An airline is analyzing the documentation process for its domestic flights. To do this, they carried out a queuing theory analysis where they discovered that in recent weeks they have had an Lq of 42.5 passengers and a Wq of 22.3 minutes. At an airport with statistically equal traffic and characteristics, an additional employee was hired to help make this flow faster, achieving a La of 35.8 passengers and a Wq of 18.2 minutes. It is considered that for each passenger in line, 1.5m2 of space is needed, and the airport rents at a cost of $ 1,500 per m2 per month and that the values of Lq remain constant throughout the day and the employee's salary additional that is had in the second airport is of $ 15,500 per month. Considering all the important aspects for the company (cost, customer satisfaction, efficiency, etc.) Would you recommend hiring the additional employee? justify your answer.

Question

23-09-2023
Mathematics

High School

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An airline is analyzing the documentation process for its domestic flights. To do this, they carried out a queuing theory analysis where they discovered that in recent weeks they have had an Lq of 42.5 passengers and a Wq of 22.3 minutes. At an airport with statistically equal traffic and characteristics, an additional employee was hired to help make this flow faster, achieving a La of 35.8 passengers and a Wq of 18.2 minutes. It is considered that for each passenger in line, 1.5m2 of space is needed, and the airport rents at a cost of $ 1,500 per m2 per month and that the values of Lq remain constant throughout the day and the employee's salary additional that is had in the second airport is of $ 15,500 per month. Considering all the important aspects for the company (cost, customer satisfaction, efficiency, etc.) Would you recommend hiring the additional employee? justify your answer.

Answer :

Final answer:

To improve the documentation process, hiring an additional employee is recommended based on factors such as cost, customer satisfaction, and efficiency.

Explanation:

Queuing theory analysis allows the airline to evaluate the efficiency of its documentation process. In this case, the airline has calculated the number of passengers in the queue (Lq) and the average waiting time in the queue (Wq). They compared the results before and after hiring an additional employee. To determine whether hiring an additional employee is recommended, we need to consider the cost, customer satisfaction, and efficiency.

Cost: Hiring an additional employee incurs a monthly salary cost of $15,500. Additionally, the airport rent cost per passenger in line is $1,500 per m2 per month.
Customer Satisfaction: A lower average waiting time (Wq) indicates improved customer satisfaction. The second airport achieved a shorter waiting time after hiring the additional employee.
Efficiency: The second airport achieved a lower number of passengers in the queue (Lq) after hiring an additional employee. This means the waiting area requires less space.

Based on these factors, it is recommended to hire an additional employee as it improves customer satisfaction, reduces the number of passengers in the queue, and optimizes the use of space.

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