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Develop a report that presents the activity schedule (Earliest/Latest Start and Earliest/Latest Finish) and expected project completion time for the warehouse expansion project. Include a project network in the report. In addition, take into consideration the following issues: R.C. Coleman’s top management established a required 40-week completion time for the project. Can this completion time be achieved? Include probability information in your discussion. What recommendation do you have if the 40-week completion time is required? Suppose that management requests that activity times be shortened to provide an 80% chance of meeting the 40-week completion time. If the variance in the project completion time is the same as you found in question (1), how much should the expected project completion time be shortened to achieve the goal of an 80% chance of completion within 40 weeks?

Paper For Above instruction

The project to automate R.C. Coleman’s warehouse operations involves a detailed activity schedule and critical path analysis, vital for understanding the project's timeline and feasibility within specified constraints. This paper develops a comprehensive project schedule, assesses the probability of completing within the designated 40-week deadline, and recommends adjustments to meet management's goals.

Introduction

R.C. Coleman’s recent initiative to automate its warehouse, including installing a computer-controlled order-picking system and conveyor system, aims to enhance efficiency and reduce labor costs. Proper planning using project management techniques such as Critical Path Method (CPM) and PERT (Program Evaluation and Review Technique) is essential in estimating the project's duration and ensuring punctual completion. This report constructs the activity schedule, evaluates the project's feasibility against the 40-week management deadline, and proposes possible modifications to activity durations to satisfy probabilistic requirements.

Activity Schedule and Project Network

The first step involves defining activities, their durations, and establishing a network diagram. Based on the provided optimistic (O), most probable (M), and pessimistic (P) time estimates for each activity, expected durations (TE) are computed using the PERT formula:

TE = (O + 4M + P) / 6.

Suppose the project comprises activities labeled A through F, with specific time estimates as follows (example data for illustration):

• Activity A: O=2, M=3, P=5
• Activity B: O=1, M=2, P=4
• Activity C: O=2, M=4, P=6
• Activity D: O=3, M=5, P=8
• Activity E: O=1, M=2, P=3
• Activity F: O=4, M=6, P=9

The expected durations are calculated accordingly and inputted into the project network. Using the network, we identify the critical path — the sequence of activities that determines the earliest possible project completion time. Using CPM calculations, the Earliest Start (ES), Earliest Finish (EF), Latest Start (LS), and Latest Finish (LF) times are determined for each activity, thus establishing the project schedule.

Expected Project Completion Time and Critical Path Analysis

By summing the expected durations along the critical path, the mean expected project completion time is estimated. For instance, if the critical path involves activities A → D → F, the total expected duration sums to approximately 15 weeks, with an associated variance derived from the activity time estimates:

Variance for each activity: (P - O)/6)^2.

The sum of the variances along the critical path gives the project variance, which determines the project completion time distribution under the assumption of normality, facilitating probability calculations.

Probability of Completing within 40 Weeks

To evaluate whether the project can meet the 40-week deadline, the Z-score is calculated:

Z = (Desired time - Expected time) / Standard deviation.

Using the mean and variance estimates, the Z-score indicates the probability of timely completion. For example, if the expected time is 15 weeks with a standard deviation of 2 weeks, the Z-score for 40 weeks is:

Z = (40 - 15) / 2 = 12.5,

which corresponds to a probability practically of 1 (100%), indicating an almost certain chance of completing within 40 weeks. Conversely, if the expected project duration exceeds the deadline, the probability diminishes, highlighting the need for schedule adjustments.

Recommendations for Achieving the 40-Week Deadline

If analysis shows that the expected project duration with current activity estimates exceeds 40 weeks significantly, management should consider crashing activities—reducing durations through additional resources or overlapping tasks. Schedule compression techniques, such as crashing critical path activities, can effectively shorten the project timeline. Additionally, reassessing activity estimates for potential underestimations, or increasing resource allocation, may be warranted to ensure the 40-week target.

Adjusting Activity Times for an 80% Completion Probability

To increase the probability of completing within 40 weeks to 80%, the expected project duration must be reduced accordingly. Using the properties of the normal distribution, an 80% probability corresponds approximately to a Z-score of 0.84. Assuming the original project variance remains unchanged, the expected critical path duration should be decreased by:

Reduction = Z * Standard deviation.

If the current expected duration is D and the standard deviation is σ, then:

D_new = D - (0.84 * σ).

This adjustment indicates that to achieve an 80% chance of completing within 40 weeks, the project’s expected duration should be shortened by this calculated amount, which may involve further schedule crashing or activity re-estimation.

Conclusion

In conclusion, the successful planning and management of R.C. Coleman's warehouse automation project depend on detailed activity scheduling, critical path analysis, and probabilistic assessments. By computing the expected durations, variances, and success probabilities, management can make informed decisions on schedule adjustments and resource allocation to meet the 40-week deadline with high confidence. Schedule crashing and activity re-estimation are practical strategies for schedule compression, aligning project outcomes with organizational goals.

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