Bu3315 Module 5 Decision Analysis And Queuing Models Exercis

Bu3315 Module 5 Decision Analysis And Queuing Modelsexercise 51decis

Analyze and solve decision problems related to business expansion, management science courses, queuing systems, and manufacturing processes using decision criteria, probability, and queuing theory techniques, based on given scenarios and payoff tables.

Sample Paper For Above instruction

Decision analysis and queuing models are crucial tools in management science that enable organizations to optimize operations, make informed decisions, and improve efficiency. These methods help in evaluating different scenarios based on probabilistic outcomes and capacity constraints, leading to strategic insights in various contexts such as business expansion, resource allocation, and service management.

One common application of decision analysis is in evaluating expansion strategies for a restaurant. For instance, the owner of Burger Doodle Restaurant considers two options: opening a drive-up window or serving breakfast. The profitability of each option depends on whether a competitor opens a franchise nearby. The payoff table illustrates the potential profits under different conditions:

Applying decision criteria such as maximax and maximin allows the owner to evaluate the best course of action under different risk preferences. The maximax criterion seeks the highest possible profit, favoring optimistic decision-making. Conversely, maximin looks for the decision that maximizes the minimum payoff, aligning with a cautious approach.

In this scenario, the maximax approach would select the decision with the highest potential payoff, which is opening a drive-up window if the competitor does not open a franchise, yielding $20,000. The maximin criterion would favor the option that secures the best worst-case scenario—serving breakfast with a profit of $4,000 if the competitor opens, or $8,000 if not. Accordingly, the decision for the restaurant owner varies depending on risk tolerance.

Similarly, in educational decision-making, a student must choose among multiple courses based on potential grades assigned by different professors. Brooke Bentley's choice among courses taught by Fulton, Ray, or Scott involves analyzing payoffs reflecting expected grades, with the goal to maximize academic performance. Applying the maximax criterion suggests choosing the course with the highest possible grade, aligning with an optimistic outlook. The maximin approach, however, emphasizes the safest option, favoring the course with the highest minimum grade across professors, which in this case points toward courses guaranteed to meet a minimum academic standard.

Queuing theory models are instrumental in analyzing service systems such as ticket booths at events, where the goal is to reduce customer wait times and optimize resource utilization. For example, if a ticket seller handles an average of 12 customers per hour with customers arriving at a rate of 10 per hour, these data can determine the expected waiting time and system utilization using Little’s Law and Poisson distribution assumptions. The average wait time in the queue would be calculated based on the traffic intensity, which measures the proportion of time the server is busy:

Traffic intensity (ρ) = Arrival rate / Service rate = 10 / 12 ≈ 0.8333. Using queuing formulas, the average wait time in the queue is given by Wq = (ρ) / (μ - λ) = (10/12) / (12 - 10) = (0.8333) / 2 ≈ 0.4167 hours, or approximately 25 minutes, providing insights into service efficiency.

In manufacturing, queuing models assist in assessing machine performance. For instance, a drill press receives parts every 7.5 minutes, with the operator capable of processing 10 parts per hour (which equates to 6 minutes per part). The activity rate and arrival rate define the system's characteristics. The utilization rate of the operator can be calculated as:

Utilization = Arrival rate / Processing rate = (60 / 7.5) / 10 = 8 / 10 = 0.8 or 80%. This indicates that the operator is busy 80% of the time, and the average number of parts waiting can be deduced using Little’s Law, showing the efficiency of the assembly line.

Overall, these quantitative methods support managers in making data-driven decisions across diverse operational contexts. From strategic expansion choices to operational efficiency improvements, decision analysis and queuing models provide valuable frameworks for solving complex business problems and optimizing resource utilization.

References

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• Winston, W. L. (2004). Introduction to probability models. Academic press.
• Hillier, F. S., & Lieberman, G. J. (2010). Introduction to Operations Research. McGraw-Hill Education.
• Gross, D., Shortle, J. F., Thompson, J. M., & Harris, C. M. (2008). Fundamentals of Queueing Theory. Wiley.
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• Kleinrock, L. (1975). Queueing Systems, Volume 1: Theory. Wiley-Interscience.
• Cox, D. R. (1961). The Statistical Analysis of Series of Events. Chapman and Hall.
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• Everett, W. Nelson. (1994). An Introduction to Queueing Theory. Oxford University Press.