Project scheduling
It is difficult to determine the expected duration of activities of the project accurately. The triple time estimates give a reliable measure of the project completion period (Collins, 2011). The triple time estimates are used to determine the time, standard deviation and the variance for each activity as well as the entire project. The following formula gives the activity times:
Activity time = (Optimistic time+4×Most likely time+pessimistic time)6
Standard deviation = (Pessimistic time- Optimistic time)6
Network diagram
The above network diagram indicates that the project will be completed in 72.67 days. The total duration of the critical path is 72.67 days. Critical path consists of critical activities; activities that cannot be delayed without affecting the completion date of the entire project. If the start time for a critical activity is delayed, the duration of the whole project will be delayed by the same time (Maylor, 2010). As shown in the Gantt chart above, there are six critical activities in this project. They include activities A, C, D, H, J and K. The table below indicates that float for each activity.
The table above indicates that activities A, C, D, H, J, and K do not have any slack implying that they cannot be delayed beyond their normal start times without affecting the duration of the entire project. All the other activities have time floats.
Implication of time floats
The above activity time floats can be used in project scheduling. Project scheduling helps allocation of resources to each activity thereby ensuring that the project is completed within the time and resource constraints (Lock, 2013). Activities A, C, D, H, J, and K are critical activities hence they cannot be rescheduled. This implies that in any day, critical activities must be allocated adequate resources first before allocating to other activities. Non-critical activities can be rescheduled or delayed up to a maximum period equal to the time floats (Lock, 2013). For instance, activities B and C are completed in almost the same week. If there is a limited resource, for instance, labor, the project management can reschedule activity B to ensure there is adequate allocation to activity C. Activity B can be delayed for 2.67 days to allow adequate resource allocation to activity C. Activities E and F also have slacks, and they can be rescheduled or delayed for 2 days without interfering with the normal completion date of the project. Activity G has a slack of 8 days hence its start time can be delayed by eight days without affecting the project’s duration. Activity I also has a time float of 4 days. However, the duration of the project will be interfered with if the delay is more than the slack available. IC can only delay activity I by four days. Any delay beyond four days will cause a delay in the completion of the entire project.
The concept is also applied in crashing the project. Crashing involves reducing the project’s duration to complete it before the normal duration. Crashing involves additional costs such as allocating more resources than normal to reduce activity time. When crashing the project, IC should concentrate on critical activities since it is their duration that determines the project’s completion dates. Resources available for crushing the project should be allocated to critical activities. If the duration of a critical activity is reduced, the duration of the entire project will be reduced.
Project duration and probability
The above calculations indicate that the expected project completion time is 72.67 days. The standard deviation of the project’s completion time and the average completion time can be used to determine the probability of completing the project within a given period. The standard deviation for activity time is given as follows:
Activity time standard deviation = (Pessimistic time-Optimistic Time)6
The variance for the entire project is the sum of activity time variances for all critical activities. In this case, the project’s variance is calculated as follows:
Project’s variance = 1 + 1 + 4 + 4 + 1 + 21.78
= 32.78
Standard deviation of eth project = Variance
= 32.78
= 5.725
Duration of the project = 72.67 days
Average duration = 70 days
The probability of completing the project in 70 days or less is given by the Z equation below.
Z = (70-72.67)5.725 = -0.466375 = -0.47
P (Z = -0.47) = 0.3192
The above result shows that there is only a 31.92% chance that the project will be completed within 70 days. This implies that the project is likely to take longer than the average project. Therefore, to ensure it is completed within the completion time for the average project, International Capital Inc. will be forced to crash the project. If the critical activities of the project are crashed, the project could be completed within 70 days. If the company does nothing, there is a 68% chance the project will be completed in more than 70 days.
Probability = 95% = 0.95
The Z-score for P (0.95) is 1.645
1.645 = 70-x5.725
70 – X = 9.417625
X = 70 – 9.417625
= 60.58 days
The average completion time for the project must be 60.58 days to ensure a 95% probability of completing the project within 70 days. Therefore, the average time must be reduced by about 12 days to be 95% sure of completing the project within 70 days. Therefore, International Capital Inc. must establish measures to reduce the project’s expected completion time. These measures include crashing the project, enhancing efficiency through training, using appropriate methods and technology, among other measures.
References
Collins, R. (2011). Project management. New York: Nova Science Publishers.
Lock, D. (2013). Project management (10th ed.). Farnham, Surrey, England: Gower Pub.
Maylor, H. (2010). Project management. Harlow, England: Financial Times Prentice Hall.
