Project Management Network Diagram - Essay Example

Full topic and Section # of CONTENTS S.No Chapter P.No Network diagram task 1 3 2. Calculation of confidence interval 4 3. Network diagram Task 2 6 4. Determination of completion time of project 7 5. References 9 a) There are various statistical tools and diagrams used for managerial decision making. But the popular charts that are used for decision making such as the Graphs, Gantt Charts are not useful when the situation requires analysis on a sequential aspect. When the project involves series of activities which requires to be completed in an order network analysis is very essential. A network diagram shows the interdependencies of the activities that are involved in a project. Networks are composed of events and activities. An event is defined as the starting or ending point for a group of activities and an activity is the work required to proceed from one event or point of time to another.(Kerzner, 1992). The numbers over the arrow specifies the time needed. To know the relationships between activities what job precedes a particular job, what job immediately follows this job and what jobs can run concurrently have to be listed and the time required for the completion is estimated. Based on the chronological order in which they have to be completed, the following network diagram is constructed: A C F 8 12 8 6 D 5 E 7 G B H I J 8 7 4 5 From the above diagram we can understand the sequence of activities and their relative importance in the completion of the project. From the information provided we can tabulate and determine the critical path of the project. The Critical path is the sequence of activities which are crucial because delays to them will delay the completion of the project as a whole(Needham, 1997). The late finish and the late finish of the activities are calculated first. The early finish is the optimistic estimate of the completion time of the specific activity and the late finish is the pessimistic estimate of the duration of the activity. The slack time is the difference between the early finish and the late finish. In other words, the slack time denotes the time duration which can be delayed without delaying the entire project. But there are some activities which have the slack time zero, which means that these activities cannot be delayed. These activities are critical for the successful completion of the project because they cannot be delayed. The Appendix - 1 shows the calculation slack time of the activities. The calculation shows that the critical path consists of activities, A, D, H, I, J which are crucial for the completion of the project because they do not have any slack time. b) Normal distribution curves are very useful to analyze the frequency of data. When we construct a standard normal probability distribution table, the relationship between the mean of the distribution and the random variable is established. The formula used is: Z = x - / , Where, Z = number of standard deviations from x to the mean of this distribution X = value of the random variable with which we are concerned = mean of the distribution of this random variable = standard deviation of this distribution The value obtained from using the above mentioned formula is then referred in the Normal Probability distribution able. The calculation of the probability distribution in this case is shown in Appendix - 2. The tabulation shows the chances that the activity will be completed within the estimated time duration. The management should take added effort to ensure that the activities with low probability are completed without any time delay. c) To calculate the probability that the project has to be completed in 32 weeks to gain the discount and to avoid the incurrence of cost, the above mentioned formula is used again. The possibility that the project will be completed can be calculated as follows: Z = x - / Where, Z = number of standard deviations from x to the mean of this distribution x = value of the random variable with which we are concerned = 32 = mean of the distribution of this random variable = 30 = standard deviation of this distribution = 8 Here, Z = (32 - 30) / 8 = 0. 25 If we apply the standard normal distribution value from the table at 95% confidence level (0.0987), to calculate the chance that Evelina will incur the 60000, if we subtract 0.0987 from 0.5 we get 0.4013(Levin,1978). Hence, there is 40.13 chances in 100 to incur the loss. Task 2 a) The network diagram which shows the relationship between the activities that have to be done for the completion of the project is shown below: F I M Q 2 2 2 3 C 2 L 1 A B E H K O 3 1 3 5 5 1 D 4 G J N P 3 3 3 12 To calculate the minimum project duration time the table sown in Appendix -3 can be used. First the critical path is calculated. The critical path for this project consists of activities, A, D, G, J, N and P. The project completion time is 28 hours with two Type 1 staff are working. i) Currently there are 2 staff (type 1) are working and the minimum duration of the project is 28 hours. It is indicated that 4 staff type 1 can be brought in for the project. Hence, it will be possible to complete the project within the minimum time indicated by the network. ii) If 2 staff (type 1) are working the total time duration of the activities is 55 hours, but when the management is providing 4 staff (type 1), then the total time of the activities will be reduced to 27.5 hours. The expected completion time of the project by the management is 5% above the project critical path time, i.e., 28.9 hours. The project can be completed within the time expected by the management. b) For the completion of a project, the allocation of resources is very essential for the effective utilization of resources. the resources should not be over utilized or underutilized. Over utilization of resources creates strain on the smooth flow of activities and can create bottlenecks in the project. Underutilization of resources can increase the cost of the project. To survive and sustain the competition in the industry, the management of the project should keep the cost at the minimum level. Hence, any unnecessary increase in cost should be avoided. For this purpose, the management can use various statistical tools to monitor the effective usage of resources. In this case the total duration of the project can be calculated from Appendix - 3. The sum of the duration of all the activities of the project shows that the total duration of the project is 55 hours. It is mentioned that the company plans to operate three shifts. If 4 men are working in the morning and afternoon shifts and only two men are employed for the night shift, the total time duration of the activities 55 hours will be reduced to 13.75 hours (55/ 4). If one shift extends for 8 hours, the project will end in the afternoon shift because it is mentioned that the activity starts in the morning shift. From this analysis we can understand that the project can be completed within 1/4th of the original duration of the project if 4 people are employed. It does not matter that the night shift has only two workmen, because the 4 people employed in the morning and afternoon shifts are sufficient enough to complete the project before the start of the night shift. If the management plans to complete the project more quickly the addition of people employed can be justified. The costs associated with the delay in the project can be avoided and also the company can gain advantage from the early completion. Customer satisfaction can be increased by completing the project well before the original completion time. c) The job of a project manager is to analyze and decide upon the effective allocation of resources to achieve the desired benefits from undertaking a project. The project manager analyses various possibilities when it comes to allocation of resources to decide on the most effective utilization of resources. In this case, the project manager has to decide whether the allocation of extra maintenance staff is essential or not. If an extra maintenance staff is allotted then the activity 1 - 2 is reduced by 1 hour. The total duration of the project which is the summation of the duration of all the activities involved will be reduced from 55 hours to 54 hours because duration of the activity 1 - 2 is reduced by 1 hour. If 4 men are working in the morning and afternoon shifts and only two men are employed for the night shift then the project the time taken to complete the project can be calculated by dividing the total duration of the project by 4, which is 13.5 hours. If one shift is 8 hours and the activity starts in the morning shift, then the project will be completed in the afternoon shift. From the calculations it can be noted that there is a saving of only 0.25 hours when an extra maintenance staff is allotted. The decision to increase the number of people employed will depend on a number of factors such as the increase in the financial benefits, cost savings, increase in customer satisfaction and meeting specific customer requirements just to name a few. The manager has to compare the inherent benefits of increasing the number of people working and the cost involved. the managerial decision should be based on this comparison. REFERENCES 1. Levin, R.I (1978) Statistics for management, Prentice Hall, London 2. Needham, D and Dransfield, R (1997) Understanding Business Studies, Stanley Thornes Ltd, Glasgow Extra readings 3. Dick, B.H and Max, G (1970) Project control standards, Brandon system press, Princeton 4. Lock, D (1996) Essentials of Project management, Oxford university press, New York 5. Kerzner, H ( 1992) Project management: a systems approach to planning, scheduling and controlling, 4th ed, Van Nostrand Reinhold, New York 6. Dick, B.H and Max, G (1970) Project control standards, Brandon system press, Princeton. 7. Avots, I (1975) "Making project management work: the right tools for the wrong project manager", S. A. M Advanced management journal, Vol 40, pp 20-26 8. Frankwicz, M, J (1973) "A study of project management techniques", Journal of Systems management 24, October, PP 150 - 165 Appendix 1 Calculation of slack time ( task 1) NODE CODE ACTIVITY CODE IMMEDIATE PREDECESSOR DURATION ( WEEKS) EARLY FINISH LATE FINISH SLACK 1 A 10 - 20 - 8 8 8 0 2 B 10 - 50 - 5 5 14 9 3 C 20 - 30 20-Oct 12 20 22 2 4 D 20 - 40 20-Oct 6 14 14 0 5 E 20 - 50 20-Oct 5 13 14 1 6 F 30 - 80 20 - 30 8 28 30 2 7 G 40 - 70 20 - 40 7 21 25 4 8 H 50 - 60 10 - 50, 20 - 40, 20 - 50 7 21 21 0 9 I 60 - 70 50 - 60 4 25 25 0 10 J 70 - 80 40 - 70, 60 - 70 5 30 30 0 Appendix 2 Calculation of standard normal probability distribution Activity code Immediate Predecessor Duration (weeks) SD z 95% confidence C* 20-Oct - 8 Oct-50 - 5 20 - 30 20-Oct 12 2.5 2.12 0.4842 0.0158 20 - 40 20-Oct 6 1 0.7 0.2734 0.7734 20 - 50 20-Oct 5 30 - 80 20 - 30 8 1 1.3 0.4115 0.0885 40 - 70 20 - 40 7 50 - 60 10 - 50, 20 - 40, 20 - 50 7 2 0.15 0.0596 0.4404 60 - 70 50 - 60 4 0.5 5.4 70 - 80 40 - 70, 60 - 70 5 1 1.7 0.4599 0.9599 Appendix - 3 Calculation of slack time (Task - 2) Node Code Activity Immediate Duration Resource Requirements Early Late Slack Predecessors (Hours) Type 1 (staff) Type 2 (hoist) Finish Finish 1 A 2-Jan - 3 2 0 3 3 0 2 B 3-Feb 2-Jan 1 2 1 4 14 10 3 C 4-Feb 2-Jan 2 2 1 5 19 14 4 D 5-Feb 2-Jan 4 2 0 7 7 0 5 E 6-Mar 3-Feb 3 2 0 7 17 10 6 F 7-Apr 4-Feb 2 2 0 7 21 14 7 G 8-May 2-5, 2-4 3 2 1 10 10 0 8 H 9-Jun 6-Mar 5 2 1 12 22 10 9 I 10-Jul 7-Apr 2 2 0 9 23 14 10 J 11-Aug 4-7, 5-8 3 2 1 13 13 0 11 K 12-Sep 6-9, 2-4, 2-5 5 2 1 17 27 10 12 L 12-Oct 10-Jul 1 2 0 18 23 5 13 M 14-Oct 10-Jul 2 2 0 11 25 14 14 N 13-Nov 8-11, 7-10 3 2 0 16 16 0 15 O 15-Dec 9-12, 10-12 1 2 1 18 28 10 16 P 13-15 13-Nov 12 2 0 28 28 0 17 Q 14-15 14-Oct 3 2 1 14 28 14 Read More