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Chapter 2: Q11-17OQ (page 291)

The National State Bank is trying to make sure that it has enough tellers to handle the Friday afternoon rush of workers wanting to cash their paychecks. It is only concerned with the last hour of the day from 4:00 to 5:00 p.m. It takes 5 minutes per customer to be processed by the tellers. The average customer arrivals are shown in the table below.

The bank currently has 8 teller stations, and all are staffed during the Friday afternoon rush hour.

a. What is the current maximum output at the bank during rush hour?

b. Can the bank process all the customers by 5:00 p.m.?

c. What is the maximum waiting time for customers, and what time period does it occur?

Short Answer

Expert verified

A bank is a financial entity that accepts public deposits as well as develops deposit accounts while also issuing mortgages.

Step by step solution

01

(a) The current maximum output at the bank during rush hour

The current maximum output at the bank during rush hour is given below:

Service time = 1 hour or 60 minutesService time = 5 minutes / CustomerNumber of counter = 8P = 8; as the number of teller is 8.

MaximumOutput=TotalavailableCapacity(inmins)Servicetimepercustomer(inmins)MaximumOutput=60脳P5MaximumOutput=96CustomersTherefore, the maximum output is96customers.

02

(b) The bank processes all the customers by 5:00 p.m.

As there are only 93 clients as well as 96 can be handled, the bank will be able to process all of the clients before 5:00 PM. The institution may need more time to get to know its clients and service them correctly. A variety of operations related to client processing should not be overlooked. As a result, the bank will be unable to process all of the clients before 5:00 PM.

The calculated customer arrival is calculated as shown in the table below:

03

(c) The maximum waiting time for customers and what time period does it occurs in

The maximum waiting time is 10 minutes and it occurs 4:30-$4:35 since there are 19 customers and only 8 can be served per 5 min.

The calculation of maximum waiting time for customers is shown below:

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Most popular questions from this chapter

Question: I-mart is a discount optical shop that can fill most prescription orders in around 1 hour. The management is analyzing the processes at the store. There currently is one person assigned to each task below. The optometrist assigned to task B takes an hour off for lunch and the other employees work the entire day.

Task

Time

Greet/register the patient

2 minutes

An optometrist conducts an eye exam

25 minutes

Frame/lenses selection

20 minutes

Glasses made (the process can run 6 pairs of glasses at the same time).

60 minutes

Final fitting

5 minutes

For a typical 10-hour retail day (10 a.m.鈥�8 p.m.), the manager would like to calculate the following:

a. What is the current maximum output of the process per day (assuming every patient requires glasses)?

b. If another person were added, where would be the logical place?

c. What effect would a mail-order lab (where the glasses are made off-site and returned in 5鈥�7 days) have on the process?

L. Winston Martin (an allergist) has an excellent system for handling his regular patients who come in just for allergy injections. Patients arrive for injection and fill out a name slip, which is then placed in an open slot that passes into another room staffed by one or two nurses. The special injections for a patient are prepared, and the patient is called through a speaker system into the room to receive the injection. At certain times during the day, patient load drops, and only one nurse is needed to administer the injections. Let鈥檚 focus on the simpler case of the two鈥攏amely when there is one nurse. Also, assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentially distributed. During this slower period, patients arrive with an inter-arrival time of approximately three minutes. It takes the nurse an average of two minutes to prepare the patients鈥� serum and administer the injection.

a.What is the average number you would expect to see in Dr. Martin鈥檚 facilities?

b.How long would it take for a patient to arrive, get an injection, and leave?

c.What is the probability that there will be three or more patients on the premises?

d.What is the utilization of the nurse?

e.Assume three nurses are available. Each takes an average of two minutes to prepare the patients鈥� serum and administer the injection. What is the average total time of a patient in the system?

The desired daily output for an assembly line is 360 units. This assembly line will operate for 450 minutes per day. The following table contains information on this product鈥檚 task times and precedence relationships:

TASK

Task Time (Seconds)

Immediate Predecessor

A

30

-

B

35

A

C

30

A

D

35

B

E

15

C

F

65

C

G

40

E, F

h

25

D, G

a. Draw the precedence diagram.

b. What is the workstation cycle time required to produce 360 units per day?

c. Balance this line using the largest number of following tasks. Use the longest task time as a secondary criterion.

d. What is the efficiency of your line balance, assuming it is running at the cycle time from part (b)?

Question: Avis Company is a car rental company that is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 2 minutes. The average traveling time (round-trip) is 20 minutes.

a. How many Avis buses are traveling to and from the airport?

b. The branch manager wants to improve the service and suggests dispatching buses every 0.5 minutes. She argues that this will reduce the average traveling time from the airport to Avis offices to 2.5 minutes. Is she correct? If your answer is negative, then what will the average traveling time be?

Question: The following represents a process used to assemble a chair with an upholstered seat. Stations A, B, and C make the seat; stations J, K, and L assemble the chair frame; station X is where the two subassemblies are brought together; and some final tasks are completed in stations Y and Z. One worker is assigned to each of the stations. The line is paced using a countdown clock to synchronize production at each station.

Generally there is no inventory kept anywhere in the system, although there is

room for one unit between each of the stations that might be used for a brief amount of time.

Given the following amount of work in seconds required at each station:

a

38

j

32

x

22

b

34

k

30

y

18

c

35

l

34

z

20

a. What is the possible daily output of this 鈥減rocess鈥� if 8 hours of processing time is available each day?

b. Given your output rate in part (a), what is the efficiency of the process?

c. What is the flow time of the process?
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