram [resources]

Activities no longer part of the project.

? Changes [resources]

Changes to activity descriptions, durations, costs or resources.

The prescription of activities and tasks permits their use with any project. Each project is unique, however, in terms of resources, requirements and constraints that apply to it. The tasks are presented as guides, and project management should consider each activity and decide whether and how it should be applied, and to what depth it should be completed. Any proposed variations should be recorded in the Project Manual, together with reasons, and the risks should be fully appreciated and consciously accepted.

When the activities have been decided in detail and their sequence established, the effort required to complete each task can be estimated. Tasking and estimating are the major evaluation activities necessary before detailed planning, scheduling and allocation of resources can be carried out.

10.1.4 Milestone Review

A formal review should conclude each phase of the project. It provides a means of monitoring technical achievement against the project milestones, offers an opportunity for improving and assuring the quality of the research, and gives approval to proceed to the next phase.

This procedure has been designed so that the user makes decisions based on the information presented by the researcher. Decisions should be visible so that those involved are responsible for them. Therefore, the researcher should ensure the best possible presentation of facts.

Documentation should be circulated to the user in advance of presentation, so that the user has no reason for not reading the material, or misunderstanding it. To obviate lack of comprehension, preconceived ideas and other interests, a formal presentation of the options for decision should be made. The project manager should:

Milestone review

? Convene the meeting, and notify all relevant parties.

? Arrange the venue to minimize interruption.

? Provide a formal agenda in advance.

? Produce and distribute the necessary background papers.

? Brief someone to chair the meeting.

? Nominate a minute secretary and produce a formal record of proceedings.

Proper organization and polished presentation are essential. The following guidelines ensure better understanding of the options:

� Use good speakers who are confident with the subject matter.

� Make maximum use of good quality visual aids and diagrams.

� Rehearse the presentation to avoid pitfalls and establish timings.

� Give the presentation as rehearsed.

� Leave questions until the end.

� Provide ample time for discussion following the presentation.

� Answer questions directly, but do not attempt to solve problems until later.

� Ensure that those who are to make decisions are aware of their role and responsibilities, and that the decisions are properly recorded.

10.2 Staffing requirements

The staffing arrangements for each research project vary widely. The important point is to ensure that all staff know and understand what is expected of them.

It is the responsibility of senior staff to ensure that all staff have a good working knowledge of the research project procedures and encourage other staff to acquire such knowledge. It is important to ensure that all staff are suitably qualified and have received experience or training appropriate to the research involved.

Short summaries should be provided in the Project Manual for all staff involved on the research project. These should clearly show the functions to be fulfilled by each member with regard to internal management and external liaison, and should include their CV�s.

10.2.1 Staff management

Management of research has to provide a balance between support for existing research projects, and development of new research projects, from a limited staff resource. A functional organization can be used primarily to group together individuals with high technical skills such as engineers, scientists, data processors, and so forth.

The project structure is built across the functional organization. The research project is accomplished by passing the project from functional organization to functional organization as the project passes through the life cycle phases.

The project organization is multi-disciplinary in nature, drawn from various line or functional units in the hierarchical organization. The organization so developed is temporary in nature, since it is built around the project or specific task to be done rather than around organizational functions.

Research management can be successfully organized on a matrix structure in which there is dual or multiple managerial accountability and responsibility. There are two chains of command, one along functional lines and the other along project lines.

In a matrix organization, a balanced matrix means that both the functional and project organizations that contribute tangible and intangible resources to the project will have equivalent responsibilities, authority and status.

The Research Manager is the group project manager for all projects, makes the crucial project decisions and is the negotiating authority with the customer or user. The Research Manager routinely delegates certain authority to project managers for individual projects, retaining approval rights over their decisions. The Research Manager must meet the project goal within the resources of the organization, with the responsibility to hire, discharge, train, and promote staff within the organization.

Existing projects do not have to be retrofitted, but all new projects should comply. Requests for exceptions to this policy, together with the associated reasons, should be addressed to the Research Manager.

10.3 Project Manual

A document should be prepared, and continuously updated as necessary, which fully describes in detail terms of reference, all procedures, flow of information, approval formats, responsible personnel, acceptance criteria, record management, and other matters relating to the process by which the research products are quality assured, quality controlled, verified and certified as necessary. This document is subject to regular review and should be updated, corrected, changed, and otherwise modified in accordance with the specified requirements. This is a milestone event.

Records should be kept which document the qualifications of the personnel who are directly involved in any aspect of the research project. Qualifications should note education level, fields of expertise, scope and depth of knowledge, range of professional experience, licences to practice, and any other information which can be used to verify that the researcher is properly and sufficiently qualified to research, manage and technically support the research.

The Project Manual provides a permanent record of relevant information collected and alternatives considered during the processes of proposing, designing, developing and implementing the research. It records suggestions concerning possible modifications or enhancements, additional applications and alternative ways of using the results of the research. It contains a record of development and maintenance of the project for all activities, milestones, resources, projected and completion dates for each phase of the project.

Separate and complete evidence of each and every change made to the research should be maintained including all fixes, functional improvements, feature enhancements, performance improvements, and any other modifications whatsoever. Each document of such change should be signed off by the individual researcher responsible for the change and a responsible technically competent manager who confirms that the change was properly formulated and implemented.

10.3.1 Project Manual specification

The Project Manual should include:

Background Terms of reference: objectives, constraints.

Supporting notes and directives.

Communication Information about decisions made, and facts gathered during the design and implementation of the research and concerning its purpose and scope.

Record of discussions and meetings.

Correspondence.

Personnel Management structure and responsibilities.

Research personnel qualifications.

Supervisors.

Users.

Support staff.

Materials Computer requirements (hardware and software).

Laboratory requirements.

Accommodation.

Consumables.

Costs Budget.

Overheads.

Information about computing, experimentation, laboratory and operating costs.

Performance Quality assurance issues associated with the research project.

Specification of test requirements.

Test plans.

Information about timings, volumes, etc.

Project Organization and plan.

Schedule.

Milestones and key dates.

Resource requirements and the basis of estimation.

Progress reports.

Risk and contingency allowances.

Documentation Information relevant to the use of information files and current reliability.

Copy control � whereabouts of copies and master documents.

Amendment list � those amendments incorporated or awaiting action.

Training Training arrangements for support staff.

Standards Application to this research.

10.4 Project management representation

To introduce this section we first have to look at the following two definitions :

Project: Combines a set of interrelated activities that must be executed in a certain order before the entire task can be completed.

Activity: Is viewed as a task requiring time and resources for its completion

In the past, the scheduling of a project was done with little planning. The best-known tool was the Gantt Bar chart which specified the start and finish times for each activity on a horizontal time scale. Project Management has evolved as a new field with the development of two analytic techniques:

� Critical Path method (CPM)

� Project Evaluation and Review Technique (PERT)

PERT was developed in the 1950's to control the Polaris missile programme, a massive project which had 250 prime contractors and over 9000 subcontractors. Imagine the problems faced by the project director in attempting to keep track of hundreds of thousands of individual tasks on this project. The introduction of PERT help management answer questions like:

� When will the project be finished?

� When is each individual part of the project scheduled to start and finish?

� Of the many parts of the project, which ones must be finished on time to avoid being late?

� Is it possible to shift resources to critical parts of the project from non-critical parts of the project without affecting the overall completion time of the project?

� Among all the many sub-projects where should management concentrate its efforts at any time?

CPM was developed in 1957, based on the same networking principles as that of PERT, but with the fundamental difference of including the concept of cost into the planning and control process. When time can be estimated rather well and when costs can be calculated rather accurately in advance, CPM may be superior to PERT. But when there is an extreme degree of uncertainty and when control of time outweighs control over costs, PERT may well be the better choice.

Project Scheduling by PERT- CPM consists of three basic phases:

1 Planning

2 Scheduling

3 Control

Steps in CPM

i list tasks involved in the project

ii estimate completion time for each task

iii arrange in logical sequence

iv draw network

v analyse

Consider a simple example.

Construct a concrete foundation

Excavate in 3 stages A B C

Pour concrete in 3 stages A B C

Task Logical sequence Duration

? Excavation A follows start 1 day

? Excavation B follows excavation A 2 days

? Excavation C follows excavation B 2 days

? Pour A follows excavation A 1 day

? Pour B follows excavation B and pour A 1 day

? Pour C follows excavation C and pour B 1 day

Network arrow diagram (arrow represents task; node represents event) [activity on arrow]

solid lines ? tasks or activities

nodes ? events ie start and finish of task

dashed line --- dummy activity required to show logical sequence of task (0 time) ie 2-3 shows that task 3-4 cannot start until task 1-2 is complete

Rule: only one arrow between two nodes. Each node must be identified by separate node numbers

Earliest start time (ES) for a task = duration of longest route from start of project to start of task (use forward pass through network)

Latest start time (LS) = duration of project - duration of longest route from terminal node to start of task (use backward pass)

Minimum project completion time = duration of longest route, called critical path,

ie 0 ? 1 ? 2 ? 4 ? 5

Activity float ? ES < LS (excess time or float)

TOTAL FLOAT: LSj - (ESi - tij) = extra time which can be allocated to task ij without increasing project duration

FREE FLOAT: ESj - (ESi - tij) = if allocated to a task does not interfere with float time for next task

INTERFERING FLOAT: LSj - ESj = if allocated to task it reduces float of next task

Bar chart

Task

0 � 1

1 � 2

2 � 4

4 � 5

1 � 3 FF IF

3 � 4 FF

Days 0 1 2 3 4 5 6

Assume task start at ES (don�t show dummy event)

10.4.1 Activity list

The beginning of any scheduling exercise is a listing of all the possible activities that will form part of the project. This list should include a symbol for every activity that can be used in any diagrammatic representation, a description of the activity and a list of its immediate predecessors.

Activity Symbol Description Immediate Predecessors

A Clear and establish site -

B Dig foundations A

C Fix steel for foundations B

D Pour Foundations C

10.4.2 Network diagram representations

The project can then be represented graphically using the following:

� Arrow: Commonly used to represent an activity. The head indicates the direction of progress.

� The precedence relationships between the activities is specified by using events/nodes.

� Event/Node: Represents a point in time that signifies the completion of some activities and the beginning of new ones.

� The beginning and end points of an activity are thus described by two events (known as tail and head events).

The rules for constructing the Network Diagram are as follows:

Rule 1: Each activity is represented by one and only one arrow in the network

Rule 2: No two activities can be identified by the same head & tail events.

Rule 3: To ensure correct precedence relationship, ask:

� Which activities must be completed before this one can start?

� Which activities must follow this activity?

� Which activities must occur concurrently with this one?

10.4.3 Critical path calculations

� The applications of PERT-CPM should ultimately yield a schedule specifying the start and completion dates of each activity.

� These calculations are performed directly on the arrow diagram. We then classify the activities of the project as critical or non-critical.

� An activity is said to be critical if a delay in its start will cause a delay in the completion date of the project. A non-critical activity is such that the time between its earliest start and its latest completion dates is longer than its actual duration. In this case the non-critical activity is said to have a slack or float time.

� A critical path defines a chain of critical activities that connects the start and end of the arrow diagram.

� The critical path calculations include two phases:

i Forward Pass: Calculations begin from �Start� node and move to �end� node. At each node computing the earliest occurrence time of the corresponding event.

ii Backward Pass: Begin calculations from �end� node and move to �start� node. At each node computing the latest occurrence time of the corresponding event.

In the process the following are defined :

ESi � the earliest start time of all the activities emanating from event i [from forward pass]

LCi � the latest completion time for all activities coming into event i [from backward pass]

The critical path activities can now be identified by using the results of the forward and backward passes.

An activity (i, j) lies on the critical path if it satisfies all of the following three conditions:

(Dij � duration of activity)

ESi = LCi

ESj = LCj

ESj - ESi = LCj - LCi = Dij

10.4.4 Determination of floats

Following critical path computations, the floats for the non-critical activities must be computed (a critical activity must have zero float). To do this we define the following two new times:

Latest start (LS) : LSij = LCj - Dij

Earliest completion (EC): ECij = ESi + Dij

From the critical path calculations we have the following:

Earliest start (ES) : ESj = max (ESi + Dij)

Latest completion(LC): LCi = min (LCj - Dij)

There are two important types of floats:

Total Float (TF): The total float TFij for activity (i, j) is the difference between the maximum time available to perform the activity and its duration

TFij = LCj - ESi - Dij = LCj - ECij = LSij - ESi

Free Float (FF): Assume all activities start as early as possible then the FFij for activity (i, j) is the excess of available time (ESj - ESi) over its duration (Dij)

FFij = ESj - ESi - Dij

Thus: How much can an activity float without affecting the early start of the next activity? The calculations for the critical path and floats can be summarized as in the following table where:

TFij = LSij - ESi = LCj - ECij

FFij = ESj - ESj - Dij

Given the duration of each activity, complete the table.

Activity

Duration Earliest Latest

Total float

Free float

Start Completion Start Completion

(i,j)

1 Dij

2 ESi

3 ECij

4 LSij

5 LCj

6 TFij

7 FFij

8

(0,1) 2 0 2 2 4 2 0

(0,2) 3 0 3 0 3 0* 0

(1,3) 2 2 4 4 6 2 2

(2,3) 3 3 6 3 6 0* 0

(2,4) 2 3 5 4 6 1 1

(3,4) 0 6 6 6 6 0* 0

(3,5) 3 6 9 10 13 4 4

(3,7) 6 6 12 11 17 5 1

(4,5) 7 6 13 6 13 0* 0

(4,8) 4 6 10 10 14 4 0

(5,6) 6 13 19 13 19 0* 0

(8,6) 5 10 15 14 19 4 4

(7,6) 2 12 14 17 19 4 4

Columns 1, 2, 3 & 6 are obtained from the Network Calculations and the rest from the formulas:

LSij = LCj - Dij

ECij = ESi + Dij

The critical activities are marked with an asterisk (*).

Note: A critical activity, and only a critical activity must have zero total floats. The free float must also be zero when the total float is zero. The inverse is not true. (e.g. activity (0,1))

10.4.5 Precedence relationships

Up to now we have only encountered activities preceding one another with a finish � start relationship. There are however other precedence relationships:

� Finish - to - Start (Conventional) (FS)

� Start - to - Start (SS)

� Finish - to - Finish (FF)

These are not necessarily exact relationships but they can have a lag. Most software packages which can be used to schedule networks require these relationships.

10.4.6 Resource levelling

Proper management should avoid large fluctuations in resources (such as labour, plant, materials, money). Float non-critical tasks to smooth resources.

Delay start of activity 1-2 by 6 days until completion of 1-3.

10.4.7 Resource distribution

Task DAYS LABOUR PLANT

1-2 2 2 -

1-4 2 6 A

1-7 1 4 -

2-3 4 A

3-6 1 4 A

4-5 5 A

4-8 8 4 -

5-6 4 2 -

6-9 3 4 A

7-8 3 4 -

8-9 5 2 -

Require uniform labour and continuous use of A. Plant A cannot be used on 2 tasks at the same time.

Bar chart

1-4 (6)A

4-8 (4)-

8-9 (2)-

1-7 (4)- IF=6

7-8 (4)- FF=6

1-2 (2)- IF=5

2-3 (-)A IF=5

3-6 4(A) FF=4 IF=1

6-9 (4)A FF=1

4-5 (-)A IF=1

5-6 (2)- IF=1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Distribution of labour

12

10

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Plant

A

A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

After redistribution of resources:

Bar chart

1-4 (6)A

4-8 (4)-

8-9 (2)-

1-7 (4)- IF=4

7-8 (4)- IF=4

1-2 (2)- IF=5

2-3 (-)A

3-6 4(A)

6-9 (4)A

4-5 (-)A IF=1

5-6 (2)- IF=1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Distribution of labour

12

10 Distribution after shifted labour

8

6

4

2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Plant

A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

10.4.8 Network compression

The least-time solution is the plan necessary for completing the project in the shortest possible time, at the minimum cost for that completion time. In order to reduce the time, a large number of the activities must be speeded up (crashed); but it is not necessary to crash every activity in the project to attain the least-time solution. If all activities are fully crashed, the result is called the all-crash solution. This will always cost more than the least-time programme, and therefore is never economical. Hence the objective of the least-time programme approach is the selection of only those activities that should be crashed for the optimum solution. For example:

i-j

Task Duration (hr) Cost Range

(hr) Rate

(R/hr)

Normal Crash Normal Crash

1-2 A: materials to site 5 4 30 40 1 10

2-5 B: erect structure 6 2 12 20 4 2*

2-3 C: install plumbing 4 3 10 18 1 8

2-4 D: install electricity 5 3 12 20 2 4

5-6 E: connect services 3 16

3-5 0 * smallest

4-5 0 Crash cost = normal cost + range�rate

? = R80 ? = R98

Logical sequence A occurs first

E occurs last

B, C, D occur at same time

Somewhere between the all-normal and crashed least-time solutions, however, lies the overall optimum economic solution for the project. This solution must be derived if the planning is to take full advantage of critical path methods. It can only be found after a series of optimal solutions have been evolved, followed by a cost analysis of the project, taking into account resources. An investigation is made into the effect of successively crashing various activities. This may be continued with consecutive optimal solutions until the project can be speeded up no more economically. This procedure is known as network compression.

Direct cost for task

Steps:

1. Select task on critical path with smallest rate.

2. Compress task either by its range or smallest float on non-critical path.

3. If more than one critical path compress more than one task.

In this example Select task with rate R20/hr.

Range 2-5 = 4 hours

Min float = 1 hour (path 14 � 5)

Compress by 1 hour = smallest value (rate = R2 / hr)

New duration = 14 - 1 = 13

New cost = 80 + 2 = 82 (Path 2 � 4 � 5 also becomes critical)

Second step Must compress tasks 2 � 5 and 2 � 4

Objective is to minimize total cost.

Tasks

Given the following network determine the minimum completion time and indicate the activities on the critical path. Construct the network diagram and, assuming that each activity starts at its earliest possible starting time, a bar chart indicating the amount and type of activity float. Carry out resource levelling within the minimum project duration for the smoothest use of equipment and the smallest number of people. Only one piece of equipment �A� is available, and this should be operated continuously.

Activity Duration People Equipment

(days) (including operator)

1-2 2 2 -

1-4 2 6 A

1-7 1 4 -

2-3 4 - A

3-6 1 4 A

4-5 5 - A

4-8 8 4 -

5-6 4 2 -

6-9 3 4 A

7-8 3 4 -

9-9 5 2 -