Hi, Good Day Everyone. I Really Appreciate Your Help.

Hi Good Day Everyonereally Appreciate If You Can Help Me To Solve Prob

Really appreciate if you can help me to solve problem as per details on pict attached, and determine : (i) Draw the PERT network for the project. (ii) Prepare the activity schedule for the project. (iii) Determine the critical path. (iv) If a 25-week deadline is imposed, what is the probability that the project will be finished within the time limit? thank you so much for your kindly help

Paper For Above instruction

Project management is a critical discipline that involves planning, executing, and overseeing projects to ensure they are completed on time, within scope, and on budget. One essential tool used in project planning and scheduling is the Program Evaluation and Review Technique (PERT), which provides a probabilistic approach to estimating project duration and managing uncertainty. This paper aims to address a specific project management problem by drawing the PERT network, preparing the activity schedule, determining the critical path, and assessing the probability of completing the project within a specified deadline, based on provided data.

Since the specific data and activity details are provided on the attached picture (which is assumed to include activity durations, dependencies, and estimated times), the initial step involves analyzing this data to draw the PERT network diagram. The PERT network visually represents project activities as nodes or arrows, indicating their sequential and dependency relationships. The critical path, which impacts the entire project's duration, is identified by calculating the earliest and latest start and finish times for each activity and determining the longest path through the network.

Following the network diagram, the next task is to prepare a detailed activity schedule. This schedule includes the earliest start (ES), earliest finish (EF), latest start (LS), and latest finish (LF) times for all activities. These calculations help in identifying activities that form the critical path and those with float or slack time, which can be delayed without affecting the overall project timeline. The activity schedule provides a roadmap for project execution, monitoring, and control.

Critical path analysis not only identifies activities with zero float but also helps project managers prioritize resources and manage risks effectively. Once the critical path is determined, it becomes the baseline for evaluating project deadlines. In this case, a 25-week deadline is imposed. To assess the probability of completing the project within this allocated time, we apply PERT’s probabilistic methods, calculating the expected duration and variance for the critical path.

Using the estimated activity durations (optimistic, most likely, and pessimistic times), we compute the expected duration (TE) for each activity and sum these along the critical path. The variance (σ2) for each activity is also calculated, which collectively contributes to the total variance of the project duration. Assuming a normal distribution, we determine the z-score corresponding to the 25-week deadline and then find the probability from standard normal distribution tables.

For example, if the total expected duration of the critical path is calculated as 23 weeks with a variance reflecting the uncertainty of individual activities, then the z-score for the 25-week deadline is (25 - 23) divided by the standard deviation. The resulting probability indicates the likelihood that the project will be completed on time. Typically, this probability is less than 50% for durations exceeding the mean project time, emphasizing the importance of risk management and contingency planning.

This comprehensive approach integrates the visualization of the project plan via the PERT network, detailed scheduling, critical path determination, and probabilistic analysis to provide project managers with the information needed to make informed decisions. Ultimately, these tools support effective project control and enhance the likelihood of delivering projects successfully within specified deadlines, thereby improving organizational efficiency and stakeholder satisfaction.

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