Critical Path Analysis

Critical Path Analysis INTRODUCTION Planning, programming and Controlling ar tierce important functions of counselling. Planning involves the formulation of objectives and goals that argon subsequently translated into special(prenominal) plans and projects. Scheduling is concerned ab turn up the implementation of activities necessary to achieve the dictated down plans. The function of control is to institute a mechanism that tooshie trigger a warning signal if actual mathematical process is deviating (in equipment casualty of time, cost and some other measures of effectiveness) from the plan.If much(prenominal) a deviation is impossible to the concerned manager, he will be required to land disciplinal bring through to bring performance in conformity with the plans. The PERT and CPM models atomic number 18 extremely useful for the purpose of planning, scheduling and controlling the progress and issue of large and complex projects or for carrying out the depth psycholo gy of these triad managerial functions. Before we describe the primary concepts used in the construction and analysis of these models, let us first understand the meaning of a project. What is a project?A project can be defined as a set of large number of activities or jobs that be performed in a certain period decided logic entirelyy or technologic altogethery and it has to be completed within (i) a specify time, (ii) a specified cost and (iii) meeting the performance standards. Examples of a project from fairly divers(a) fields ar given beneath 1. Introducing a wise point of intersection 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. Sending a b allistic capsule to the mars. GENERAL FRAMEWORK OF PERT/CPMA network is a graphical theatrical performance of a project, depicting the flow as well as the sequence of well-defined activities and consequences . Developed during the 1950s, both CPM (Critical Path Method) and PERT (Programme Evaluation and recap Technique) be network techniques/models. The network approach helps project managers in planning, Scheduling and controlling. As a planning tool it helps the manager to hazard the requirements of resources that is to say , materials, equipment, manpower, cost and time for distributively natural action or tasks of the project. This approach can non impinge on terminations by its own.It only provide additional information to executives to facilitate decision making process. Also it does not provide solution to every management problem. It certainly helps in identification of those activities, jobs or burdens which control the closure of the project. The running(a) methodology of minute lane analysis (CPA) which includes both CPM and PERT, consists of quest atomic number 23 travel 1. Analyse and break down the project in damage of specific activities and/ or events. 2 . Determine the interdependence and sequence of specific activities and take a crap a net work. . Assign estimates of time, cost or both to all the activities of the network. 4. Identify the lasting or faultfinding path through the network. 5. Monitor, prise 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 signalize the longest path through the network. The longest path is the critical path because it equals the minimum time required to complete the project. exclusively other paths other than the critical path (i. e. o critical or slack paths) offer flexibility in scheduling and transferring resources, because they take less time to complete than the critical path. ADVANTAGES OF CRITICAL 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 simultane ous relationships, time scheduling becomes 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 angiotensin-converting enzyments 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 quantity review, a reformulation of the network, and finding the current path of relevance and optimum resources allocation.FUNDAMENTALS OF A CPA NETWORK ( action An bodily function is any portion of a project which consumes time or resources and has a definable beginning and ending. For example, lay of pipe is an application requiring th e use of resource mainly effort. Activity whitethorn involve labour, paper work, contractual negotiations, machinery operations, etc. Commonly used name synonymous with legal action are task and job. Figure 1 and 2 Activities are graphically stand for by cursors, usually with translation and time estimates written along the arrows.The do-nothing of the arrow portraying an performance represents the get weavinging point of the activity and its maneuver 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 displace to scale. ( Events The beginning and ending points of an activity or a group of activities are called events. Synonyms of an event are node and connectors An event is often equal graphically by a numbered circle (see figure-2), although any geometric figure such(prenominal) as square, oval, rectangle etc. will serve the purpose.We shall, however, stick to the most ordina rily used convention for representing an event viz, the circle. A few examples of events are as follows (i) Material procured, (ii) Design completed, (iii) Project started, (iv) Bricks laid, etc. All activities in a network must(prenominal) 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 spend a penny terminal points called the school principal event because it is at the learning ability of an activity. These are shown in figure-4.Figure-5 depicts tail and transfer events connected by arrows representing activities i. e. it depicts the dual role of an event. Event 14 is the breaker point event for angiotensin converting enzyme activity and tail event for another. In a network, symbol i is used for the tail event ( excessively called preceding event) and j for the head event (or succeeding event) of an activity. The activity, then be ing I-j. If an event represents the articulate completion of more than one activity, it is called a merge event. If an event represents the articulation initiation of more than one activity, it is called a burst event.A network is, then, a graphical representation of a project plan, showing the inter-relationship of the various activities. meshworks 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 lucking networks There are two conventions normally adopted period drawing networks. In the early stages of network drawing, it is suggested that the conventions should be respected until qualified experience has been gained to justify dropping them.These conventions are a) Time flows from left to right. b) foreman events al focusings have a number higher than that of the tail events. The preceding(prenominal) stated conventions allow activit ies to be referred uniquely by their tail and head event come, 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. Graphical 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 orientation of the arrow are of no significance whatever (chosen only for the convenience of drawing). The activity of leaving place A and paseo 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 dependency rule which requires that an activity which depends upon another activity is shown to erupt from the head event of the activity upon which it depends and that only dependent activities are bony 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 add up until all activities leading to it are complete. 2. No activity can start until its tail event in reached. The above two properties can be combined into a champion one, namely that no activity may start until all previous activity in the same cooking stove are completed. Logical sequencing are connection of activities A project entails some(prenominal) 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 anoth er activity without any intervening 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 position a pipe line, the three activities involved may be trenching, place pipe and welding 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 deuce types of errors in logic may arise opus drawing a network, particularly when it is a complicated one. These are known as circulate dangling. 1)Looping Normally in a network, the arrow points from left to right. This convention is to be strictly adhered, as this would suspend illogical loop ing, 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, following rules may be adopted. (i) All events, except the first and the last, must have at to the lowest degree one activity entering and one activity leaving them, ii) All activities must start and finish with an event. (3)Duplicate activities guide 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 remedy for such a situation is the introduction of a dummy activity (4) booby 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 clarify activity recitation under the following situations ) It i s created to make activities with common starting and finishing events distinguishable. ii) To identify and maintain the proper precedence relationship between activities that are not connected by events. iii) To bring all loose ends to a single initial and a single 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 clearly 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 fundamental 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 trine 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. When 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- co-ordinate is assigned the smallest integer, say 1. other events are assigned more and more 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 oversight or having become necessary in view of certain logic revisions. It was mentioned introductory that it is desirable that all the activity arrows point from left to right. If the arrow is steep it may point downwards or u pwards.For the sake of preventability it is to be recommended that activities emanating from one event or converging to another may make as great angles between themselves as possible. A few more conventions are given below (i) Keep the arrow to the extreme right. (ii) As outlying(prenominal) 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. Draw boldly a big network. Smaller ones are confusing. Use of pencil and rubber is recommended.Exercise read 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 b y 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. Answer 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 convocation of tasks into a project.Network Construction Problem 1 The activities involved in the figurer inst allation 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 ConversionF H. instal standards and controlsF I. Programme preparationH J. Programme TestingI K. Parallel operationsD, E, G, J. L. Finalize systems documentationI M. Follow upK, L B C (ii) AA None A None B B B D C D A A D (iii)C