A project has an expected duration of 34 weeks with a critical path variance of 6. Suppose the project network is given and the critical path is identified on the network. Suppose the normal time, crash time, and the associated cost for each activity is given. You have been asked by your supervisor to prepare a research paper that addresses the follow criteria:

•What is the probability that the project will be completed in 32 weeks or less?
•If the project is to be shortened by four days, list the process you would take to determine which activities, in order of reduction, would be shortened and the resulting cost.
•Describe project cost and the requirements for it's determination and application in a production facility.
•Analyze implications of changes in the parameters of project timing and cost determination.
•Evaluate application of project cost and timing concepts on a firm's business operations

Where are the answers

To address the criteria mentioned, here are step-by-step answers:

1. What is the probability that the project will be completed in 32 weeks or less?
To determine the probability, you need to calculate the Z-score (also known as standard score) using the critical path variance. The formula for calculating the Z-score is:
Z = (Expected duration - Target duration) / √(Critical path variance)

In this case:
Expected duration = 34 weeks
Target duration = 32 weeks
Critical path variance = 6

Substituting the values into the formula:
Z = (34 - 32) / √6

Now use a Z-table (standard normal distribution table) to find the probability corresponding to the calculated Z-score. The table will give you the probability corresponding to the area under the curve.

2. If the project is to be shortened by four days, list the process you would take to determine which activities, in order of reduction, would be shortened and the resulting cost.
To determine which activities to shorten, you need to identify the activities on the critical path. The critical path is the longest path through the project network, and any delay on this path would delay the overall project.

Once you have identified the critical path, you can analyze each activity on the path and identify how much it can be shortened. This can be done by comparing the normal time and crash time for each activity. The difference between these two values represents the amount of time that can be shortened.

To determine the resulting cost, multiply the reduction in time for each activity by the associated crash cost. Summing up these costs for all the activities on the critical path will give you the total resulting cost.

3. Describe project cost and the requirements for its determination and application in a production facility.
Project cost refers to the total financial cost required to complete a project. It includes various components such as labor costs, material costs, equipment costs, overhead costs, and any other expenses incurred during the project's execution.

Determining project cost requires a comprehensive understanding of all the activities involved in the project, their associated costs, and the required resources. This information can be obtained through cost estimation techniques such as bottom-up estimating, analogous estimating, or parametric estimating.

In a production facility, determining project cost is crucial for budgeting, resource allocation, and financial decision-making. Accurate cost estimation helps in optimizing resource allocation, identifying cost-saving opportunities, and ensuring profitability.

4. Analyze implications of changes in the parameters of project timing and cost determination.
Changes in parameters like project timing and cost determination can have significant implications on project outcomes. These changes can affect project schedules, resource allocation, budget management, and ultimately project success.

Timing changes: Delays in project timing can lead to missed deadlines, increased costs, and impacts on subsequent activities or dependencies. Similarly, speeding up project timing may require additional resources, incur higher costs, and increase the risk of errors.

Cost determination changes: Incorrect or inadequate cost determination can lead to underestimation or overestimation of project costs. Underestimation can result in budget overruns, while overestimation may lead to unnecessary expenses and reduced profitability. Accurate cost determination helps in effective resource management, risk analysis, and decision-making.

5. Evaluate the application of project cost and timing concepts on a firm's business operations.
Project cost and timing concepts are essential for effective business operations. They help firms in planning, executing, and controlling projects to ensure successful outcomes. Some key benefits include:

a) Effective budgeting: Proper cost estimation and tracking allow firms to allocate resources efficiently and manage project budgets.

b) Resource optimization: Understanding project timing enables firms to plan resource utilization, identify bottlenecks, and make informed decisions to optimize resource allocation.

c) Risk management: Accurate cost and timing analysis helps firms identify potential risks, develop risk mitigation strategies, and minimize project uncertainties.

d) Stakeholder expectations: Clear understanding of project cost and timing assists in managing stakeholder expectations, ensuring transparency in communication, and building trust.

e) Continuous improvement: Regular evaluation and analysis of project cost and timing data enable firms to identify areas for improvement, learn from past experiences, and implement better strategies in future projects.

Overall, the application of project cost and timing concepts provides firms with valuable insights to enhance their operational efficiency, cost-effectiveness, and overall project performance.

To prepare the research paper, you will need to address each of the given criteria in a comprehensive manner. Let's go through each criterion and discuss how to approach it:

1. Probability of completing the project in 32 weeks or less:
To calculate the probability, you need to determine the z-score corresponding to the desired completion time. The formula to calculate the z-score is given by (X - µ) / σ, where X is the desired completion time, µ is the expected duration, and σ is the square root of the critical path variance. By using statistical tables or a statistical calculator, you can determine the probability associated with the obtained z-score.

2. Determining activities for reduction if the project is to be shortened by four days:
To identify the activities that can be shortened, you would need to analyze the critical path and the associated time and cost information for each activity. Start by identifying the activities on the critical path and estimating the time reduction required for each. Calculate the crash cost and crash time for each activity to determine which activities can be shortened by four days while keeping the additional cost within acceptable limits. Rank the activities based on their crash time reduction potential and select them accordingly.

3. Project cost determination and its requirements in a production facility:
Describe the concept of project cost, including direct costs (such as materials and labor) and indirect costs (such as overhead and administrative expenses). Explain the importance of accurate cost estimation and the use of techniques like cost breakdown structure, cost estimation methods, and cost tracking during the project's execution. Discuss the specific requirements for determining project costs in a production facility, such as understanding the production process, identifying cost drivers, and allocating costs to various activities.

4. Implications of changes in project timing and cost determination parameters:
Analyze how changes in project timing and cost determination parameters can impact the overall project. Discuss how variations in activity durations, critical path, and costs can affect project completion time, resource allocation, and budget. Highlight the potential risks and opportunities associated with such changes and discuss effective strategies for managing them.

5. Application of project cost and timing concepts on a firm's business operations:
Evaluate the application of project cost and timing concepts in a firm's business operations. Discuss how project management techniques can be utilized to optimize resource allocation, minimize costs, and improve overall operational efficiency. Provide examples of how these concepts can be implemented in real-world scenarios to achieve better project outcomes and enhance business performance.

By addressing each of these criteria comprehensively in your research paper, you will provide a thorough analysis of the given topics and demonstrate a strong understanding of project management principles and their practical applications.