EBK OPERATIONS MANAGEMENT
14th Edition
ISBN: 9781260718447
Author: Stevenson
Publisher: MCG COURSE
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Question
Chapter 18, Problem 9DRQ
Summary Introduction
To explain: The changes that take place to the length of a waiting line in a variable queuing system if a manager tries to achieve a high percentage of capacity utilization.
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In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds. Assume the Poisson and exponential distributions.
a.
What is λ?
b.
What is μ?
c.
Find probability of no units in the system.
d.
Find average number of units in the system.
e.
Find average time in the waiting line.
f.
Find average time in the system.
g.
Find probability that there is one person waiting.
h.
Find probability an arrival will have to wait.
Please show a corrct solution and answer. Thank you.
A new customer walks into SLC Barber Shop every 60 minutes on average, with a standard deviation of the interarrival times being 60 minutes. At SLC Barber Shop, the average service time is 30 minutes, with a standard deviation of service times being 45 minutes.
1.What is the demand for SLC Barber shop in [customer/minute]?
2.What is the average waiting time of a customer in minutes?
If the restaurant runs a sale and the customer arrival rate increases by 20 percent how would this change the total time expected to serve a customer? How would this change the average number of cars in the drive-thru line?
Chapter 18 Solutions
EBK OPERATIONS MANAGEMENT
Ch. 18.1 - Prob. 1.1RQCh. 18.1 - Prob. 1.2RQCh. 18 - Prob. 1DRQCh. 18 - Why do waiting lines form even though a service...Ch. 18 - Prob. 3DRQCh. 18 - Prob. 4DRQCh. 18 - What approaches do supermarkets use to offset...Ch. 18 - Prob. 6DRQCh. 18 - Prob. 7DRQCh. 18 - Prob. 8DRQ
Ch. 18 - Prob. 9DRQCh. 18 - Prob. 1TSCh. 18 - Prob. 2TSCh. 18 - Prob. 3TSCh. 18 - Prob. 1CTECh. 18 - Prob. 2CTECh. 18 - Prob. 3CTECh. 18 - The owner of Eat Now Restaurant implemented an...Ch. 18 - Prob. 5CTECh. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - Prob. 4PCh. 18 - Prob. 5PCh. 18 - Prob. 6PCh. 18 - Prob. 7PCh. 18 - Prob. 8PCh. 18 - Prob. 9PCh. 18 - Prob. 10PCh. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Prob. 14PCh. 18 - Prob. 15PCh. 18 - A priority waiting system assigns arriving...Ch. 18 - Prob. 17PCh. 18 - Prob. 18PCh. 18 - Prob. 1CQ
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- The bank manager is concerned with its waiting line system in his bank. Currently bank uses a single-server, single-line, single-phase system. Based on historical evidence, the average number of customers arriving per hour is C1 and is described by a Poisson distribution. The service rate is <=15 >11 customers per hour with the service times following an exponential distribution. The customers are come from an infinite population. The manager of the bank would like calculate the operational characteristics of the waiting line system that:(a) What is the average system utilization?(b) What is the average number of customers in the system? (c) What is the average number of customers waiting in line?(d) What is the average time a customer spends in the system?(e) What is the average time a customer spends waiting in line?arrow_forwardWestern National Bank wants to provide a drive-through window for its customers. Management estimates that customers will arrive in their cars at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of 20 per hour. Assuming Poisson arrivals and exponential service, find the following: Capacity utilization of the teller. Average number of cars in the waiting line Average number in the system. Average waiting time in line. Average waiting time in the system, including service.arrow_forwardA small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers. What is the approximate average time in minutes that truckers wait to be seated?arrow_forward
- An airline is planning to open a satellite ticket desk in a new shopping plaza, staffed byone ticket agent. It is estimated that requests for tickets and information will average15 per hour, and requests will have a Poisson distribution. Service time is assumed to be exponentially distributed. Previous experience with similar satellite operations suggeststhat mean service time should average about three minutes per request. Determine each ofthe following:a. System utilizationb. Percentage of time the server (agent) will be idlec. The expected number of customers waiting to be servedd. The average time customers will spend in the systeme. The probability of zero customers in the system and the probability of four customersin the systemarrow_forwardBurger Dome sells hamburgers, cheeseburgers, French fries, soft drinks, and milk shakes, as well as a limited number of specialty items and dessert selections. Although Burger Dome would like to serve each customer immediately, at times more customers arrive than can be handled by the Burger Dome food service staff. Thus, customers wait in line to place and receive their orders. Suppose that Burger Dome analyzed data on customer arrivals and concluded that the arrival rate is 33 customers per hour and 1 customer processed per minute. Compare a multiple-server waiting line system with a shared queue to a multiple-server waiting line system with a dedicated queue for each server. Suppose Burger Dome establishes two servers but arranges the restaurant layout so that an arriving customer must decide which server's queue to join. Assume that this system equally splits the customer arrivals so that each server sees half of the customers. How does this system compare with the two-server…arrow_forwardConsider this situation: A manager is contemplating making changes to a single-server system that is expected to double the service rate, and still have just one server. (a). Would you (intuitively) think that doubling the service rate of a single-server system would cut the average waiting time in line in half? (b). For the sake of analysis, suppose the current system has an arrival rate of 8 customers per hour and a service rate of 10 customers per hour. If the service rate is doubled, what impact will that have on the average number waiting in line? (c). What are some managerial implications of your analysis?arrow_forward
- At a fashion retailer, there are three cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It is estimated that the customer arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 15 minutes. Suppose that customers form a single line. What is the average waiting time in minutes for a customer? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.arrow_forwardA bank teller takes 24 minutes on average to serve a customer. What would be the hourly servicerate used in the queuing formulas?arrow_forward12-11 The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ=3 per day (approximately Poisson in nature). The crew can service an average of μ=8 machines per day, with a repair time distribution that resembles the exponential distribution. a. What is the utilization rate of this service system? b. What is the average downtime for a machine that is broken? c. How many machines are waiting to be serviced at any given time? d. What is the probability that more than one machine is in the system? Probability that more than two are broken and waiting to be repaired or being serviced? More than three? More than four?arrow_forward
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