Vitaminas

Introduction

PERT and CPM are two well known network techniques or models especially useful for planning, scheduling and executing large time-bound projects which involve careful co-ordination of a variety of complex and inter-related activities and resources. PERT is the abbreviated form for Program Evaluation and Review Techniques and CPM for Critical Path Method. Both the techniques were developed in U.S.A. during the late 1950s. PERT was developed by US Navy Engineers to plan and control the huge Polaris Submarine Program. CPM was developed by E.I. Dupont Nemours & Co., U.S.A. and the Univac Division of Remington Rand Corporation in 1956 in connection with the periodic overhauling and maintenance of chemical plants. It resulted in reducing the shut-down period from 130 hours to 90 hours and saving hours and saving the company $1 million.

Both the techniques have been applied successfully to improve efficiency of execution of large projects within pre-determined time and cost limits. Any new venture may be regarded as a project, such as constructing a new plant, bridge, dam, shopping centre or residential complex, design of a new aircraft, manufacture of ships, R& D projects, introduction of a new product, installing pipeline, floating a new issue of shares, major repairs and overhaul of plant and machinery units, organizing a large conference/convention, handling an earthquake relief work and so on.

PERT and CPM converge on several aspects, and are almost treated as twins; there are, however, some points of difference between them which will be discussed later. The techniques recognize the systems or inter-related nature of activities on large work projects and translate the job proposed into a model by drawing a network of the activities involved. They are used in planning and controlling (monitoring) the projects. Planning in this context implies developing the overall layout of the project with estimates of time, the resources required and the detailed time scheduling and sequence of various jobs to be performed. The control, on the hand takes place during the work on the project. Gradually as resources get used and completion times are obtained, project management techniques can be used to reallocate, if necessary, the rescues, according to the revised criticality rankings of the jobs remaining to be done. In general the application of PERT and CPM is intended to answer the following:

1. The expected project completion date

2. The scheduled start and completion time for the different activities comprising the project

3. The key activities of the project which must be completed at the scheduled time (or else would result in delaying the entire project completion time) and require close managerial attention, the time period by which non-key activities may be delayed without causing a delay in the completion of the whole project.

In fact, PERT and CPM are suitable for any situation where

a. The project consists of well-defined collection of activities or tasks

b. The activities can be started and terminated independently of each other, even if the resources employed on the various activities are not independent.

c. The activities are ordered so that they can be performed in a technological sequence. Thus precedence relations exist which preclude the start of certain activities until others are completed. For example, the overhead water tank in a high-rise building cannot be installed until the top floor of the infrastructure has been constructed.

Notes:- Facility Planning 6th Sem

INSTITUTE OF HOTEL MANAGEMENT CATERING AND NUTRITION, KUFRI, SHIMLA | 44

Advantages of using networking techniques (like PERT/CPM) as management tools of project control

 Compels management to plan a project before it begins.

 Requires an analytical approach to planning

 Separates the planning and scheduling functions.

 Permits the planner to concentrate on the relationship of items of work without considering their occurrence in time.

 Allows the planner to develop a more detailed plan, since he is concerned with how the work will be performed, not when.

 Results in a more realistic schedule.

 Clearly shows dependency between work tasks.

 Facilities control of a project.

 Simplifies maintenance of the plan and schedule.

 Informs of management‟s current status regarding the project.

 Focuses management‟s attention on critical items of work.

 Gives management the ability to assess consequences of anticipated changes to the plan.

 Makes it easy to relate other functions of project control to the basic planning and scheduling function.

 Meets contractual requirements of government, private industry and customers. The application of PERT and CPM for project management involves the following steps:

1. Establishment of objectives: The first step in the development of a PERT network is the establishment of objectives. There will be a major objective to be accomplished, linked by supporting objectives. When these are identified, they must be linked together so as to enable to planner to see the project in its true perspective.

2. Identification of all key activities and events or phases for completion of the project. In this connection, the term activity is defined as an operation or job to be carried out which consumes time and resources. In the AOA network diagram, activities are denoted by arrows (). An event is defined as a beginning or completion of an activity. It is denoted by a circle (O). while identifying the key activities, sequencing activities and estimating activity times, both technical and managerial persons should work together.

3. Determination of sequence of activities and events in a project and arranging them in a network that brings out their interrelationship to satisfy the technological sequencing requirements. The network diagram so constructed is a beginning point for the project. For the sake of convenience, each event is given a serial number. In a project, some activities have to be undertaken sequentially while others may be carried out concurrently. All these form part of the project network. The network so formed, shows a number of paths of activities and events from beginning to completion.

4. Determination and assignment of time for starting and completion of each activity in the network, which will help to arrive at the total time required for completion of the project. In CPM only one time rating per activity is used. In PERT, three estimates of time span for completion of each activity are evaluated. They are optimistic time (shortest time denoted by to), pessimistic time (longest time denoted by tp) and normal time (most likely time denoted by tm). After these three time estimates have been made, they are combined into a single workable time value known as expected time (denoted by te). This is done algebraically by using a weighted average.

te = tp + 4tm + tp 6

where te is the expected time, to optimistic time, tp – pessimistic time and tm – normal time.

The three time estimates are used in PERT because the originators of PERT thought that the estimated time for an activity is better described by a probability distribution than by a single estimate.

Notes:- Facility Planning 6th Sem

INSTITUTE OF HOTEL MANAGEMENT CATERING AND NUTRITION, KUFRI, SHIMLA | 45 5. Determination of the total period of time required for completion of project. This calls for

identification of the sequence of those activities, the completion of which is critical for the timely completion of entire project. The line connecting the critical activities from start to finish of the project is the critical path. The completion time of activities along the critical path cannot be delayed. Any delay in completion of activities that lie on the critical path, will delay the entire project. The critical path is the path with the longest duration (compared to all the other possible paths) running through the network in a continuous manner from the beginning to the end. It is of the longest duration since it allows for the fact that certain activities cannot be started unless certain other related activities that precede them are completed. It also is the period of time required for completion of the project. Other useful figures that may be calculated for control are event slacks, activity floats, variability duration and the probability of completing the project or part of it by or within a particular time. 6. Implementing the network model created as a tool of control once the project commences. This

stage calls for periodic updating of the network amongst other tings to monitor the progress of the project. This is done by comparing the actual activity completion times with their estimated times. Necessary changes are made in schedules in case of intolerable deviations to ensure completion of the project as close to the target time as possible.

7. Resource Allocation and Scheduling: Based on the network calculations and assessment of resources required for each of the activities, the plan is translated into a time schedule. If it is possible to expedite the activities by incurring additional cost, the economics of doing so are also examined before finalising the schedule.

Each person who participates in the application of PERT to the control of the project should have some basic familiarity with the general nature of the work and with the ultimate objective desired.

Types of network diagrams

In general there are two ways in which network diagrams may be constructed. CPM and PERT (which is what is taught here), both use the Activity on Arrow (AOA) manner of representing networks. STUDENTS WILL FOLLOW THIS AND ONLY THIS MANNER (AOA) OF DRAWING NETWORKS. SIMPLY SPEAKING THESE DIAGRAMS REPRESENT THE ACTIVITY ON THE ARROW (AND THE EVENT ON NODE) IN PRESENTING THE PROJECT LOGIC.

For information purpose only, there exists another manner called the Activity On Node (AON) diagram to present the project logic. In this, the activities are represented on the node (and not the arrow) and the

precedence relationships are represented by the arrows. This technique of project networking was developed by John W Fondahl in USA and by Bernard Roy in France, at about the same time when PERT and CPM came into existence. All of these techniques were developed independent of each other. Fondahl called his technique of AON diagram by the name “precedence diagram”. The AON diagram is claimed to have some merits as compared to AOA diagram as it does not require dummy activities, and because it is considered to be simple and easier to explain as well as to understand and facilitates revision and updating. Irrespective of these advantages, the AOA diagrams continue to be more popular than the AON diagram and the AOA diagrams add dynamism to the network. Both types have their relative advantages and disadvantages and have carved their respective niches in terms of application and usage.

Assumptions of PERT/CPM

1. A project can be sub-divided into a set of predictable and independent activities.

2. The precedence relations of project activities can be completely represented be a non-cyclical network graph in which each activity connects directly into its immediate successors.

Notes:- Facility Planning 6th Sem

INSTITUTE OF HOTEL MANAGEMENT CATERING AND NUTRITION, KUFRI, SHIMLA | 46 3. Activity items may be estimated either as single-point estimates or as three-point PERT estimates and

are independent of each other.

4. In CPM, the duration of an activity is linearly (and inversely) related to the cost of resources applied to the activity. (This means less the time more the cost as it happens when crashing activity time). 5. In PERT model, activity duration is assumed to follow the beta distribution, the standard deviation of

the distribution is assumed to be 1/6th of its range, the mean is approximated by 1/6th (to+4tm+tp) and the variance in length of project is assumed to be equal to the sum of the variances of activities on the critical path.

6. Cost time-trade off for deriving the cost curve slopes are subjective again and call for great deal of expertise of the technology as well as genuine efforts to estimate.

Constructing the Network

A project network is a directed graph that consists of finite collection of elements called events (or nodes) together with a subset of the ordered pairs (i, j,) of nodes called activities (or jobs or tasks or operations). In other words, a network is the graphical representation of logically and sequentially connected arrows and nodes representing activities and events of a project. (Also called arrow diagrams) diagrams show the

operations/activities to be performed to complete a job, the sequence and inter-relationship of various activities involved.

In networks, an activity is a clearly identifiable and manageable operation or an element of work entailed in the project and it is represented by an arrow. An event (or node), is the and/or finish of an activity or group of activities. Others terms used are junction, milestone or stage. In general milestone is reserved for particularly significant events that require special monitoring. An activity arrow (i, j,) extends between two nodes, the tail node (or event), i, represents the start of an activity and the head node (event) j, represents the completion of an activity as shown below:

Activity

(i) (j,)

Starting event completion event

Activities may also be termed jobs, tasks or operations. Activities which must be completed before a certain other activity starts are called the predecessor activity starts are called successors activities.

Predecessor activity: Activities that must be completed immediately prior to the start of another activity called predecessor activities.

Successor activities: Activities that cannot be started until one or more of the other activities are completed, but immediately succeed them are called successor activities.

Concurrent activity: Activities which can be accomplished at the same time are known as concurrent activities.

Path: An unbroken chain of activity arrows connecting the initial event to the final event via other events is called a path.

Notes:- Facility Planning 6th Sem

INSTITUTE OF HOTEL MANAGEMENT CATERING AND NUTRITION, KUFRI, SHIMLA | 47

Rules of Network Construction

Following are some of the rules that have to be followed while constructing a network:

1. Each defined activity is represented by one and only one arrow in the network. Therefore, no single activity can be represented more than once in the network. These arrows should be kept straight and not curved. Sometimes bending activity arrows so that the main portion of the arrows both straight and parallel to the main horizontal axis of the diagram will improve the appearance of the network. This is illustrated below:

Angles between arrows should be as large as possible. Arrows should not cross each other. Where crossing cannot be avoided, the method shown below should be adopted.

2. Before an activity can be undertaken all activities preceding it must be completed. Thus, a network should be developed on the basis of logical or technical dependencies between various activities of the project. The discipline of networking requires that the project be considered in a thorough and analytic manner and the predecessor-successor relationships between the various activities clearly laid.

3. The arrows depicting various activities are indicative of the local precedence only. The length and bearing of the arrows are of no significance, although arrows in network diagrams should be drawn to show time flow left to right i.e. in the forward direction.

4. The arrow direction indicates the general progression in time. Each activity must start and end in a node (or event). The tail of an activity represents the point in time at which the “activity start” occurs and the node marking this start is called the tail event for this event. The head of an activity represents the point in time at which the “activity completion” occurs and the node marking this termination is called the head event for that activity.

5. When a number of activities terminate at one event, it indicates that no activity emanating from that event may start unless all activities terminating there have been completed.

1 2 1 1 1 3 2 4 3 3

Notes:- Facility Planning 6th Sem

INSTITUTE OF HOTEL MANAGEMENT CATERING AND NUTRITION, KUFRI, SHIMLA | 48

Fig.(I) Fig.(ii)

6. Events are identified by numbers. Each event identified by a number higher than that allotted to the event immediate preceding one. I.e., events should be numbered such that for every arrow (i,j) (i, < j). In assigning numbers to the events, care should be taken that there is no duplication of event numbers in a network. The event numbered 1 denotes start of the project and is called initial node (or event) while the event carrying the highest number denotes the final event in the network. A network should have only one initial and one terminal node. (Students are advised to keep the project start event and the project completion event in a straight line for a more aesthetic looking network diagram).

7. The activities are identified by the numbers of their starting and the ending events. They are expressed as i,j, where i represents the starting event, or the tail node number, and j represents the ending event or the head node number. Naturally head nodes always have a higher number than tail nodes. No two activities may be described by the same set of ordered pairs. All activities emerging (or taking off) from event 1 should not be preceded by any other activity or activities. In fig.I activities B, C, D and E can be expressed as 3-6, 4-6, 5-6 and 6-7 respectively. Event 3 represents the beginning of the activity B while event 6 represents the completion of activities B, C and D, and the beginning of the activity E. 8. An event which represents the joint completion of more than one activity is known as a merge event,

while an event which portrays the initiation of more than one activity is called the burst event. In Fig.(I) above event 6 and event 2 in Fig (ii) is a burst event.

9. Parallel activities between two events, without intervening events, are prohibited. Thus two or more activities cannot be identified by the same beginning and ending events. By implication, any two events should not be connected with more than one arrow. When two or more activities in a project have the same head and tail events, dummy activities are needed in constructing the network. The figure on the left is the wrong way to represent the two activities while the figure on the right shows the correct representation of the two activities using a dummy.

WRONG

RIGHT

A dummy used in this manner is called an identity dummy. Dummies do not consume time or resources. As a result of using dummy activities, other activities can be identified by unique end- events. Dummy activities are usually shown by arrows with dashed lines.

Dummy activities are also very useful in establishing proper logical relationships in the networks which cannot, otherwise, be adequately represented. Known as logic dummies they are used when two chains of activities have a common event, although they are in themselves wholly or partly independent

2 1 6 4 5 7 4 5 1 2 1 2 3

Notes:- Facility Planning 6th Sem

INSTITUTE OF HOTEL MANAGEMENT CATERING AND NUTRITION, KUFRI, SHIMLA | 49 of each other. Thus, when two or more activities have some, but not all, of their inputs in common, the use of a logic dummy resolves the problem of representation.

Dummy

If a dummy is the only activity emanating from a node, it can be eliminated. If a dummy activity converging to its final node, it can be eliminated. Dummy activities which portray predecessor relations that are already implied by other activities may be removed as redundant.

A third reason to use dummies is to improve the layout of a network when they may not be strictly necessary to represent the logic involved. This often happens at the start or finish of a network where a number of activities