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Albany State University *
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Course
1101
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
Pages
3
Uploaded by MegaMoose3765
Operations - Lesson 5 Problem Set - Solution
Part 1
Consider an urgent care facility with a single doctor. Patients arrive at this facility according to a Poisson process with rate of 3 patients per hour. The doctor sees the patients on a first-come-
first-serve basis. On average, the doctor spends 15 minutes with each patient. The actual time of seeing a patient follows an exponential distribution.
1.
The utilization of this doctor is: (4 points)
a.
0.20
b.
0.75
c.
0.85
d.
1.33
2.
The average time that a patient spends in the clinic (in minutes) is: (4 points)
a.
10
b.
25
c.
45
d.
60
3.
Realizing that the patients spend too long in the clinic, the doctor is considering adopting
an electronic medical record (EMR) system that would help her reduce the time she spends with each patient. If she would like the patients to spend less than or equal to half an hour in the system, how long should she plan to spend with a patient on average (in minutes)? Choose the largest number possible. (4 points)
a.
10
b.
12
c.
15
d.
18
4.
The doctor considers the cost of keeping a patient in the system to be $8 per patient per hour. How much cost savings per hour would the doctor incur if she ends up switching her average service time from 15 minutes to the duration you selected in the previous question? (4 points)
a.
$4
b.
$8
c.
$12
d.
$16
5.
Assuming that implementing the EMR system costs $10 per hour, should the doctor adopt this system? (4 points)
a.
Yes
b.
No
Part 2 The manager of the call center of a large bank needs to determine the optimal number of operators that she should hire. The call center serves two types of clients: Platinum (P) and Standard (S) customers. She has determined that P calls arrive according to a Poisson process at a rate of 10 calls per hour and S calls arrive according to a Poisson process at a rate of 40 calls per hour.
Two types of operators are available on the market: High skill (H) and Average skill (A), which differ with respect to their ability and speed. H operators can serve both types of customers and the average amount of time that they need is 12 minutes per call independent of the type. In contrast, A operators can serve only S calls and they need on average 20 minutes per call. Assume that all service times are exponentially distributed.
The cost of hiring an H operator is $30 per hour while the cost of hiring an A operator is $15 per hour. The manager has determined that a P customers should not be kept on line (before their call is answered) for more than 2 minutes, on average and that an S customer should not be kept in line for more than 5 minutes, on average.
The manager is interested in minimizing the cost of operators while maintaining the average speed of answer specifications for both groups of customers. She is considering two possible queue configurations:
Configuration 1: Single queue
Have a single queue for both type of calls and hire only H operators that will serve both types of calls. Calls will be served on a first-come-first-serve basis independent of their type.
Configuration 2: Two separate queues
Have two separate queues for each type of call. For the P calls queue she will naturally hire only
H operators. For the S calls queue she can either hire H operators or A operators. However, she
does not want to mix H and A operators. So she has to decide which one of the two types of operators to use.
1.
If the manager chooses configuration 1, she should hire _13___ H operators. (4 points)
2.
Given your answer from the previous question, the associated cost per hour is $_390___. (4 points)
3.
If the manager chooses configuration 2, she should hire _4___ H operators for P calls. (4 points)
4.
Under configuration 2, she should she use this type of operator for S calls: (4 points)
a.
A
b.
H
c.
They are both equally effective
Explanation: With H operators, they need to hire 10 operators for a total cost of $300 per hour. With A operators, they need to hire 16 operators for a total cost of $240 per hour.
5.
The optimal total cost per hour associated with Configuration 2 given your answers to questions 3 and 4 is $_360___. (4 points)
6.
Which one of the two alternatives do you recommend? (4 points)
a.
Configuration 1
b.
Configuration 2
c.
They are both equally effective
7.
Comment on the relationship between this question and the tradeoffs between pooled versus dedicated queue configuration discussed in the “pooled versus dedicated queues” video. How is this situation similar to the one discussed in the video? In what ways are they different? (6 points)
Similarities: Configurations 1 is a pooled system (a single line) whereas Configuration 2 resembles a dedicated queue. Differences:
The operators are not all the same in this case.
The customers are not all the same either.
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