In book: Essentials of Operations Research, Chapter: Network Techniques critical path analysis is an important aspect of project planning. There is multitude of operations research situations that can models. Network analysis is known by many names _PERT (Programme Evaluation and. the techniques of operational research to plan the optimum use of resources. PERT and CPM are the two most popular network analysis technique used to.
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analysis which can bo applied to P&RT/CPH networks. mant, Operations Research (OR)$ and Inuustrial Engineoring texts and .. 'Ihis triangular pdf is then. INTRODUCTION AND BASIC DEFINITIONS IN NETWORK ANALYSIS. Introduction. A Project such as setting up of a new milk plant, research and. Network Analysis. •. Network Scheduling: •. Main purpose of CPM is to determine the “critical path”. •. Critical path determines the minimum completion time for a.
Further, this network analysis determines in advance the normal duration and cost, as well as minimum duration and cost, of a project to be implemented. Importantly, this technique helps managing risks and waste, and determining in advance possible implementation of events and activities in a project.
It is also difficult to complete massive scaled projects without having network analysis, since such projects employ large amount of financial, human, physical and other resources at an optimum level.
Further, as they have alternative utilizations, network analysis becomes essential for determining and managing their mobilization within projects. Hence, the application of network analysis is useful to facilitate planning and implementing management activities, allocating resources for their optimum utilizations, and defining, designing and completing activities within stipulated time frames.
A basic design of network analysis was introduced in the USA and the UK in the middle of in view of reducing durations of projects. In , a team formed under the US Special Navy Project Office devised a technique for planning and controlling complex and complicated projects. Lucey indicates that this technique was useful to plan and control a missile project, called Polaris in the USA and had helped to save two years in implementing the missile project.
Since , this technique has been in use in various fields and its developments and improvements are still in progress.
In general, different terminologies are used to indicate this technique. Further, he indicates that network analysis is a basic terminology consisting of a set of techniques that has been developed for planning and controlling of projects in view of facilitating the management of an organization.
He also indicates that while these techniques show the relationships among functions and activities, they are useful to identify critically and clearly each section and to provide information in terms of activities, and their respective individual time, cost and resource requirement in a project. According to Lucey , a network analysis for a project plays a critically important role, when the project consists of following identical features.
Complexity of the project: this is possible, when the project consists of many activities, which are much dependent on other activities. Large scale projects: it refers to the project that requires many facilities, large amount of capital and labour density.
A large number of restrictions: this happens when the project needs to be completed within a time frame and cost limit that are related to utilizing the resources of raw material and labour, partially or as a whole. In these sectors, in relation to a project, network analysis significantly contributes to manage effectively and efficiently the project s completing duration, resource utilization and resource-related cost control; and further, it critically facilitates devising and implementing appropriate controlling process in accordance with the project duration.
In Sri Lanka, in practical application, it is notable that the use of network analysis is significantly very less. Particularly, this technique is rarely used in the government sector. If the government sector utilizes the network analysis, at least in building projects, it is possible to reduce the delay in completing duration, to allocate right resources with right quantity, to avoid unnecessary wastage of the resources and to estimate the relevant cost, effectively and efficiently in relation to the building projects.
Compared to other countries, the application of network analysis in government sector of Sri Lanka is very less and she needs a critical attention on the application of this networking technique in the building projects of government sector. It is notable that there is a considerable improvement in the private sector in the application of the network analysis.
However, the importance of applying this technique in projects can be realized meaningfully in near future through current rapid development in Sri Lanka. Other terms in the network are relatively and appropriately introduced and illustrated in the following chapters. Generally, it is custom to represent an activity by an arrow and hence, there are two 2 events for each and every activity and an event is normally shown by a circle in the network diagram.
When placing an event in a network diagram, the event at the beginning of an activity is called Tail Event; and the event at the end of the activity is called Head Event.
It is notable that the action of representing an activity by an arrow places itself both tail and head events for the activity, because the activity itself consists of tail event at its commencement starting point and head event at its completion ending point.
An activity represents its importance in a project to be completed in a particular time span and requires sufficient amount of resources for its completion, for an example: building a wall or digging for putting up a foundation for a building. The time required to complete a particular activity is known as its completion duration. Generally, there are many identical activities in a project. These activities should be arranged in a sequential order of completion, based on their individual dependency on preceding activity ies.
There are two general approaches to draw a network diagram of a project that consists of different and identical activities. Activity-on-arrow diagram 2. Activity-on-node diagram In the activity-on-arrow network diagram, it is customary to show an activity with an arrow.
The head of the arrow indicates where the activity ends completes and the tail of the arrow indicates the beginning of the activity. In a project, an activity can depend on other activity for its commencement.
When drawing such dependent activities in a network diagram of the project, the events are used to connect and differentiate those activities.
Figure 1. It is shown in the network diagram in Figure 1. In this diagram, every rectangle represents an activity. Further, no event takes place in a network diagram of activity-on-node.
When a network diagram is of activity-on-node, two additional nodes for Start and Finish must be placed, apart from the nodes representing the activities. Graphical Method. Simplex Method. Theoretical Probability Distributions. IT Skills. Management Skills. Communication Skills. Business Skills. Digital Marketing Skills. Human Resources Skills. Health Care Skills. Finance Skills. All Courses.
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This value is the TE for event 2. Step 4: Repeat the same procedure from step 3 till the end event. Step 1: Begin from end event and move towards the start event.
Assume thatthe direction of arrows is reversed. Latest Time TL for the last event is the earliest time. TE of the lastevent. Go to the next event, if there is an incoming activity, subtract the valueof TL of previous event from the activity duration time. The arrived value isTL for that event. If there are more than one incoming activities, take theminimum TE value.
Network Analysis.pdf - OPERATIONS RESEARCH O R NETWORK...
Repeat the same procedure from step 2 till the start event. The float of an activity is the amount of time available by which it ispossible to delay its completion time without extending the overallproject completion time.
The total float of an activity is the difference between the latest start time and the earliest start time of that activity. Free Float FFij: The time by which the completion of an activity can bedelayed from its earliest finish time without affecting the earliest starttime of the succeeding activity is called free float.
Network Analysis.pdf - OPERATIONS RESEARCH O R NETWORK...
The amount of time by which the start of an activitycan be delayed without affecting the earliest start time of any immediatelyfollowing activities, assuming that the preceding activity has finished at itslatest finish time. Critical Path: After determining the earliest and the latest scheduled times forvarious activities, the minimum time required to complete theproject is calculated.
In a network, among various paths, thelongest path which determines the total time duration of theproject is called the critical path. The following conditions mustbe satisfied in locating the critical path of a network. An activity is said to be critical only if both the conditions are satisfied. A project schedule has the following characteristics as shown in Table i.
Construct PERT network. Compute TE and TL for each activity. Find the critical path. The calculations of TE and TL are as follows: In certain projects like research anddevelopment, new product introductions, it is difficult to estimatethe time of various activities.
Hence PERT is used in such projects with a probabilistic method using three timeestimates for an activity, rather than a single estimate, as shown in Figure 8.
Optimistic time tO: It is the shortest time taken to complete the activity.
It means that if everything goes well then there is more chance of completing the activity within this time. Most likely time tm: It is the normal time taken to complete an activity, if the activity were frequently repeated under the same conditions. Pessimistic time tp: It is the longest time that an activity would take to complete.
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It is the worst time estimate that an activity would take if unexpected problems are faced. Taking all these time estimates into consideration, the expected time of an activity is arrived at.
The average or mean ta value ofthe activity duration is given by,The variance of the activity timeis calculated using the formula,Probability for Project DurationThe probability of completing theproject within the scheduled time Ts orcontracted time may be obtained byusing the standard normal deviatewhere Te is the expected time of projectcompletion. Probability of completing the projectwithin the scheduled time is, Draw the project network.
Find the probability that the project is completed in 19 days. Time expected for each activity iscalculated using the formula 5: Similarly, the expected time iscalculated for all the activities. The variance of activity time iscalculated using the formula 6. Similarly, variances of all theactivities are calculated. Construct a network diagram: From the network diagram Figure 8.
Cost isdirectly proportional to time and vice versa.
For example, in constructing a shopping complex, the expected time of completion can be calculated using be time estimates of various activities. But if the construction has to the finished earlier, it requires additional cost to complete the project. Normal time: Normal time is the time required to completethe activity at normal conditions and cost.
Crash time: Crash time is the shortest possible activitytime; crashing more than the normal timewill increase the direct cost. Cost SlopeCost slope is the increase in cost per unit oftime saved by crashing. A linear cost curveis shown in Figure 8.
ExampleAn activity takes 4 days to complete at a normal cost of Rs. If it is possibleto complete the activity in 2 days with an additional cost of Rs.
Project CrashingProcedure for crashingStep1: Draw the network diagram and mark the Normal time and Crash time. Calculate TE and TL for all the activities.
Find the critical path and other paths. Find the slope for all activities and rank them in ascending order.
Step 5: Establish a tabular column with required field. Step 6: Select the lowest ranked activity; check whether it is a critical activity. If so,crash the activity, else go to the next highest ranked activity.A network diagram needs to be placed with events and activities from left to right or top to bottom up-down. Activity-on-node diagram In the activity-on-arrow network diagram, it is customary to show an activity with an arrow.
Identifying various activities to be performed and determining the requirement of resources such as men, materials, machines, etc. It helps an organization mainly to facilitate in designing, activating and implementing a project within a time span. Published in: In these sectors, in relation to a project, network analysis significantly contributes to manage effectively and efficiently the project s completing duration, resource utilization and resource-related cost control; and further, it critically facilitates devising and implementing appropriate controlling process in accordance with the project duration.
Marketing Research Practice Tests. Figure 1. In the same way, another activity where activity E only can be organized, where the activity can have both or more activities D and F as preceding activities as in Table 1. Go to the next event i.