Critical Path Analysis

Critical passage Analysis INTRODUCTION Planning, plan and Controlling atomic weigh 18 three important functions of management. Planning involves the formulation of objectives and goals that argon subsequently translated into Specific plans and reckons. scheduling is concerned abtaboo the implementation of activities required to achieve the laid down plans. The function of escort is to establish a mechanism that shtup trigger a warning signal if actual proceeding is deviating (in scathe of time, address and some other measures of efficientness) from the plan.If such a deviation is unacceptable to the concerned manager, he entrust be need to take disciplinary action to bring performance in conformation with the plans. The irreverent and CPM models atomic matter 18 extremely useful for the purpose of planning, scheduling and controlling the progress and completion of large and labyrinthine protrudes or for carrying out the analysis of these three managerial functio ns. Before we describe the basic concepts employ in the mental synthesis and analysis of these models, let us first understand the meaning of a witness. What is a project?A project can be defined as a set of large emergence of activities or jobs that atomic number 18 performed in a certain succession resolved logic aloney or technologic aloney and it has to be completed within (i) a specified time, (ii) a specified cost and (iii) meeting the performance standards. Examples of a project from fairly diverse fields are given below 1. Introducing a wise product in the market. 2. Construction of a new bridge over a river or construction of a 25 storied building, 3. Executing a large and complex order on jobbing production. 4. dis get in a spacecraft to the mars. GENERAL FRAMEWORK OF smart/CPMA entanglement is a graphical representation of a project, depicting the flow as well as the sequence of well-defined activities and takes. Developed during the 1950s, both(prenominal) C PM (Critical Path Method) and PERT (Programme Evaluation and Review Technique) are net profit techniques/models. The network approach helps project managers in planning, computer programming and controlling. As a planning tool it helps the manager to estimate the requirements of alternatives viz. , materials, equipment, manpower, cost and time for distributively legal action or tasks of the project. This approach cannot make decisions by its own.It only provide additional information to executives to relieve decision making process. Also it does not provide solution to every management problem. It certainly helps in identification of those activities, jobs or causas which control the completion of the project. The working methodology of de dopeed elbow room analysis (CPA) which includes both CPM and PERT, consists of celebrateing five go 1. Analyse and break down the project in hurt of precise activities and/ or features. 2. Determine the interdependence and sequence o f specific activities and prepare a net work. . Assign estimates of time, cost or both to all in all the activities of the network. 4. Identify the longest or critical path through the network. 5. Monitor, value and control the progress of the project by replanning, rescheduling and reassignment of resources. The central task in the control aspect of these models is to secernate the longest path through the network. The longest path is the critical path because it equals the minimum time required to complete the project. all(prenominal) other paths other than the critical path (i. e. o critical or on the loose(p) paths) offer flexibility in scheduling and transferring resources, because they take less time to complete than the critical path. ADVANTAGES OF sarcastic PATH ANALYSIS There are a number of advantages in using critical path analysis. 1. It allows for a comprehensive view of the entire project. Because of the sequential and concurrent relationships, time scheduling bec omes very effective. Identifying the critical activities keeps the executive alert and in a state of preparedness, with alternative plans ready in case these are needed.Breaking down the project into smaller comp virtuoso(a)nts permits better and closer control. 2. Critical path analysis offers economical and effective system of control based on the principle of management by exception i. e. need for corrective action arises only in exceptional situations and in most of other cases, performance is in conformity with the plans. 3. It is a dynamic tool of management which calls for constant review, a reformulation of the network, and finding the current path of relevance and optimum resources allocation.FUNDAMENTALS OF A CPA NETWORK ( Activity An activity is any portion of a project which consumes time or resources and has a definable beginning and ending. For example, laying of pipe is an activity requiring the use of resource mainly effort. Activity whitethorn involve labour, pape r work, contractual negotiations, machinery operations, etc. Commonly used terms synonymous with activity are task and job. consider 1 and 2 Activities are graphically represented by arrows, usually with description and time estimates written along the arrows.The tail of the arrow portrayal an activity represents the starting point of the activity and its mastermind represents its completion. The arrow may be straight slanting, or bent but not broken (see figure-1). The arrow is not a vector and need not be force to scale. ( Events The beginning and ending points of an activity or a group of activities are called issues. Synonyms of an event are node and connectors An event is often represented graphically by a numbered circle (see figure-2), although any geometric figure such as square, oval, rectangle etc. will serve the purpose.We shall, however, stick to the most ordinarily used pattern for representing an event viz, the circle. A few examples of events are as follows (i) Material procured, (ii) Design completed, (iii) tolerate started, (iv) Bricks laid, etc. All activities in a network must commence from some event. Such events are called the tail events because they are connected to the tail of an activity. These are shown in figure 3. Similarly, all activities in a network must have terminal points called the head event because it is at the head of an activity. These are shown in figure-4.Figure-5 depicts tail and head events connected by arrows representing activities i. e. it depicts the dual role of an event. Event 14 is the head event for one activity and tail event for some other. In a network, symbol i is used for the tail event (also called preceding event) and j for the head event (or succeeding event) of an activity. The activity, then being I-j. If an event represents the roast completion of more than than one activity, it is called a merge event. If an event represents the joint initiation of more than one activity, it is call ed a burst event.A network is, then, a graphical representation of a project plan, showing the inter-relationship of the motley activities. Networks are also called arrow diagrams (see figure 6). When the results of time estimates and computations have been added to a network, it may be used as a project schedule. Conventions adopted in drawing networks There are two conventions normally adopted while drawing networks. In the early stages of network drawing, it is suggested that the conventions should be respected until sufficient develop has been gained to justify dropping them.These conventions are a) Time flows from left to right. b) Head events always have a number higher than that of the tail events. The above stated conventions allow activities to be referred uniquely by their tail and head event numbers, so that activity 3-4 means only the activity which starts from event 3 proceeds to event 4 it cannot mean the activity which starts from event 4 and finishes event 3. Grap hical representation of events and activities Events are represents by numbers within circles. Activities are represented by arrows, the arrow-heads represent the completion of the activities.The length and druthers of the arrow are of no significance whatsoever (chosen only for the convenience of drawing). The activity of leaving place A and walking to place B can equally well be represented by figure-7. Fundamental properties governing the representation of events and activities The representation of events and activities is governed by one simple settlement regulate which requires that an activity which depends upon another activity is shown to emerge from the head event of the activity upon which it depends and that only dependent activities are drawn in this way.Thus, if activity B depends upon activity A, then the two activities are drawn in figure-8. Figure 7 AB 1. An event cannot occur until all activities leading to it are complete. 2. No activity can start until its tai l event in r from each oneed. The above two properties can be combined into a single one, namely that no activity may start until all previous activity in the same chain are completed. Logical sequencing are connection of activities A project entails several activities. The arrows are arranged to show the plan of logical sequence in which the activities of the project are to be accomplished.The sequence is ascertained for each activity by answering the following three quires viz (i)Which activity or activities must be completed before the start of a particular activity ? (ii) Which activity or activities should follow this? (iii) Which activities can be accomplished simultaneously? The activity or activities which immediately come before another activity without any interpose activities are called predecessor activities to that activity. The activities which follow another activity without any intervening activities are called successor activities to that activity.In a project of l aying a pipe line, the three activities involved may be trenching, laying pipe and weld pipe. To decide the logical connection between these three activities necessary that they be carried out in series, the reasoning being that the pipe cannot be laid until trenching has been done and welding cannot be undertaken until the pipe has been laid. This way we decide the logical sequencing between different activities. Errors in logical sequencing ii types of errors in logic may arise while drawing a network, particularly when it is a alter one. These are known as looping dangling. 1)Looping Normally in a network, the arrow points from left to right. This convention is to be strictly adhered, as this would avoid illogical looping, as shown wrongly below (2)Dangling The situation represented by the following diagram is also at fault, since the activity represented by the dangling arrow 9-11 is undertaken with no result. A To overcome the problem arising due to dangling arrows, followin g rules may be adopted. (i) All events, except the first and the stick up, must have at least one activity entering and one activity leaving them, ii) All activities must start and finish with an event. (3)Duplicate activities Consider the following figure 11 A XY B Figure 11 In the above figure, activities A and B may be called duplicate activities because they have same head event (i. e. 6) and the same tail event (i. e. 7). One amends for such a situation is the introduction of a locoweed activity (4) Dummy activity It is a hypothetical activity which consumes no resource and time. It is represented by dotted lines and is inserted in the network to polish off activity pattern under the following situations ) It is nominated to make activities with common starting and finishing events distinguishable. ii) To identify and have got the proper precedence relationship between activities that are not connected by events. iii) To bring all loose ends to a single initial and a sing le terminal event in each network using dummies, if necessary. For example, problem of duplicate activities in the figure-11 above may be circumvented as shown in figure-12. A XY B Figure 12 Figure 13 shows three cases for the following set of dependency relationships Activity C is dependent upon both A and B.Activity D is dependent upon A alone. BC AC A DD BA C B AD The first portrayal (on top left of figure-13) is distinctly wrong since it shows D as dependent upon not only A but also B which is not desired. The other portrayal (ii) is also wrong since A is being shown twice and thus contravenes the positive axiom of network that three must be one arrow for each activity. The way out to this dilemma is the representation by means of the dummy activity. In the third portrayal of figure -13, C is dependent upon both A and B (via dummy) whereas D is dependent upon just A.Numbering the events The event numbers in a network should in some respect reflect their logical sequences. Whe n a complicated network has been drawn then the problem of assigning numbers to the events involved in the network arises. A rule devised by D. R. Fulkerson, involving the following steps may be followed to resolve the problem numbering the events. i) An initial event is one which has arrow/arrows coming out of it and none of the arrow entering it. In a network there will be only one such event. Call it 1. (ii) Delete all arrows coming out from the event 1. This will give us at least one more initial event. i) Number these events as 2, 3. (iv) Delete all emerging arrows from these numbered events which will create new initial events. Then follow step (iii). (v) Continue the above steps till last event is obtained which has no arrows coming out of it. Consider the numbering of events in the following figure. Figure 14 F AFA BG B CH CG AF AF BG BG CH CH AF AF BG BG CH CH Figure 15 Here we proceed from left to right. The event with least x- orchestrate is assigned the smallest intege r, say 1. other events are assigned progressively higher integers with regard to x-co-ordinate.If two or more events (4 and 5 above) have the same x-co-ordinate, the one towards arrow should have higher number. Further, it is not necessary, and in fact also not desirable to number the events consecutively. It would be a better scheme to number the events as 10, 20, 30, 40, 50, 60, 70 in the above diagram instead of 1, 2, 3, 4, 5, 6, 7. This affords insertion of more activities and events omitted by wariness or having become necessary in view of certain logic revisions. It was mentioned earlier that it is desirable that all the activity arrows point from left to right. If the arrow is vertical it may point downwards or upwards.For the pastime of preventability it is to be recommended that activities emanating from one event or converging to another may make as grand angles between themselves as possible. A few more conventions are given below (i) Keep the arrow to the extreme righ t. (ii) As far as possible avoid drawing arrows that cross each other. usually by suitable stretching the network diagram it is possible to avoid this. (iii) Where, however, crossing is unavoidable, bridging may be done. This applies to dummies as well. tempt boldly a big network. Smaller ones are confusing. Use of pencil and golosh is recommended.Exercise Depict the following dependency relationships by means of network diagrams. The Alphabets stand for activities. 1. A & B control F B and C control G. 2. A & B control F B Controls G while C controls G and H. 3. A controls F and G B controls G while C controls G and H. 4. A controls F and G B and C control G with H depending upon C. 5. F & G are controlled by A, G and H are controlled by B with H controlled by B and C. 6. A controls F, G and H B controls G and H with H controlled by C. state The required networks are given in figure -15 Exercise Find out the superfluous (unnecessary) dummy activities in the network below. BEH C AF G D Figure 16 JKL M FG AB CDE H M IK Figure 14 Basic steps involved in drawing a CPM/PERT network Network is defined as a diagram representing the activities and events of a project, their sequence and inter-relationships. The basic steps involved in drawing a network are i) Breaking up of the entire project into smaller systems known as tasks. ii) For each tack ascertain the activities and events to be performed. iii) For each activity determine the preceding and succeeding activities. iv) For each activity determine or estimate the time and other resources needed. v) Draw a network depicting the assembly of tasks into a project.Network Construction Problem 1 The activities involved in the computer installation process are detailed below. You are required to draw the network. ActivityPredecessor Activities A. Physical preparationnone B. organizational planningnone C. Personal SelectionB D. Equipment InstallationA E. Personal TrainingC F. Detailed systems designC G. File Conve rsionF H. Establish standards and controlsF I. Programme preparationH J. Programme TestingI K. Parallel operationsD, E, G, J. L. Finalize systems documentationI M. acquire upK, L B C (ii) AA None A None B B B D C D A A D (iii)C