Question

56) One employee is in charge of the following activities at a refreshment stand: Activity Greet customer Take order Process order Print receipt Activity Time per Customer 5 seconds 25 seconds 1.5 minutes 30 seconds If demand rate is 20 customers per hour, what are the flow rate (in customers per hour), utilization, and cycle time (in minutes per customer)? A) 20, 0.83, 0.05 B) 24, 1, 0.04 c)20,0.83, 3 D) 24, 1,25 57) Patients are arriving at a clinic at a rate of two per minute. Each patient's visit consists of four steps: check in, record vital signs, receive treatment, and check out. A receptionist takes 1 minute to check a patient in. A nurse takes 2 minutes to record the patient's vital signs. A doctor spends 10 minutes with a patient. A staff member takes 3 minutes to check a patient out. What is the cycle time of the process in minutes? A) 30 c) 20 B) 10 D) Cannot be deterimined 58) Students are going through a three-step process to obtain their ID cards. Each student will spend 2 minutes at the registration desk before going to one of three cashiers to pay a fee for the ID card. After that, he/she will visit one of four ID processing stations to have his/her picture taken and ID card printed. Visits to the cashier and ID processing station take 10 and 20 minutes respectively. If the demand rate is 0.125 student per minute, how long does it take to process 20 students assuming the system is full? A) 152 minutes B) 100 minutes c) 160 minutes D) 184 minutes 59) During the two hours of the morning rush from 8 a.m. to 10 a.m., 100 customers per hour arrive at the coffee shop. The coffee shop has a capacity of 80 customers per hour. How long does the customer arriving at 10 a.m. have to wait to be served? A) 2 hours B) 0.5 hour D) 0.25 hour C)1 hour 60) Packages arrive at a facility at a rate of 30 per hour and are processed continuously at a rate of 25 per hour. The facility is open from 8 a.m. to 4 p.m. How long does the last package wait before it is processed? A) 1.20 hours D) 1.75 hours B) 1.33 hours C) 1.60 hours 61) A server operates with 80% utilization. The coefficient of variation for the service process is 0.5 and the coefficient of variation of the arrival process is 1. The average processing time is 3 minutes. What is the average time a customer waits in the queue according to the single-server queue model? A) 7.5 minutes c) 3 minutes D) 10.5 minutes B) 3.75 minutes

Answer 1

56). C-[ 20, 0.833, 3]

Processing time(in seconds)= 5+25+90+30.

=150 seconds/ customer

Seconds/hour= 60 × 60 = 3600 seconds

Process capacity= 3600÷ 150 = 24 customers/ hour

• Flow rate= minimum(demand, process capacity). = Minimum(20 , 24) = 20 customer/ hour
• Utilization= flow rate ÷ process capacity = 20÷ 24 = 0.833
• Cycle time = 1 ÷ flow rate. = (1÷20)÷ 60 = 3 minutes/ customer.

58) D 184 minutes

process time( per student) = 2+ 10 + 20 = 32 minutes

Process capacity= min capacity among 3 phases

1. 1÷ 2= 0.5
2. 3÷10= 0.3
3. 4 ÷ 20 = 0.2

Process capacity = 0.2 student/ minute

Flow rate= min (demand, process capacity). = Minimum(0.125, 0.2) = 0125

Cycle time= 1 ÷ flow rate. = 1÷ 0.125 8 minutes

Time to process remaining 19 students = 19 × 8 = 152 minutes

Total time to process 20 students = 152 + 32 = 184 minutes.

59) B- 0.5 hour.

time ( rush hours) = 2

Demand= 100

Capacity= 80

Waiting Time of customer arriving at 10 = Time (Demand÷ capacity- 1)

= 2(100÷80-1)

= 2(1.25 - 1)

= 0.5 hour

60) C - 1.60 hours

Time( 8 am - 4 pm)= 8 hours

Demand= 30

Capacity = 25

Waitkng time for last package to be processed = Time(demand÷ capacity - 1)

= 8(30÷ 25 - 1)

= 8(1.2 - 1)

=8(0.2)

=1.6 hours