Network Diagram Full PDF

Introduction to CPM / PERT Techniques CPM/PERT or Network Analysis as the technique is sometimes called, developed along two parallel streams, one industrial and the other military. CPM (Critical Path Method) was the discovery of M.R.Walker of E.I.Du Pont de Nemours & Co. and J.E.Kelly of Remingto...

Introduction to CPM / PERT Techniques CPM/PERT or Network Analysis as the technique is sometimes called, developed along two parallel streams, one industrial and the other military. CPM (Critical Path Method) was the discovery of M.R.Walker of E.I.Du Pont de Nemours & Co. and J.E.Kelly of Remington Rand, circa 1957. The computation was designed for the UNIVAC-I computer. The first test was made in 1958, when CPM was applied to the construction of a new chemical plant. In March 1959, the method was applied to maintenance shut-down at the Du Pont works in Louisville, Kentucky. Unproductive time was reduced from 125 to 93 hours. PERT (Project Evaluation and Review Technique) was devised in 1958 for the POLARIS missile program by the Program Evaluation Branch of the Special Projects office of the U.S.Navy, helped by the Lockheed Missile Systems division and the Consultant firm of Booz-Allen & Hamilton. The calculations were so arranged so that they could be carried out on the IBM Naval Ordinance Research Computer (NORC) at Dahlgren, Virginia. Page 1 The methods are essentially network-oriented techniques using the same principle. PERT and CPM are basically time-oriented methods in the sense that they both lead to determination of a time schedule for the project. The significant difference between two approaches is that the time estimates for the different activities in CPM were assumed to be deterministic while in PERT these are described probabilistically. These techniques are referred as project scheduling techniques. In CPM activities are shown as a network of precedence relationships using activity-on- node network construction – Single estimate of activity time – Deterministic activity times USED IN: Production management - for the jobs of repetitive in nature where the activity time estimates can be predicted with considerable certainty due to the existenceof past experience. In PERT activities are shown as a network of precedence relationships using activity-on- arrow network construction – Multiple time estimates – Probabilistic activity times USED IN: Project management - for non-repetitive jobs (research and development work), where the time and cost estimates tend to be quite uncertain. This technique uses probabilistic time estimates. Benefits of PERT/CPM ⚫ Useful at many stages of project management ⚫ Mathematically simple Page 2  ⚫ Give critical path and slack time ⚫ Provide project documentation ⚫ Useful in monitoring costs Limitations of PERT/CPM ⚫ Clearly defined, independent and stable activities ⚫ Specified precedence relationships ⚫ Over emphasis on critical paths 2.2 Applications of CPM / PERT These methods have been applied to a wide variety of problems in industries and have found acceptance even in government organizations. These include Construction of a dam or a canal system in a region Construction of a building or highway Maintenance or overhaul of airplanes or oil refinery Space flight Cost control of a project using PERT / COST Designing a prototype of a machine Development of supersonic planes 2.3 Basic Steps in PERT / CPM Project scheduling by PERT / CPM consists of four main steps 1. Planning Page 3  The planning phase is started by splitting the total project in to small projects. These smaller projects in turn are divided into activities and are analyzed by the department or section. The relationship of each activity with respect to other activities are defined and established and the corresponding responsibilities and the authority are also stated. Thus the possibility of overlooking any task necessary for the completion of the project is reduced substantially. 2. Scheduling The ultimate objective of the scheduling phase is to prepare a time chart showing the start and finish times for each activity as well as its relationship to other activities of the project. Moreover the schedule must pinpoint the critical path activities which require special attention if the project is to be completed in time. For non-critical activities, the schedule must show the amount of slack or float times which can be used advantageously when such activities are delayed or when limited resources are to be utilized effectively. 3. Allocation of resources Allocation of resources is performed to achieve the desired objective. A resource is a physical variable such as labour, finance, equipment and space which will impose a limitation on time for the project. When resources are limited and conflicting, demands are made for the same type of resources a systematic method for allocation of resources become essential. Resource allocation usually incurs a compromise and the choice of this compromise depends on the judgment of managers. 4. Controlling Page 4  The final phase in project management is controlling. Critical path methods facilitate the application of the principle of management by expectation to identify areas that are critical to the completion of the project. By having progress reports from time to time and updating the network continuously, a better financial as well as technical control over the project is exercised. Arrow diagrams and time charts are used for making periodic progress reports. If required, a new course of action is determined for the remaining portion of the project. 2.4 The Framework for PERT and CPM Essentially, there are six steps which are common to both the techniques. The procedure is listed below: I. Define the Project and all of its significant activities or tasks. The Project (made up of several tasks) should have only a single start activity and a single finish activity. II. Develop the relationships among the activities. Decide which activities must precede and which must follow others. III. Draw the "Network" connecting all the activities. Each Activity should have unique event numbers. Dummy arrows are used where required to avoid giving the same numbering to two activities. IV. Assign time and/or cost estimates to each activity V. Compute the longest time path through the network. This is called the critical path. Page 5  VI. Use the Network to help plan, schedule, and monitor and control the project. The Key Concept used by CPM/PERT is that a small set of activities, which make up the longest path through the activity network control the entire project. If these "critical" activities could be identified and assigned to responsible persons, management resources could be optimally used by concentrating on the few activities which determine the fate of the entire project. Non-critical activities can be replanned, rescheduled and resources for them can be reallocated flexibly, without affecting the whole project. Five useful questions to ask when preparing an activity network are: ▪ Is this a Start Activity? ▪ Is this a Finish Activity? ▪ What Activity Precedes this? ▪ What Activity Follows this? ▪ What Activity is Concurrent with this? 2.5 Network Diagram Representation A network diagram in project management is a visual representation of a project's tasks, activities, or events, illustrating the sequence in which they need to be completed. It's a key tool in project scheduling and planning, as it helps identify the critical path, potential bottlenecks, and dependencies between tasks. It is the graphical representation of logically and sequentially connected arrows and nodes representing activities and events of a project 1. Activity Any individual operation which utilizes resources and has an end and a beginning is called activity. An arrow is commonly used to represent an activity with its head indicating the direction of progress in the project. These are classified into four categories 1. Predecessor activity – Activities that must be completed immediately prior to the Page 6  start of another activity are called predecessor activities. A B A is predecessor of B 2. Successor activity – Activities that cannot be started until one or more of other activities are completed but immediately succeed them are called successor activities. A B B is successor of A 3. Concurrent activity – Activities which can be accomplished concurrently are known as concurrent activities. It may be noted that an activity can be a predecessor or a successor to an event or it may be concurrent with one or more of other activities. 4. Dummy activity – An activity which does not consume any kind of resource but merely depicts the technological dependence is called a dummy activity. The dummy activity is inserted in the network to clarify the activity pattern in the following two situations To make activities with common starting and finishing points distinguishable To identify and maintain the proper precedence relationship between activities that is not connected by events. For example, consider a situation where A and B are concurrent activities. C is dependent Page 7 on A and D is dependent on A and B both. Such a situation can be handled by using a dummy activity as shown in the figure. 2. Event An event represents a point in time signifying the completion of some activities and the beginning of new ones. This is usually represented by a circle in a network which is also called a node or connector. The events are classified in to three categories 1. Merge event – When more than one activity comes and joins an event such an event is known as merge event. 2. Burst event – When more than one activity leaves an event such an event is known as burst event. 3. Merge and Burst event – An activity may be merge and burst event at the same time as with respect to some activities it can be a merge event and with respect to some other activities it may be a burst event. 3. Sequencing The first prerequisite in the development of network is to maintain the precedence relationships. In order to make a network, the following points should be taken into considerations What job or jobs precede it? What job or jobs could run concurrently? What job or jobs follow it? What controls the start and finish of a job? Since all further calculations are based on the network, it is necessary that a network be drawn with full care. Page 8 Key Elements of a Network Diagram 1. Nodes: Represent activities or events in the project. These are usually depicted as rectangles or circles. 2. Arrows: Show the dependencies and the sequence between tasks. Arrows indicate the flow of the project, pointing from one task to another. 3. Start and End Points: Indicate the beginning and completion of the project. 4. Critical Path: The longest path through the network, representing the sequence of activities that determine the minimum project duration. 5. Float or Slack: The amount of time that a task can be delayed without delaying the project. Types of Network Diagrams 1. Arrow Diagramming Method (ADM): Uses arrows to represent activities and nodes to represent events. This method is also known as Activity on Arrow (AOA). 2. Precedence Diagramming Method (PDM): Uses nodes to represent activities and arrows to show the relationships and dependencies between these activities. This method is also known as Activity on Node (AON). Purposes of a Network Diagram Visualize Project Workflow: Provides a clear picture of task sequences and relationships. Identify the Critical Path: Helps determine which tasks are critical and which have flexibility. Improve Project Scheduling: Assists in effective time management by identifying task dependencies. Resource Allocation: Helps in planning resource allocation more efficiently. Risk Management: Highlights potential bottlenecks and areas where delays might occur. Rules for Drawing Network Diagram Rule 1 Each activity is represented by one and only one arrow in the network Page 9 Rule 2 No two activities can be identified by the same end events Rule 3 In order to ensure the correct precedence relationship in the arrow diagram, following questions must be checked whenever any activity is added to the network What activity must be completed immediately before this activity can start? What activities must follow this activity? What activities must occur simultaneously with this activity? In case of large network, it is essential that certain good habits be practiced to draw an easy to follow network Try to avoid arrows which cross each other Use straight arrows Do not attempt to represent duration of activity by its arrow length Use arrows from left to right. Avoid mixing two directions, vertical and standing arrows may be used if necessary. Use dummies freely in rough draft but final network should not have any redundant dummies. The network has only one entry point called start event and one point of emergence called the end event. 2.6 Common Errors in Drawing Networks Page 10 The three types of errors are most commonly observed in drawing network diagrams 1. Dangling To disconnect an activity before the completion of all activities in a network diagram is known as dangling. As shown in the figure activities (5 – 10) and (6 – 7) are not the last activities in the network. So the diagram is wrong and indicates the error of dangling 2. Looping or Cycling Looping error is also known as cycling error in a network diagram. Drawing an endless loop in a network is known as error of looping as shown in the following figure. 3. Redundancy Page 11  Unnecessarily inserting the dummy activity in network logic is known as the error of redundancy as shown in the following diagram Ignoring Parallel Activities Error: Not considering activities that can occur simultaneously. Impact: Results in an inefficient schedule, where some tasks unnecessarily delay others. Solution: Identify tasks that can run in parallel and adjust the network to optimize the project timeline. Overlapping or Crossed Lines Error: Drawing the diagram with overlapping or crossing lines, making it hard to read. Impact: Causes confusion and misinterpretation of task sequences and dependencies. Solution: Keep the diagram clean and organized. Use dummy activities or rearrange nodes to avoid overlaps. Missing Dependencies Error: Failing to identify and include dependencies between activities. Impact: Can result in resource conflicts, incorrect critical paths, and an inaccurate project timeline. Solution: Review the project to ensure all dependencies are captured, including mandatory, discretionary, and external dependencies. Page 12 Draw the AOA & AON network diagram for the project whose activities and their precedence relationship are as given below Fulkerson's Rules for Numbering Network Nodes 1. Unique Event Numbering: o Each event (node) must have a unique number. This helps in identifying the sequence of activities and prevents ambiguity. 2. Start Node with Lower Number: o An event that marks the start of an activity should always have a lower number than the event marking the end of that activity. This implies that the flow of activities in the diagram always moves from lower- numbered nodes to higher- numbered nodes, ensuring a forward progression of time. 3. Sequencing: o The numbering should start from the initial event (usually numbered as 1) and proceed sequentially as the network is developed. o Put number from top to bottom 4. Proper Network Flow: o Ensure that each activity starts at one node and ends at another, adhering to the direction indicated by the arrow. The numbering should align with the logical order of activities and dependencies. Page 13  Activity on node B D A F E C Draw the AOA & AON network diagram for the project whose activities and their precedence relationship are as given below Activity Predecessor Activity A - B - C A D A E B F C G D,E Activity on node E B G START D END A F C A project consists of a series of tasks labelled A,B,..... H,I with the following relationships (w< x, d ; means x and y cannot stat until w is completed; x,y< w means w cannot start until both x and y are completed ) with this notation construct the AOA &AON network. Diagram having the following constraints. A