Chapter C Waiting Lines


 Alan Daniel
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1 Supplement C Waiting Lines Chapter C Waiting Lines TRUE/FALSE 1. Waiting lines cannot develop if the time to process a customer is constant. Answer: False Reference: Why Waiting Lines Form Keywords: waiting, line, customers 2. The four elements common to all waitingline situations are a customer population, a waiting line of customers, the service facility, and a priority rule. Answer: True Keywords: priority, rule, customer, line, population 3. A phase represents a single step in providing a service. Answer: True Keywords: phase, service 4. A bank that dedicates one window for commercial account customers and one window for personal account channel has two channels. Answer: True Keywords: queue, channel 5. If the service system generates customers according to a Poisson distribution, the exponential distribution describes the probability that the next customer will arrive in the next T time periods. Answer: True Reference: Probability Distributions Keywords: Poisson, exponential, distribution 180
2 6. The mean of the Poisson distribution is equal to its standard deviation. Answer: False Reference: Probability Distributions Keywords: Poisson, distribution, mean, variance 7. Short queue lengths typically mean not enough capacity. Answer: False Keywords: queue, capacity, length 8. The number of customers in queue and being served also relates to service efficiency and capacity. Answer: True Keywords: customer, queue, capacity, efficiency 9. Long lines always mean long waiting times. Answer: False Keywords: line, waiting, time 10. It is impossible for management to affect the rate of customer arrivals. Answer: False Reference: Decision Areas for Management Keywords: arrival, rate, affect 11. Management, servers, and customers would all be happy if, in a singleserver situation, the parameter µ is much greater than λ. Answer: True Keywords: single, server, arrival, service, rate 181
3 MULTIPLE CHOICE 12. Which of the following is LEAST likely to benefit from waiting line analysis? a. Capacity planning b. Inventory management c. Budget planning d. Scheduling Reference: Uses of WaitingLine Theory Keywords: single, server, service, rate 13. The best example of a finite customer population is: a. the carbuying public of an automotive manufacturer. b. the constituents in a precinct lining up to vote. c. the messages arriving at a major ISP mail server. d. the members of the Management department at your university waiting to speak to the Dean about their department chairman. Keywords: customer, population, finite 14. The distinction between an infinite customer population and a finite customer population is: a. whether the potential number of customers is appreciably affected by the number of customers already in the system. b. whether the number of potential customers exceeds the square of the number of servers. c. whether the number of potential customers exceeds the number of servers raised to the power of the number of channels. d. if the number of customers exceeds infinity. Keywords: customer, population, finite 15. Ed Deadbeat races to the Bursar s Office on the first day of class and notes that the line is four students long. Ed figures that the wait will be at least ten minutes and, having better uses of his time, he decides to proceed to the next item on his todo list. Ed s behavior is best described as: a. reneging. b. balking. c. blocking. d. queuing. Keywords: balking, balk 182
4 16. India Sisson wants to grab a latte before heading to her marketing class, knowing that the jolt of a double tall mocha is the only thing that can possibly keep her eyes open during today s presentation on the four P s. The barista is slower than molasses in January and India notes that the pace of the line won t permit her to grab her favorite seat in the back row of her class. She decides to risk marketing without a latte and leaves the line before getting served. India s behavior is best described as: a. balking. b. blocking. c. reneging. d. queuing. Keywords: reneging, renege 17. The single, multiple, and finite queuing models all assume that: a. the arrival rate exceeds the service rate.. b. the number of servers exceeds the number of customers. c. the number of customers exceeds the number of servers. d. the customers are patient. Keywords: reneging, renege, balking, balk, patient 18. An automatic, drivethrough car wash is an example of a: a. singlechannel, singlephase arrangement. b. singlechannel, multiplephase arrangement. c. multiplechannel, singlephase arrangement. d. multiplechannel, multiplephase arrangement. Keywords: single, channel, phase 19. A drivethrough system at a fast food restaurant where the first facility takes the order, the second takes the money, and the third provides the food is an example of: a. singlechannel, singlephase arrangement. b. singlechannel, multiplephase arrangement. c. multiplechannel, singlephase arrangement. d. multiplechannel, multiplephase arrangement. Keywords: single, channel, multiple, phase 183
5 20. A bank lobby with six teller windows, each with a separate line, is an example of a: a. singlechannel, singlephase arrangement. b. singlechannel, multiplephase arrangement. c. multiplechannel, singlephase arrangement. d. multiplechannel, multiplephase arrangement. Keywords: multiple, channel, single, phase 21. A Laundromat where there are washing machines and dryers is an example of a: a. singlechannel, singlephase arrangement. b. singlechannel, multiplephase arrangement. c. multiplechannel, singlephase arrangement. d. multiplechannel, multiplephase arrangement. Keywords: multiple, channel, phase 22. A super computeraccessory discount store often has customers who leave the checkout line before being served because of excessive waiting times. The store has a(n): a. infinite customer population with balking customers. b. infinite customer population with reneging customers. c. finite customer population with balking customers. d. finite customer population with reneging customers. Keywords: infinite, customer, balk 23. A homemadeice cream shop owner has noticed that, often, potential customers will stop outside the store, assess the wait in line, and then pass by. The shop has a(n): a. infinite customer population with balking customers. b. infinite customer population with reneging customers. c. finite customer population with balking customers. d. finite customer population with reneging customers. Keywords: customer, balk, infinite, population 184
6 24. The owner of a desktop publishing company has seven loyal clients who periodically require his services. The owner has: a. an infinite customer population of patient customers. b. an infinite population of impatient customers. c. a finite customer population. d. a finite customer population with balking customers. Keywords: finite, customer, population 25. Customers arrive according to a Poisson distribution. The average number of customer arrivals per hour is four. The probability that three customers will arrive in the next two hours is: a. less than or equal to b. greater than but less than or equal to c. greater than but less than or equal to d. greater than Reference: Probability Distributions Keywords: probability, customer, arrival 26. Customers arrive according to a Poisson distribution. The average number of customer arrivals per hour is six. The probability that four customers will arrive in the next three hours is: a. less than or equal to b. greater than 0.01 but less than or equal to c. greater than 0.02 but less than or equal to d. greater than Reference: Probability Distributions Keywords: arrival, probability 27. Customers arrive according to a Poisson distribution. The average number of customer arrivals per hour is three. The probability that four customers will arrive in the next two hours is: a. less than or equal to b. greater than 0.10 but less than or equal to c. greater than 0.12 but less than or equal to d. greater than Reference: Probability Distributions Keywords: arrival, probability 185
7 28. Customers arrive according to a Poisson distribution. The average number of customer arrivals per hour is two. The probability that five customers will arrive in the next three hours is: a. less than or equal to b. greater than 0.10 but less than or equal to c. greater than 0.12 but less than or equal to d. greater than Reference: Probability Distributions Keywords: probability, arrival 29. Customers are serviced at a rate of four customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 30 minutes? a. Less than or equal to 0.50 b. Greater than 0.50 but less than or equal to 0.60 c. Greater than 0.60 but less than or equal to 0.70 d. Greater than 0.70 Reference: Probability Distributions Keywords: service, rate, probability 30. Customers are serviced at a rate of six customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 20 minutes? a. Less than or equal to 0.70 b. Greater than 0.70 but less than or equal to 0.80 c. Greater than 0.80 but less than or equal to 0.90 d. Greater than 0.90 Reference: Probability Distributions Keywords: service, rate, probability 31. Customers are serviced at a rate of three customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 10 minutes? a. Less than or equal to 0.40 b. Greater than 0.40 but less than or equal to 0.45 c. Greater than 0.45 but less than or equal to 0.50 d. Greater than 0.50 Reference: Probability Distributions Keywords: customer, service, rate, probability 186
8 32. Customers are serviced at a rate of five customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 20 minutes? a. Less than or equal to 0.75 b. Greater than 0.75 but less than or equal to 0.80 c. Greater than 0.80 but less than or equal to 0.85 d. Greater than 0.85 Reference: Probability Distributions Keywords: customer, service, rate, probability 33. Customers are serviced at a rate of 10 customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than two minutes? a. Less than or equal to 0.25 b. Greater than 0.25 but less than or equal to 0.30 c. Greater than 0.30 but less than or equal to 0.35 d. Greater than 0.35 Reference: Probability Distributions Keywords: customer, service, rate, probability 34. With a singleserver model, increasing the service rate while holding all other factors constant will: a. increase the utilization of the server. b. increase the time spent per customer. c. decrease the probability that there are two customers in the system at any time. d. decrease the arrival rate of customers. Keywords: single, server, service, rate 35. With a singleserver model, increasing the promotions for a service through advertising will most likely: a. increase the utilization of the server. b. decrease the average number of customers in the service system. c. decrease the average time a customer spends in the system. d. increase the probability that the server will be idle. Difficulty: Hard Keywords: single, server, utilization, arrival, rate 187
9 36. With a singleserver model, increasing the capitaltolabor ratio will most likely: a. increase the utilization of the server. b. have no effect on the operating characteristics because they are affected only by workmethods changes. c. decrease the probability that there are zero customers in the system at any time. d. decrease the average number of customers in the waiting line. Reference: Multiple sections Difficulty: Hard Keywords: single, server, capital, labor, length 37. With a singleserver model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in: a. an increase in the utilization of the server. b. an increase in the average number of customers in the system. c. a decrease in the average time spent in the system, including service. d. an increase in the waitingline time. Difficulty: Hard Keywords: single, server, arrival, service, rate 38. With a singleserver model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in: a. a decrease in the utilization of the server. b. no change in the average number of customers in the service system. c. an increase in the average number of customers in the waiting line. d. an increase in the waiting time in line. Difficulty: Hard Keywords: single, server, arrival, service, rate 39. With a singleserver model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in: a. no change in the probability that there are n customers in the system. b. a decrease in the average waiting time in line. c. an increase in the average time spent in the system, including service. d. an increase in the average number of customers in the system. Difficulty: Hard Keywords: single, server, arrival, service, rate 188
10 40. With a multipleserver model, increasing the arrival rate by 10 percent and also increasing the service rate of each server by 10 percent will result in: a. a decrease in the utilization of the system. b. no change in the average number of customers in the waiting line. c. a decrease in the average number of customers in the waiting line. d. an increase in the waiting time in line. Difficulty: Hard Keywords: multiple, server, arrival, service, rate, queue, length 41. With a finitesource model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in: a. an increase in the utilization of the server. b. an increase in the average number of customers in the service system. c. a decrease in the average time spent in the system, including service. d. an increase in the waiting time in line. Difficulty: Hard Keywords: finite, source, arrival, rate, service 42. With a finitesource model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in: a. a decrease in the utilization of the server. b. no change in the average number of customers in the system. c. an increase in the average number of customers in the waiting line. d. an increase in the waiting time in line. Difficulty: Hard Keywords: finite, source, arrival, rate, service 43. In the singleserver model: a. customers are assumed to arrive at constant intervals of time. b. the variability of customer arrivals is most often described by a Poisson distribution. c. the mean of the distribution of customer arrivals must be greater than the variance of customer arrivals to get meaningful results. d. the probability of n arrivals in T time periods comes from a normal distribution. Keywords: Poisson, single, server, arrival 189
11 44. In the singleserver model: a. the service time of a customer is most often described by an exponential distribution. b. the service time depends on the number of customers in the system as long as there is at least one customer in the waiting line. c. the mean of the servicetime distribution must be as great as the target service time for a feasible solution. d. service times are always constant to avoid large waiting lines. Keywords: single, server, exponential, distribution 45. In order to have equivalent performance on average waiting time in a single server model, an increase in interarrival time must be accompanied by: a. an increase in µ. b. an increase in the number of servers. c. an increase in the number of channels. d. an increase in the line length. Reference: Using Waiting Line Models to Analyze Operations Keywords: phase Scenario C.1 A single ticket taker can tear tickets and direct movie patrons to their seats at a rate of 90 per hour. Customers arrive every minute for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution. 46. Use the information in Scenario C.1. What is the utilization of the ticket taker? a b c d Keyword: utilization 47. Use the information in Scenario C.1. What is the probability that customers with tickets arrive and the ticket taker is not helping another patron? a b c d Keywords: probability, system, empty 190
12 48. Use the information in Scenario C.1. What is the average number of customers in line? a b c d Keywords: customers, line, queue, length 49. Use the information in Scenario C.1. What is the average number of people waiting in line and being seated? a b c d Keywords: waiting, served, queue, system 50. Use the information in Scenario C.1. What is the average time a customer must wait in line? a minutes b minutes c minutes d minutes Keywords: queue, time, waiting 51. Use the information in Scenario C.1. What is the average combined time a customer waits in line and spends being seated by the ticket taker? a minute b minutes c minutes d minutes Keywords: time, system Scenario C.2 Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute. 191
13 52. Use the information in Scenario C.2. How many minutes per hour is the attendant not serving customers? a. Fewer than or equal to 13 b. Greater than 13 but fewer than or equal to 17 c. Greater than 17 but fewer than or equal to 21 d. Greater than 21 Keyword: utilization 53. Use the information in Scenario C.2. What is the probability that a traveler will pull up to the attendant s service window without having to wait for another customer? a. Less than or equal to 0.15 b. Greater than 0.15 but less than or equal to 0.25 c. Greater than 0.25 but less than or equal to 0.35 d. Greater than 0.35 Keywords: system, empty 54. Use the information in Scenario C.2. What is the average number of customers in line? a. Fewer than or equal to 1.0 b. Greater than 1.0 but fewer than or equal to 2.0 c. Greater than 2.0 but fewer than or equal to 3.0 d. Greater than 3.0 Keywords: line, queue, length 55. Use the information in Scenario C.2. What is the average number of customers in the system? a. Fewer than or equal to 3.0. b. Greater than 3.0 but fewer than or equal to 5.0. c. Greater than 5.0 but fewer than or equal to 7.0. d. Greater than 7.0. Keywords: customer, system 56. Use the information in Scenario C.2. What is the average time a customer spends in line? a. Less than or equal to 1.0 minute. b. Greater than 1.0 but fewer than or equal to 2.0 minutes. c. Greater than 2.0 but fewer than or equal to 3.0 minutes. d. Greater than 3.0 minutes. Keywords: time, queue, line, customer 192
14 57. Use the information in Scenario C.2. What is the average amount of time a customer spends waiting in line and being served? a. Less than or equal to 1.0 minutes b. Greater than 1.0 minutes but fewer than or equal to 1.50 minutes c. Greater than 1.5 minutes but fewer than or equal to 2.0 minutes d. Greater than 2.0 minutes Keywords: customer, time, system Scenario C.3 Customers arrive at the one remaining fullservice gas station in the country at the rate of 45 per minute and are served by the first available of three pump jockeys who can dole out gas and check oil at the rate of 20 customers per minute. Both service and interarrival times are governed by the exponential distribution. The probability that no pump jockey is busy is Use the information in Scenario C.3. What is the utilization of the pump jockeys? a. Less than or equal to 60 percent b. Greater than 60 percent but less than or equal to 70 percent c. Greater than 70 percent but less than or equal to 80 percent d. Greater than 80 percent Keyword: utilization 59. Use the information in Scenario C.3. What is the probability that an arrival at the gas station must wait? a. Less than or equal to 0.50 b. Greater than 0.50 but less than or equal to 0.60 c. Greater than 0.60 but less than or equal to 0.70 d. Greater than 0.70 Keywords: probability, wait 60. Use the information in Scenario C.3. What is the average number of customers in line? a. Fewer than or equal to 2.0 b. Greater than 2.0 but fewer than or equal to 3.0 c. Greater than 3.0 but fewer than or equal to 4.0 d. Greater than 4.0 Keywords: number, customers, line, queue 193
15 61. Use the information in Scenario C.3. What is the average number of customers in the system? a. Fewer than or equal to 3.0 b. Greater than 3.0 but fewer than or equal to 3.5 c. Greater than 3.5 but fewer than or equal to 4.0 d. Greater than 4.0 Keywords: customer, system 62. Use the information in Scenario C.3. What is the average time a customer spends in the system? a. Fewer than or equal to five seconds b. Greater than five seconds but fewer than or equal to six seconds c. Greater than six seconds but fewer than or equal to seven seconds d. Greater than seven seconds Keywords: system, time Scenario C.4 Customers arrive at a ticket counter at the rate of 50 customers per hour, according to a Poisson distribution. There are three ticket agents. Customers select the first available agent from one line. Each agent can process 20 customers per hour with exponential service times. 63. Use the information in Scenario C.4. What is the average utilization of the threeagent system? a. Less than or equal to 80 percent b. Greater than 80 percent but less than or equal to 85 percent c. Greater than 85 percent but less than or equal to 90 percent d. Greater than 90 percent Keywords: utilization, system, server 64. Use the information in Scenario C.4. What is the average number of customers waiting in line for service? a. Fewer than or equal to four b. Greater than four but fewer than or equal to 4.5 c. Greater than 4.5 but fewer than or equal to five d. Greater than five Keywords: line, queue, length 194
16 65. Use the information in Scenario C.4. What is the average waiting time in line? a. Fewer than or equal to 3.5 minutes b. Greater than 3.5 minutes but fewer than or equal to 4.5 minutes c. Greater than 4.5 minutes but fewer than or equal to 5.5 minutes d. Greater than 5.5 minutes Keywords: wait, queue, line 66. Use the information in Scenario C.4. What is the average time spent in the system? a. Fewer than or equal to 6.5 minutes b. Greater than 6.5 minutes but fewer than or equal to 7.5 minutes c. Greater than 7.5 minutes but fewer than or equal to 8.5 minutes d. Greater than 8.5 minutes Keywords: time, system Scenario C.5 A trucking firm has five trucks that each requires service at an average rate of once every 50 hours, according to an exponential distribution. The firm has a mechanic who needs five hours to complete the average job with exponential service times. 67. Use the information in Scenario C.5. What is the probability that there will be no trucks in the system? a. Less than or equal to 0.50 b. Greater than 0.50 but less than or equal to 0.60 c. Greater than 0.60 but less than or equal to 0.70 d. Greater than 0.70 Keywords: probability, system, customer 68. Use the information in Scenario C.5. What is the average utilization of the mechanic? a. Less than or equal to 50 percent b. Greater than 50 percent but less than or equal to 60 percent c. Greater than 60 percent but less than or equal to 70 percent d. Greater than 70 percent Keyword: utilization 195
17 69. Use the information in Scenario C.5. What is the average number of trucks waiting for service? a. Fewer than or equal to 0.10 b. Greater than 0.10 but fewer than or equal to 0.14 c. Greater than 0.14 but fewer than or equal to 0.18 d. Greater than 0.18 Keywords: queue, line, length 70. Use the information in Scenario C.5. What is the average number of trucks in line waiting and being serviced? a. Fewer than or equal to 0.30 trucks b. Greater than 0.30 trucks but fewer than or equal to 0.40 trucks c. Greater than 0.40 trucks but fewer than or equal to 0.50 trucks d. Greater than 0.50 trucks Keywords: system, length, customers 71. Use the information in Scenario C.5. What is the average waiting time of trucks in line? a. Fewer than or equal to 1.5 hours b. Greater than 1.5 hours but fewer than or equal to 1.7 hours c. Greater than 1.7 hours but fewer than or equal to 1.9 hours d. Greater than 1.9 hours Keywords: wait, time, queue 72. Use the information in Scenario C.5. What is the average time a truck spends in the system? a. Fewer than or equal to 6.5 hours b. Greater than 6.5 hours but fewer than or equal to 7.0 hours c. Greater than 7.0 hours but fewer than or equal to 7.5 hours d. Greater than 7.5 hours Keywords: time, system, customer Scenario C.6 The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15 hours for each tool on the average, with exponential service times. 196
18 73. Use the information in Scenario C.6. What is the probability that there will be no tools in the system? a. Less than or equal to 0.09 b. Greater than 0.09 but less than or equal to 0.13 c. Greater than 0.13 but less than or equal to 0.17 d. Greater than 0.17 Keywords: probability, system, customer 74. Use the information in Scenario C.6. What is the average utilization of the refurbishing machine? a. Less than or equal to 40 percent b. Greater than 40 percent but less than or equal to 50 percent c. Greater than 50 percent but less than or equal to 60 percent d. Greater than 60 percent Keywords: utilization, server, system 75. Use the information in Scenario C.6. What is the average waiting time of tools in line? a. Fewer than or equal to 15 hours b. Greater than 15 hours but fewer than or equal to 25 hours c. Greater than 25 hours but fewer than or equal to 35 hours d. Greater than 35 hours Keywords: wait, queue, time 76. The average lead time of a unit of product through a manufacturing station is 10 minutes. The production rate has been steady at five units per hour. The average workinprocess inventory at this station is: a. 50 units. b. 10 units. c. 5 units. d units. Keywords: WIP, work, process, Little 197
19 77. The production rate has been steady at 20 units per hour. The average workinprocess inventory at this station is 15 units. What is the average lead time through this manufacturing station? a. 15 minutes b. 30 minutes c. 45 minutes d. 1 hour Keyword: Little s Law 78. The average lead time of a unit of product through a manufacturing station is 10 minutes. The average workinprocess inventory at this station has been 30 pieces. What is the production rate? a pieces per minute b pieces per minute c pieces per minute d. 3 pieces per minute Keywords: production, rate, Little s Law 79. Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these customers purchase 10 items or less and go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don t meet the express line criterion go to the other checkout line where they spend an average of 10 minutes checking out. How many people are checking out in the express line on average? a. One b. Three c. Twelve d. One hundred Forty Four Keywords: production, rate, Little s Law 80. Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these customers purchase 10 items or less and go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don t meet the express line criterion go to checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out in line #2 on average? a. Less than or equal to one b. Greater than one but less than or equal to three c. Greater than three but less than or equal to five d. Greater than five Keywords: production, rate, Little s Law 198
20 81. Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these customers purchase 10 items or less and go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don t meet the express line criterion go to checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out in both lines on average? a. Less than or equal to one b. Greater than one but less than or equal to three c. Greater than three but less than or equal to five d. Greater than five Keywords: production, rate, Little s Law 82. Customers arrive at the local grocery store every 30 seconds on average. Thirty percent of these customers spend an average of 15 minutes shopping and purchase 10 items or less. These lucky customers go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don t meet the express line criterion average 40 minutes in the store and go to checkout line #2 where they spend an average of 10 minutes checking out. How many people are shopping at any given time? a. Less than or equal to 35 b. Greater than 35 but less than or equal to 70 c. Greater than 70 but less than or equal to 105 d. Greater than 105 Difficulty: Hard Keywords: production, rate, Little s Law 83. Customers arrive at the local grocery store every 30 seconds on average. Thirty percent of these customers spend an average of 15 minutes shopping and purchase 10 items or less. These lucky customers go to the express line where they enjoy an average checkout time of 5 minutes. Customers that don t meet the express line criterion average 40 minutes in the store and go to checkout line #2 where they spend an average of 10 minutes checking out. How many people are checking out at any given time? a. Greater than 15 b. Greater than 10 but less than or equal to 15 c. Greater than 5 but less than or equal to 10 d. Less than or equal to 5 Difficulty: Hard Keywords: production, rate, Little s Law 199
21 84. In a waitingline problem, increasing advertising expenditures, increasing the number of promotions, or changing the price of a service is most likely to affect: a. customer arrival rates. b. service rates. c. the priority rule. d. the line arrangement. Reference: Decision Areas for Management Keywords: arrival, rate, price, promotion, advertising 85. In a waitingline problem, assigning additional employees to a service facility will have a direct effect on: a. the line arrangement. b. service rates. c. the size of the customer population. d. the number of service phases. Reference: Decision Areas for Management Keywords: service, rate, servers 86. An operations manager decides that customers should be processed based on the anticipated duration of their request instead of their arrival time. The system has been changed in what fashion? a. Number of phases b. Server efficiency c. Priority rule d. Line arrangement Reference: Decision Areas for Management Keywords: priority, rule 87. An operations manager organizes a process improvement team and the resulting process has a lower µ. Which statement is the best description of this change? a. Arrival rate has fallen. b. There are fewer phases in the new system. c. Interarrival time has fallen. d. Server efficiency has improved. Reference: Decision Areas for Management Keywords: efficiency, server, rate 200
22 88. Instead of having one worker perform all eight steps to process a customer, the erudite operations manager assigns each step to a different worker. In doing so, the operations manager has increased the: a. number of phases. b. number of channels. c. arrival rate. d. interarrival rate. Reference: Decision Areas for Management Keywords: phase 89. If the nature of the customer population, constraints on the line, the priority rule, and the service time distribution renders waiting line theory no longer useful, then an operations manager should rely on: a. decision tree analysis. b. linear programming. c. simulation. d. Little s Law. Reference: Decision Areas for Management Keywords: simulation FILL IN THE BLANK 90. A(n) is one or more customers waiting for service. Answer: waiting line/queue Reference: Why Waiting Lines Form Keywords: waiting, line, customer 91. The is an input that generates potential customers. ustomer population Keywords: customer, population 92. A(n) selects the next customer to be served at the service facility. Answer: priority rule Keywords: priority, rule, customer 201
23 93. You glide your finely tuned Eldorado into the parking lot of your favorite fast food establishment and get in the line for drive through service. After screaming your order into the speaker and receiving what you assume is the goahead, you proceed to the first window to pay, and then to the second window to pick up this evening s meal, mystery meat between two buns with a large sugar water that has been colored brown and carbonated. As you exit the parking lot, you ponder the vicissitudes of this channel phase queuing system. Answer: single, multiple Keywords: channel, phase, queue 94. A(n) is a single step in providing a service. Answer: phase Keywords: phase, service 95. A(n) is a rule that allows a customer of higher priority to interrupt the service of another customer. Answer: preemptive discipline Keywords: preemptive, discipline, priority 96. The distribution specifies the probability that n customers will arrive in T time periods. Answer: exponential Reference: Probability Distributions Keywords: exponential, distribution 97. is a fundamental law that relates the number of customers in a waitingline system to the waiting time of customers. Answer: Little s Law Keywords: Little, law SHORT ANSWERS 98. Explain how waiting lines can develop even when the service time is a constant. Answer: The arrival rates, being random, may exceed the service rates for short periods of time, thus causing lines to form. Reference: Why Waiting Lines Form Keywords: queue, line, form, formation 202
24 99. What are priority rules? Provide examples and indicate why a manager would choose to adopt one over another. Answer: A priority rule determines which customer to serve next. Most service systems that do not use appointments use a firstcome, firstserved (FCFS) rule. The customer who arrives first and is at the head of the line has the highest priority. Other possible rules are shortest processing time (SPT) and earliest due date (EDD). These rules are discussed outside this supplement. A preemptive discipline allows a customer of higher priority to interrupt the service of another, lower priority, customer. FCFS is perceived as being fair by all parties, a preemptive discipline is also perceived as reasonable if the priority nature of the later arrival is understood by all parties. SPT minimizes the average flow time of all parties and the earliestduedate rule minimizes the number of late customers. Reference: Structure of Waiting Line Problems Keywords: priority, rule, preemptive, FCFS, EDD, SPT 100. Your employer is considering a choice between a singleline and a multipleline arrangement. The operation involves multiple servers and a singlephase service. When would each arrangement be ideal? Answer: Single line is best when the servers can handle general transactions. Multiple lines are best when some servers require a special skill or perform only a selected set of services. Difficulty: Hard Keywords: single, multiple, line, phase 101. What is a finitesource model? Give an example of its appropriate use. Answer: A finitesource model is one in which the calling population of customers is not infinite. If N is greater than 30 customers, the singleserver model with the assumption of an infinite calling population is adequate. Otherwise, the finitesource model is the one to use. Examples may vary but might include the number of students arriving for office hours, the number of machines that need repair, or the number of items expiring in your refrigerator. Keywords: finite, source 102. Create a table that lists any three performance measures for a service system in the left column. In the center column, indicate what steps management can take to improve system performance on those metrics. In the rightmost column indicate what steps management can take to improve customers perceptions of performance on those metrics. Answer: Answers will vary. The text indicates that management might be concerned about the length of the queue, the total number of customers in the system, the waiting time in line, the total time in the system, and the service facility utilization. Ways to improve a service facility include affecting the arrival rates, increasing the number of service facilities, changing the number of phases, increasing the number of servers, changing priority rule, and changing the line arrangement. Management can improve customer perceptions a number of ways. For example, customers will be less aware of waiting time if they are entertained while waiting. Customers will be less aware of the length of the line if the line is serpentine rather than straight. Reference: Decision Areas for Management Keywords: service, system, improvement, arrival, service, rate, number 203
25 PROBLEMS 103. Customers in a small retail store arrive at the single cashier at the rate of 10 per hour. The average service time for the cashier is five minutes. Arrivals tend to follow a Poisson distribution, and service times follow an exponential distribution. a. What is the average utilization of the cashier? b. What is the average number of customers in the system? c. What is the average number of customers in line? d. What is the average time spent in the system? e. What is the average time spent in line? Answer: Servers 1(Number of servers is assumed to be one in singleserver model.) Arrival Rate ( ) 10 Service Rate ( ) 12 Probability of zero customers in the system (P0) Probability of 1 customers in the system Average utilization of the server ( ) a. Average number of customers in the system (L) b. Average number of customers in line (L q) Average waiting/service time in the system (W) Average waiting time in line (W q) Keywords: utilization, number, system, queue, line, length, time c d e. 204
26 104. A professor sits in his plush office and patiently answers questions from his students the afternoon before the final exam. His class is a mass lecture of 350 students, so he keeps socialization to a minimum and concentrates on providing explanations as quickly as possible. On average, he can answer 60 questions an hour and students arrive at his office every five minutes. Student arrivals are Poisson distributed, each student has only one question and answer times are exponentially distributed. a. What fraction of his time is the professor spending answering questions? b. What is the average number of students waiting outside his office? c. What is the average time a student spends in line outside the professor s office? Answer: a. b. c. 12 customers/hour Average utilization customers/hour Queue length L q 0.05 customers Waiting time in queue W q hours = minutes = seconds Keywords: utilization, time, length, queue, line, system 205
27 105. A harvesting crew that follows the wheat harvest has six combines, each requiring service at an average rate of once every 40 hours, according to an exponential distribution. The firm has a mechanic who needs four hours to complete the average repair with exponential service times. a. What is the average utilization of the mechanic? b. What is the average number of combines in the system? c. What is the average number of combines in line? d. What is the average time spent being repaired and waiting? e. What is the average time spent in line waiting for repair? Answer: Customers 6 Arrival Rate ( ) Service Rate ( ) 0.25 Probability of zero customers in the system (P0) Probability of 1 customers in the system #N/A Average utilization of the server ( ) a. Average number of customers in the system (L) b. Average number of customers in line (L q) c. Average waiting/service time in the system (W) d. Average waiting time in line (W q) e. Keywords: utilization, time, length, number, queue, line, system 206
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