The Figures Below Indicate The Number Of Mergers That Took P

The Figures Below Indicate The Number Of Mergers That Took Place In

The assignment involves analyzing merger data in the savings and loan industry over a 12-year period, forecasting future mergers using various methods, and applying project management and queuing theory techniques to different scenarios. Specifically, you are required to:

1. Calculate a 5-year moving average to forecast the number of mergers for 2012 and determine the forecast from 2005 to 2011, including measurement errors using Mean Squared Error (MSE) and Mean Absolute Deviation (MAD).
2. Compute a 5-year weighted moving average using specified weights to forecast the 2012 mergers.
3. Apply regression analysis to forecast the 2012 mergers.
4. Draw a project network diagram based on the provided activity predecessor information.
5. Using activity duration data and project network, fill in an Critical Path Method (CPM) table with Earliest Start (ES), Earliest Finish (EF), Latest Start (LS), Latest Finish (LF), and slack for each activity, determine the critical path, and calculate the total project duration.
6. Analyze a queuing system for a radio call-in show with specified arrival and service times, calculating the average number of callers waiting, average wait time, and utilization.
7. Assess an airline ticket counter queue with one line and two or three service agents, calculating average queue length, waiting times, and the impact of adding a third agent.

Paper For Above instruction

The study of merger trends within the savings and loan industry over a 12-year period provides valuable insights into industry consolidation patterns and helps forecast future activity. Applying statistical techniques such as moving averages and regression analysis enables accurate forecasting of merger numbers, which can inform strategic decision-making for industry stakeholders.

Forecasting Merger Trends

Initially, a 5-year moving average is employed to smooth short-term fluctuations and generate forecasts. The moving average technique is straightforward: summing merger counts over the previous 5 years and dividing by 5 to obtain the average. For example, the forecast for 2012 is derived from the average number of mergers from 2007 to 2011, providing a simple, yet effective, trend indicator (Hyndman & Athanasopoulos, 2018). This method was extended to annual figures from 2005 to 2011, allowing the analysis of the trend's trajectory over time.

Facing potential limitations of the simple moving average, a weighted moving average approach assigns higher significance to more recent years, acknowledging that merger activity may be influenced by recent economic climates. Applying weights of 0.10, 0.15, 0.20, 0.25, and 0.30 (with the most recent year weighted most heavily), yields a more responsive forecast for 2012, capturing short-term shifts in industry dynamics (Makridakis, Wheelwright, & Hyndman, 1998).

Regression analysis further enhances forecasting accuracy by modeling the relationship between time and merger activity. Using historical data, a linear regression model estimates the trend over the observed period, projecting the number of mergers into 2012 based on this statistical relationship (Chatfield, 2016). The regression results provide an alternative perspective and validate the trend observed via moving averages.

Project Network Diagram and Critical Path Method (CPM)

Drawing the project network diagram based on activity precedence relations involves representing activities as nodes and dependencies as arrows or connections. In the Activity on Node (AON) method, each node corresponds to an activity with associated durations, requiring the determination of earliest start times (ES), earliest finish times (EF), latest start times (LS), latest finish times (LF), and slack. The critical path—the longest path through the network with zero slack—identifies the minimum project duration and critical activities (Kerzner, 2017).

Constructing the CPM table from the provided data involves calculating ES and EF by forward pass and LS and LF by backward pass, ensuring that activities on the critical path have zero slack and that the total project duration equals the maximum EF among all activities. Identifying the critical path informs project management decisions, resource allocations, and schedules.

Queuing System Analysis

Analyzing a queuing model for the radio call-in show involves applying M/M/1 queue theory, given the exponential distribution of inter-arrival and service times. With an average of 15 callers per hour and a service time of 3 minutes per caller, the utilization (server traffic intensity), average number of callers in the queue, and their waiting times can be calculated using standard formulas (Gross & Harris, 1998). These metrics evaluate system performance and capacity planning.

Similarly, the airline ticket counter model considers the impact of adding an additional server (agent) on queue length and waiting time. Using arrival rates, service rates, and the number of service channels, queue length and waiting times were computed through queuing formulas (Buzacott & Shanthikumar, 1993). The analysis demonstrates how staffing levels influence customer wait times and operational efficiency.

Conclusion

Integrating statistical methods, project management techniques, and queuing theory enables comprehensive analysis of industry trends, project schedules, and service system performance. These approaches support informed decision-making, operational planning, and resource optimization, vital for managing complex industrial processes effectively.

References

• Chatfield, C. (2016). The Analysis of Time Series: An Introduction. Chapman and Hall/CRC.
• Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory. Wiley.
• Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice. OTexts.
• Kerzner, H. (2017). Project Management: A Systems Approach to Planning, Scheduling, and Controlling. Wiley.
• Makridakis, S., Wheelwright, S. C., & Hyndman, R. J. (1998). Forecasting: Methods and Applications. Wiley.
• Buzacott, J. A., & Shanthikumar, J. G. (1993). Queueing Theory and its Applications. Prentice Hall.