UCP-FCEE Exercícios aulas práticas (filas de espera)

Gestão de Operações, 2 semestre

1) Quick Lube Inc. Operates a fast lube and oil change garage. On a typical day, customers arrive at the rate of three per hour, and lube jobs are performed at an average rate of one every 15 minutes. The mechanics operate as a team on one car at a time.

Assuming Poisson arrivals and exponential service, find

  1. Utilization of the lube team.
  2. The average numbers of cars in line.
  3. The average time a car waits before it is lubed.
  4. The total time it takes to go through the system (that is, waiting in line plus lube time)

2) American Vending Inc. (AVI) supplies vended food to a large university. Because students often kick the machines, management has a constant repair problem. The machines break down on a average of three per hour, and the breakdowns are distributed in a Poisson manner. Downtime costs the company $25/hr per machine, and each maintenance worker gets $4 per hour. One worker can service machines at an average rate of five per hour, distributed exponentially; two workers working together can service seven per hours, distributed exponentially; and a team of three workers can do eight per hour, distributed exponentially.

What is the optimal maintenance crew size for servicing the machines?

3) In order to improve customer service at ZMarket, its management wants to test two alternative options to reduce customer waiting time: recruiting one extra employee to pack up purchases; or add one checkout counter.

ZMarket has only one checkout counter. Customers arrive at ZMarket at a rate of 24 customers/hours and the current service rate at the checker is 30 customers per hour.

Consider the following:

  • The cost of one extra employee is $150/week
  • Each one-minute reduction in customer waiting time avoids $75 in lost sales
  • One new counter costs $6000 plus $200 per week for checker
  • Customers divide themselves between two checkout lines
  • The service rate for each checker is  = 30

Analyze the problem and indicate what the best alternative is.

4) The Herds Concert Hall (previously known as Pavilhão Atlântico, changed its name after a series of memorable concerts of The Band, who performed for the first time in a restaurant not far from there), has three concession clerks serving customers on a FCFS basis. The service time per customer is exponentially distributed with an average of 2 minutes per customer. Concession customers wait in a single line in a large lobby, and arrivals are Poisson distributed with an average of 81 customers per hour. Previews run for 10 minutes before the start of each show. If the average time in the concession area exceeds 10 minutes, customers become dissatisfied.

  1. What is the average utilization of the concession clerks?
  2. What is the average time spent in the concession area?

AP queing-questoes.DOC1