This paper applies Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) analysis to a residential construction project for Moore Housing Contractors. Using activity-on-node (AON) network diagramming, the analysis calculates expected completion time based on optimistic, most likely, and pessimistic time estimates for each construction activity. The critical path is identified at 45.83 days, yielding only a 34% probability of meeting the 45-day deadline. The paper identifies critical activities requiring close monitoring (A, B, E, G, K, M, Q, T, V, W) and recommends resource reallocation from high-slack activities (D, H, J, S, U) to support the critical path, enabling potential schedule acceleration.
Moore Housing Contractors are working through a proposal to build six new houses in a new development. The real estate company requires a strict schedule of a maximum of 45 days to build each house. If a house is not completed within 45 days, the realtor will charge the contractors a penalty. To calculate the estimated time and steps needed to build each house, the contractors must create a CPM/PERT network chart.
The approach used to create the CPM/PERT network is the activity-on-node (AON) chart. The arrows on the chart represent the precedence relationships between activities. This visual representation shows the process flow needed to complete the project and provides a foundation for scheduling analysis and risk assessment.
To analyze whether houses can be completed within 45 days, the next step is to determine the average time required for each activity. Moore Housing provided three time estimates for each step in the construction process: a (optimistic time estimate), m (most likely time estimate), and b (pessimistic time estimate). A weighted calculation was used to find the mean of all three estimates to establish the best estimate for expected time.
With the best time estimates established, the critical path can be determined. The critical path is the longest path through the diagram and shows how long a project is expected to take if the scope does not change and everything goes according to plan. When all the mean time estimates for each activity on the critical path are added together, the total comes to 45.83 days. Using the normal probability distribution, the analysis yielded a 34% probability that the project would be completed within the 45-day deadline.
Since this probability is relatively low, the recommendation to Moore Housing would be to increase their bid to cover potential penalty charges associated with a likely schedule overrun.
The project activities that Moore Housing should monitor particularly closely are those that fall within the critical path. Since the critical path represents the minimum time required to complete the project, any delay in critical activities will delay the entire project, leading to additional costs and time overruns. The analysis identifies 10 critical activities that require close monitoring: A, B, E, G, K, M, Q, T, V, and W. These activities should receive priority in scheduling, resource allocation, and quality control to maintain the project timeline.
To identify which activities have flexibility and where workers might be reallocated, slack time for each activity was calculated. Slack denotes the amount of time each activity can be delayed without affecting the total project duration. Slack can be calculated as the difference between latest start and earliest start time, or as the difference between latest and earliest finishing time.
To find slack, the following values were calculated for each activity: ES (Earliest Start), EF (Earliest Finish), LS (Latest Start), and LF (Latest Finish). Once these times were determined, slack could be calculated for each activity. The slack calculation reveals where Moore Housing can shift resources from activities with higher slack to support activities on the critical path with minimal slack.
The activities with the most slack are D, H, J, S, and U. These activities have time buffers that allow work to be delayed without impacting the overall project schedule. By identifying these non-critical activities, project managers can strategically reallocate workers and resources to accelerate critical path activities and improve the likelihood of meeting the 45-day deadline.
"Final recommendations for schedule acceleration"
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