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Unit 1 Project management is the discipline of initiating, planning, executing, controlling, and closing the work of a team to achieve specific goals and meet specific success criteria. A project is a temporary endeavor designed to produce a unique product, service or result with a defined beginning and end to meet unique goals and objectives, typically to bring about beneficial change or added value. There are three components of project in construction industry Cost of the project (Budget) Quality and quality of construction facilities (Scope) Time of completion of the project (Schedule) The job of a project manage is to establish the balance between the mentioned three components of the project. In other ways, challenge in construction is to have a Trade-off among cost, time and quality. The challenge of project manager is to have coordination among the owner, designer and contractor. There is only one goal of the project to have construction facility i.e. all the three should work a as a team in amenable manner. The other responsibilities may include: daily operations of field work activities and organization of subcontractors; coordination of the implementation of a project, ensuring it is being built correctly; project schedules and forecasts; interpretation of drawings for tradesmen; review of engineering deliverables; redlining drawings; regular project status reports; budget monitoring and trend tracking; bill of materials creation and maintenance; effective communications between engineering, technical, construction, and project controls groups;
Project Planning In the process of planning, alternatives are examined and the best alternative is chosen. The goal of planning is to minimize resource use (cost) while satisfactorily completing the task. Efficient use of equipment’s, material, labour and ensuring coordinated effort are the basic aim. The outcome of planning is predetermined course of action. Thus, the planning creates an orderly sequence of events, defines strategies to be followed in carrying forth the plan and describes ultimate disposition of the result. Putting the various activity of the project in the sequence on the time frame is the process of scheduling. Scheduling is required for continuous checking of the project (control), for resource mobilization, to minimize the cost and use of resources optimally. Various scheduling techniques have been employed to plan the activity in sequence in project management. In construction project, bar chart and critical path method (CPM) have been widely used. Objectives The main objective of planning is to execute the project most economically both in terms of money and time. Effective planning includes the following factors. Proper design of each element of the project Proper selection of equipment and machinery; in big projects, the use of larger capacity plants are found economical. Proper arrangement of repair of equipment and machinery near the site of work to keep them ready to work Procurement of material well in advance Employment of trained and experienced staff on the project. To provide welfare schemes for the staff and workers such as medical and recreational facilities. To provide incentive for good workers To arrange constant flow of funds for completion of the project. To provide proper safety measures such as proper ventilation, proper arrangement of light and water. Proper arrangements of means of communications and feedbacks etc. Principles of planning The plan should provide information in a readily understandable form, however, complex the situation it may describe. The plan should be realistic. There is no point for example, in planning a building to be completed in six months if the delivery period for the cement is five months. The plan should be flexible. The plan should serve as a basis for project monitoring and control. The plan should be comprehensive. During the planning process, a manager builds the facilities on paper, thus identifies each of the various tasks and time. During construction, this predetermined course of action form the basis for monitoring and the checking the progress of the work. Following steps are followed during planning, scheduling and control. Identifying and defining activity. Defining activity interdependence. Estimate time and resources for each activity. Constructing the network. Calculations on network for project time, earliest start and finish of activity, resource requirement, etc. Project control and project review. Identifying and defining activity
∑tE = (∑t 0 +4∑ tL + tP)/ Estimation of resources: In order to estimate the resources, the project manager must consider the efficiency of the machine, productivity of labour, learning process, site conditions, impact of weather. For example, person at floor level can do more plastering than standing on the scaffolding. Similarly a person's efficiency is less at the start of the work and increases slowly and reaches the saturation level following the learning curve as shown
The above curve is called the learning curve. All these points should be taken into account while planning resources. Construction the network : In the critical path method, network is a directed graph. A directed graph is a structure formulated by nodes, which are tied by directed arrow. Let N= {1, 2……….n} be the set of nodes, and P= {(1, 2) (5, 6)………. (l, j)} be the directed arrow The graph of the activity network is represented mathematically by the symbol [N, P]. There are two logic diagramming formats used in CPM - Activity on the arrow .(AOA) Activity on the node. (AON) Activity on the arrow (AOA): In this format, activity is denoted by the arrow and nodes merely serve as connecting points for the activity. We often require to use activity with zero time called dummy activity to retain the logic and grammatical rules of the network. The network is constructed on the logic that an activity leaving a node cannot begin until the entire activity heading into that node has been completed. This diagramming format has widely been used. Activity on the node (AON): Now-a-days, CPM users employ activity on node format and many of the software also use this diagramming format. This format is also referred to as “Precedence Diagramming”. In this format, logic in the network is represented by node and precedence arrow. The precedence arrows show the order sequence and relationship between activities. The logic behind the network diagram is that an activity cannot start until all preceding activities are complete. The logic network simply represents the relationship between the activities, provides project understanding and improves communications. The network is constructed without considering the activity duration or the resource requirement of the activity. With the advent of computers, this stage has lost its earlier significance. Now there are many software’s available, which provide the network if succeeding activity/proceeding activity lists are fed. Calculation on Network : In this stage , the earliest start , the earliest finish time , latest start time , latest finish time , critical activity ,optimization for time-cost , resource planning through the network , etc , are carried out. We shall illustrate these calculations through examples. Project Control and project review: The planning is pre-construction activity. The schedule of the project tells the project manager how to arrange the various activities and what resources will be required at a particular instant of time, and how much progress is to be expected. During the construction phase, the schedule serves as the yard-stick to check whether the project may be ahead of plan or behind the plan. If it is behind, then network schedule also helps for further resource mobilization. Stages of planning The various stages in planning process are Preplanning: This is the stage of planning before the decision has been taken to take up the project. During this stage, the objectives are to be clearly spelt out, general framework of the project to be formulated, justification of taking up the project, a cost benefit analysis and investment alternatives are all to be given.
Detailed planning: This stage includes the preparation of detailed design, detailed working drawings, specifications and detailed bill of quantities. Also the project breakdown i.e. breaking up the entire project into small component jobs and also establishing the sequence of various operations and allocation of time duration to the different activities in the project. Monitoring and control: This phase involves monitoring of the progress of the project according to the proposed schedule. Also this includes the updating of the schedules, taking into account the actual progress of the project and preparing revised forecasting regarding the availability of the various resources. Advantages of planning Advantages to contractor The contractor knows more about the job. A properly drawn up programme in conjunction with the cost control can prevent the loss of money and help to relieve the financial burden of the contractor. Labor required week by week for each operation can gauged properly if the program has been drawn up earlier. It is a simple matter to produce various schedules from the programme. The programme provides standard against which actual work can be measured. A programme lays down a preconceived plan not only for the whole job but also for the various stages in the job. Advantages to the clients The client will know exactly how long it will take to construct the building and for what length of time his capital will be unproductive, while tied up in construction work. Advantages to the architects/Engineers The programme will normally be prepared by the contractor in closed consultation with the architect. After the contractor has prepared a concise picture of the construction in the form of a programme and the target has been laid down for the various operations, then a draft should be submitted to the architect or engineers for his approval. Limitation of planning The effectiveness of the plan depends upon the correctness of assumption. Planning is expensive. Planning delays action. Planning encourages a false sense of security. Scheduling Graphical representation showing the phase rate of construction activities with start and completion dates and sequential relationship among the various activities or operations in a project so that work can be carried out in an orderly and effective manner. Preparation of construction schedules The project is divided into number of operations and sequences of these operations can be derived after knowing their relationship properly. The quantity of work involved in operation has to be cancelled The time required for completion of project as well as the different activities are to be calculated. This can be done from the quantity of work involved and the rate of performing each work. Uses of scheduling It gives the quality of work involved, labor, materials and equipment for each stage of work. The actual progress of work can be checked. The project can be carried out in a systematic manner using scheduling. Advantages of scheduling By studying the schedule of any work and the many alternative methods of execution, we can choose the best one It gives a clear idea regarding the required men, materials and equipment at different stages of the work. Since the starting time of the each work is known, proper arrangements and requirements can be done prior to the starting of the work. Resource utilization is optimized.
the activity. It has been noticed that when a particular activity represented by a bar is very long, the details will be lacking, if, however, the activity is broken into a number of sub-activities or key events, each one of which can be recognized during the progress of the project, controlling can be done easily and also some interrelationship between the activities established. Mile stone chart Limitations of milestone charts Though controlling can be better achieved with the help of the milestone chart, still some deficiency as bar chart, i.e.; the interdependencies between the milestone charts shown. Within an activity, the relationship between two specific milestones is revealed by the milestone charts but the relationship between and among milestone contained in different activities is indicated. Project management through networks The project scheduling and control can be done by network techniques like CPM, PERT and other allied techniques provided for a more formal and generalized approach towards project control. Objectives of network techniques The term network techniques refer to the method of planning, scheduling and controlling the progress on various components of the projects, especially those projects which are complex in nature. Primarily, it provides an integrated construction management of projects, determines project duration more accurately, identifies the effect of schedule delays well in advance for timely corrective action, facilitates optimization of resources and provides a scientific method of progress reporting and progress control, enabling the management to take better decisions for the effective monitoring of projects. Work breakdown structure In any construction project, the various activities that make up the project have to be clearly identified. The process of breaking the project into easily identifiable major systems, their sub system and discrete activities is called as the work breakdown structures. The major project is first identified in terms of its end items then split into systems, sub systems then their components and elements. Hence work breakdown structure is a device that identifies the functional elements of a project and their inter relationship, when the project is split up in this way into its various functional elements, this will not only help in preparing the network for the project but also in planning and scheduling the activities e.g. the concreting work for the roof slab of a residential building can be split up into various elements as follows: Line of balance Line of balance is a planning technique for repetitive work. In this technique, the required resources for each stages or operation are found out so that, the subsequent stages of the activities are not interfered with and the target output can be achieved. The technique can be applied in repetitive works involving construction projects such as mass housing developments, high rise building, tunnels etc. In a repetitive fashion of construction projects, cost and time effectiveness can be achieved by providing standardization of design for different units of work. It can be achieved by balancing the crews with each other and with constraining resources. By such planning, we can achieve continuity in the placement of all repetitive elements, thus maximizing the productivity of labour and equipment. The technique of LOB can be used for assembling, selecting, interpreting and presenting in graphical form, the essential factor involved in construction from initial stage to the completion of construction against a background of time. This technique is highly effective in determining areas of weakness and focusing on items requiring immediate attention. Advantage of lob techniques
Combining the logic of network analysis with the principles of line of balance provides a very detailed picture of any repetitive projects. Reduce the amount of network planning and scheduling since one network is used for each type of planning. Provide a simple and effective tool for programming the ordering and delivery of materials and subsequently their incorporation into the construction. By monitoring the progress, individual jobs which are falling behind schedule can be easily identified and early corrective measures. Basic terms and definitions used in construction planning Activity Any portion of a project which consumes time or resources and has a definite beginning and an end is called an activity. An activity is denoted by an arrow. Length of the arrow has no significance, the symbol above the arrow indicates activity description and number below indicates activity description and the number below indicates activity duration in time units DESCRIPTION DURATION (T) Representation of an activity Event : The beginning or completion of an activity is termed as an event. It indicates a particular instant of time at which some specific milestone had been achieved. It does not consume any time or resources by itself. Representation of an event Network logic This denotes the technical dependencies among the activities. Good network logic reflects the cost-effectiveness of the project in long-run. Network logic Dummy A dummy is similar to an activity but it does not come any resources. It is merely a method by which interdependence of activities or events can be clearly. A dummy is represented by a dashed arrow. Dummy activity Types of events Tail event An event which marks the beginning of an activity is called a tail event Head event It is that event which marks the completion of an activity Dual role events If an event acts as the tail event for some activity and as the head event for some other activity or activities, it is a dual role event. Burst and merge events In arrow diagrams, there are some nodes to which a number of activities converge; and there may be others from which a number of other activities may diverge. The nodes to which a number of activities converge are called as merge nodes or merge events. The nodes from which a number of activities emerge are called burst events or burst nodes.
A-O-A networks It is composed of arrows and nodes. The arrows represent the activities and nodes represent the events. Each activity carries a brief description usually printed on the logical diagram, the activity name or symbol on the time duration. At present, this method seems to be the most popular method and it was the first method to be introduced, developed and computerized. It is also earlier to associate with time flow of the activities. A major difficulty to arrow diagramming is dummy activity. Learning the usage and significance of dummies requires time and experience. It is also cumbersome to modify A-O-N networks In A-O-N networks, the nodes represent the activities and the arrows, their interdependencies or precedence relationships. Nodes are usually represented by squares or rectangles, but circles and other convenient geometrical shapes may also be used. Activity number and description are written within the boxes representing the nodes. Length and direction of the arrows have no significance as they indicate only the dependency of one activity on another. Precedence diagramming allows more flexibility in modeling relationships than A-O-A networks, as it eliminates dummy activities. Basic assumptions made for creating a network scheme The project can be broken down into a group of activities. Each activity can be assigned a duration Logical relationships among activities ae known and fixed in the network chains. Rules for drawing a network A network will have only one initial node. Initial node will have only one outgoing arrows. Z network can have only one final node. Final node will have only incoming arrows. No activity can start until its tail event occurred. An event cannot occur until all the activities leading up to it are completed. An event cannot occur twice. Hence network looping is not permitted. An arrow should represent a singular situation. Individuality and separate entity of each activity should be maintained The network should be drafted such that all the activities are completed to reach the end objective. All the constrains and interdependencies should be shown properly on the network using dummies Network logic should always be maintained The time flow is usually shown left to right Fulkerson’s rule for numbering the events Activities are generally identified by node number i.e. the number of events on either end of the activity arrow. Hence, it is essential to number events or nodes. The numbering should be carefully done so that logical sequence is maintained. Fulkerson’s rule helps us to do this scientifically. The numbering can be done in the following steps: There will be a single initial event in a network which has only arrows coming out of it. This event is given the number (1) All the arrows coming out of event (1) are neglected. This provides us with one or more initial events. These events are numbered (2), (3), (4) … etc. Again, neglect all the arrows coming out of these numbered events. A few more initial events will be created. These are also numbered similarly This operation is continued until the last event is reached and numbered. Advantages of network techniques over conventional techniques While using network techniques, the inter-relationship of all operations are clearly shown logically. The normal bar chart doesn’t do this and consequently the planner requires remembering the dependencies between various operations and in case of large projects, this becomes extremely cumbersome. When delays occur, while using network techniques, the critical operations call out for extra attention; while, if bar charts are used, unnecessary crashing of operations need to be done, as it becomes impossible for the planner to remember inter-dependencies. Planning, analyzing and scheduling ae separated when using networks, as it allows a greater concentration on planning aspects
Critical path method These methods are usually used for repetitive type of projects, where fairly accurate estimates of time can be made for the activities of the project. The activities of project are characteristically subject to relatively small amount of variation. Hence CPM is not suitable for research and development type of projects. Difference between CPM and PERT CPM is an activity oriented network while PERT is event oriented. In CPM, the time estimates are of fair degree of accuracy, while in PERT, the time estimates are not that accurate and there is an uncertainty attached to it. CPM follows the ‘deterministic approach’ and PERT follows ‘probabilistic approach’. In CPM, cost is the governing factor while in PERT, time is governing factor. In CPM, the project duration is so fixed that cost is minimum. In PERT, it is assumes that cost is directly proportional to time. So time is reduced to maximum possible so as to enjoy least cost. The critical path in CPM is that path which joins the critical activities, while in PERT, critical path is the path which joins the critical events. Activity Time In the network, it is important to know the criticality of the activity, time available to perform the activity provided date of completion of a project. In the previous section we have already talked about various method of obtaining activity duration. We shall be interested in the question that How early we can start the activity. How much we can delay the activity such that target date of completion of project is not affected What the time available to perform the activity. To answer the above question we shall associate (define) following time with an activity. Early start time Early finish time Latest start time Latest finish time Early start time: - It is the earliest time by which an activity can start. Let tij^ be the activity between events i and j. Let T (^) E i^ is the earliest expected time of the event i then Earliest start time is equal is to EST = T E i Earliest finish time: The earliest finish time of an activity is the time by which an activity can be finished earliest. The earliest finish time of an activity is earliest start time plus activity duration. EFT = EST + activity duration Latest finish time: The latest finish time is the time by which an activity must be finished such that completion of the project is not delayed the latest finish time of an activity between events i and j is the latest allowable event time of LFT= T (^) Lj Latest start Time: The latest start time is the time by which an activity must start such that completion of project is not delayed. The latest start time of an activity between events i and j is latest finish time minus activity duration. LST = LFT – activity duration Float: In the last reading we have discuss that in the project with art interested in time available to execute particular task(activity) during the project period. We shall introduce the concept float which tells us how much an activity can fluctuate without affecting the completion of a project. We shall introduce following float Total float. Free float. Independent float Interfering float. Total float: Total float is the maximum time available during which an activity can fluctuate. It is maximum time available minus activity duration. The maximum time available in the difference between latest finish times minus earliest start time. Maximum time available to execute the work = LFT – EST Hence total float = maximum time available – activity duration
TE of 9 = 20 These computations can be done in the network itself, by entering the values of T E for each node near that node itself. If there is more than one TE value obtained from different paths, all the values are first written and then, only the largest value is retained while others are scored off. This practice is generally followed only in the initial stages. As experience is gained, only the largest value will be written after computing and comparing mentally as shown in figure. In large and complicated networks, the calculations are usually done in tabular forms, so as to avoid mistakes that might creep in. In the tabular format, the first column is for the event whose TE is to be computed or in other words, the head event are successor event. The second column contains the predecessor event/ events of the successor event in the I column. If there are more than one predecessor event for a successor event, all the predecessor events are entered one after the other down the column. Third column indicates the activity between the corresponding events in the I and II columns. These are the activities that culminate in the event in the I column. The fourth column contains the duration of the corresponding activity on the third column. The fifth column contains the TE values of the event in the first column calculated for all paths. There might be more than T E value if the head event has more than one predecessor. These TE values are obtained by adding the TE values of the corresponding predecessor event with the corresponding tij^ value in the fourth column. If there is more than one TE value for a particular event, the largest among them is taken as the TE of the event and entered in the sixth colmn. .
The TE values of the event is calculated as follows
s.no Successor event j Predecessor event i Activity i-j Duration tij^ TEj^ TE 1 1 0 - - 0 0 2 2 1 1-2 3 3 3 3 3 1 1-3 4 4 4 4 4 2 2-4 2 5 7 3 3-4 3 7 5 5 3 3-5 6 10 10 6 6 3 3-6 4 8 8 7 7 4 4-7 4 11 15 5 5-7 5 15 8 8 5 5-8 7 17 17 6 6-8 4 12 9 9 6 6-9 3 11 20 7 7-9 2 17 8 8-9 3 20 Example 2 Find the latest event time in the network given below Since Ts is not given the TL of event 9 can be taken to be equal to TE of event 9. TL of event 9= TL of event 8=20-3= TL of event 7= 20-2 = TL of event 6=20-3 =
Therefore TL6 = TL of event 5 =17-7= 18-5= Therefore TL5 = TL of event 4=18-4= TL of event 3=10-6= 13-4 = Therefore TL3 = TL of event 2=14-2= TL of event 1=12-3= 4-4= Therefore TL1 = These values can be calculated from the network itself by writing down the values near the nodes themselves. If there are more than one value arising out of different paths, only the smallest value is retained and the others are scored off. As practice is gained, it is usual to do the computation and comparison mentally and only the smallest value will be written near the node
For large and complicated networks, these calculations are done in a tabular form for ease. In this
process, the computations are started from the last event and are done backwards till the first event is
reached, as shown in the table.
s.no Predecessor event i Successor event j Activity i-j Duration tij^ TLj^ TL 1 1 2 1-2 3 9 0 3 1-3 4 0 2 2 4 2-4 2 12 12 3 3 4 3-4 3 11 4 5 3-5 6 4 6 3-6 4 9 4 4 7 4-7 4 14 14 5 5 7 5-7 5 13 10 8 5-8 7 10 6 6 8 6-8 4 13 13 9 6-9 3 17 7 7 9 7-9 2 18 18 8 8 9 8-9 3 17 17 9 9 - - - 20 20 Example 3 Find the floats of all the activities and the critical path of the network given below The TE and TL values of all events are computed and marked in the network
The expected mean time is derived from the following equation Te = (to +4tm+tp)/ The standard deviation is given by σt = (tp-to)/ Variance is defines as square of standard deviation so that vt = (σt)^2 = (tp-to)^2 / Earliest expected time ( TE) The earliest expected time is the time when an event can be expected to occur. It is usually put above or below the node. It is calculated by adding the expected times (te) of all the activities along the path leading to that event. If more than one activity path lead to the end activity, the maximum value of the sums of expected times along various paths up to that event is taken as TE of that particular event. For large complicated networks, TE can be found by TEj^ = TEi^ + teij^ for only one predecessor event Here TEj^ is the event for which TE is to be found TEi^ is the predecessor event of TEj teij^ is the expected time of activity i-j If there are more than one predecessor events, the TEi^ for each event is found out and maximum value from among them is taken as TE of that event j. Latest allowable occurrence time (TL) The latest time by which an event must occur to keep the project on schedule is called the latest allowable occurrence time. TL can be calculated by TLi^ = TLj^ - teij^ for one successor event Here TLj^ is the event for which TL is to be found TLi^ is the predecessor event of TLj teij^ is the expected time of activity i-j If there are more than one successor events, the TLi^ for each successor is found out and minimum value from among them is taken as TL of that event i. Slack The difference between the earliest occurrence time and latest allowable occurrence time of an event is called the slack of the event. Slack can be positive, zero or negative Positive slack is obtained when TL is more than TE. It indicated ahead of schedule condition Zero slack is obtained when TL is equal to TE. It indicates on schedule condition. Negative slack is obtained when TL is less than TE. It indicates behind the schedule condition. Example 1 Find the TE of all the events in the network
Since event 1 is the initial event: TE of 1= TE of 2= 0+4=4 since it has only one path. TE of 3=0+4=4 since it has only one path. TE of 4= in this case, there are three paths leading up to event 4:1-2-3, 1-3-4 and 1-4. TE along 1-2-4= 4+3= Along1-3-4=4+4= Along 1-4=0+6= Of these, TE along 1-3-4 is the largest = Hence TE of event 4= TE of event 5= 8+5= The TE of each event can be shown in the network itself. Example 2 Find the TE of all the events in the network given below Event one is the initial event hence TE 1 of 1= For event 2, TE 2 =0+4= For event 3, TE 3 =0+5= For event 4, TE 4 =4+3= =0+6= =5+4= Of these, 9 is the largest value Therefore TE 4 = For event 5, TE 5 =4+4= For event 6, TE 6 =5+6= For event 7, TE 7 =8+6= =9+8= =11+3= Of these, 17 is the largest value. Therefore TE 7 = For event 8 TE 8 = 17+5= The network can be redrawn to incorporate the TE values of each event. Example 3 Find the TE of each event in the network given below
Of these, the least value is taken TL^3 = Event 2 has two successors 4 and 5. TL^2 = TL^5 - te2-5^ = 11-4= TL^2 = TL^4 - te2-4^ = 9-3= TL^2 = Event 1 has three successors 2,3 and 4. TL^1 = TL^2 - te1-2^ = 6-4= TL^1 = TL^3 - te1-3^ = 5-5= TL^1 = TL^4 - te1-4^ = 9-6= TL^1 =0 as it is the least value of the three values. The TL values can be noted in the network itself as shown in figure Example 5 Find the TE and TL of all the events of the network given below event Earliest expected time Latest allowable occurrence time Predecessor event teij^ TEj^ TE Successor event teij^ TLi^ TL 1 - - 0 0 2 3 8 0 3 4 7 4 6 0 2 1 3 3 3 5 4 11 11 3 1 4 4 4 5 2 13 11 6 3 11 4 1 6 6 6 6 8 6 6 7 4 12 5 2 4 7 7 9 6 15 15 3 2 6 6 3 3 7 14 4 8 14 14 9 7 14 7 4 4 10 10 8 3 16 16 8 7 3 13 13 10 6 19 19 9 5 6 13 21 6 7 21 21 10 4 21 10 8 6 19 25 9 4 25 25 - - 25 These values can be written in the network itself as follows:
Example 6 If the scheduled date of completion of the project is 36 weeks find the slack of each event as well as the critical path of the network shown below. event Earliest expected time Latest allowable occurrence time Predecessor event teij^ TEj^ TE Successor event teij^ TLi^ TL 1 - - - 0 2 3 -2 - 2 1 3 3 3 3 4 1 1 4 3 4 6 4 7 3 2 4 7 7 5 5 5 5 4 2 3 6 6 6 4 7 7 7 7 11 5 3 5 12 12 6 0 11 10 7 6 10 6 2 4 7 12 7 5 11 11 4 4 10 5 0 12 7 4 7 13 18 8 5 16 16 5 6 18 9 4 17 6 5 17 8 7 5 23 23 10 3 21 21 9 7 4 22 22 10 3 21 21 11 5 25 10 8 3 26 26 11 6 24 24 9 3 25 11 9 5 27 32 12 6 30 30 10 6 32 12 11 6 38 38 - - 36 36 The TE and TL of each event is found out from the tabular form since TS is given as 36 weeks, TL of 12 is taken as 36 weeks. The TE and TL values of each event are calculated. From the values we find that TE^12 = 38 weeks. Whereas the scheduled completion date is 36 weeks. This means that the project will have to completed two weeks earlier than what it would normally take for its completion. This means that additional resources will have to be provided to complete the project within the scheduled time of completion.
The slack for each event is found out by deducting TE from TL it is tabulated below.
Event TE TL slack 1 0 -2 - 2 3 1 - 3 7 5 -
