practice problems for Process Analysis
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School
University of Southern California *
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Course
504A
Subject
Industrial Engineering
Date
Feb 20, 2024
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docx
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7
Uploaded by MegaWillpower13255
P
RACTICE
PROBLEMS
FOR
P
ROCESS
A
NALYSIS
: S
OLUTIONS
P
ROCESS
A
NALYSIS
These practice problems are intended to help you prepare for the exams. The best way to
use these practice problems is to work through them yourself first, without looking at the
solutions. You do not need to all these practice problems, it is up to you to determine when
you are ready. I recommend reviewing numerical examples that we did in class in addition
to these practice problems. The quiz is timed: once you start the quiz, you will have 60
minutes to finish it, so you should not attempt the quiz until you are comfortable with these
practice problems. Q
UESTION
1
Consider the following simple assembly process:
The numbers below each step refer to the time necessary to process one unit of the product
at that step.
The process is staffed by three operators with one operator assigned to each of the three
steps. Assume no setups are required, processing times are constant, and no Work in
Process (WIP) is permitted beyond that actually being worked on at each process step (i.e.,
there are no buffers between process steps).
a)
What is the Capacity of the process in steady state?
b)
What is the Direct Labor Utilization of the operator at Step A?
c)
Each operator receives regular wages of $12/hour for the first 8 hours, and overtime
wages of $18/hour for any additional time. Twelve hours per day is the maximum
work time permitted. A finished unit sells for $10 while its direct material cost is
$6/unit. Does it pay to use overtime under this cost structure (assuming sufficient
demand exists)? (You can assume steady state in your analysis, i.e., ignore the
startup effects in the first hour.)
d)
Would you hire a skilled operator whose wage rate were $20/hour (regular time), but
could perform Step B at a processing time of 4 minutes/unit? (Assume no overtime.
Assume also that, if you hire the skilled operator, you no longer need a regular
operator at Step B.)
e)
Would you hire a skilled operator whose wage rate were $20/hour (regular time), but
could perform Step A at a processing time of 2 minutes/unit? (Assume no overtime.
Assume also that, if you hire the skilled operator, you no longer need a regular
operator at Step A.)
P
AGE
1
Q
UESTION
2
Professors Corbett and Roels are thinking of buying a pizza carry-out shop in West Los
Angeles and have asked you to help them evaluate the current operation. The shop, OTM’s
Pizza, currently operates in a build-to-order fashion with four employees: an order taker who
receives/processes orders and does bookkeeping; a pizza tosser who tosses the pizza shell;
a pizza assembler who prepares the pizza shell and customizes the pizza and a chef who
supervises the placement of the pizza in the oven.
The production process begins when an order is transmitted to a computer in the kitchen.
Order processing takes a negligible amount of time. It takes one half of a minute for the
pizza assembler to prepare the pizza shell to give to the pizza tosser. The pizza tosser then
tosses the shell for two minutes to obtain proper shape and consistency. The tossing
operation is highly skilled and can only be performed by the tosser. It then takes one minute
for the pizza assembler to customize the pizza by adding the correct sauce and ingredients
(e.g., cheese, pepperoni, mushrooms). The secret to OTM’s famous taste is a three-minute
wait prior to placing the pizza in the oven. This wait allows the flavors of the ingredients to
blend. After this three-minute delay, the chef places the pizza in one of six ovens (with a
capacity of one pizza each) for a baking time of ten minutes.
a)
Draw a process flow chart of the pizza production process. Identify the key resources
involved in each task.
b)
What is the capacity of the current cooking process? Specifically, what is the
maximum number of pizzas that OTM’s can produce in the first hour (assuming an
empty system at the beginning of the day) and in each subsequent hour?
c)
Somebody has suggested producing pizza shells for inventory before each day’s
hours of operations. That is, the pizza tosser would arrive prior to the business hours
and perform all of the work associated with pizza shell production (shell preparation
and tossing). These shells would then be available to the assembler for customization
during store hours. How would producing pizza shells to inventory change your
answer to question (b)? (You can adopt a back-of-the-envelope approach, similar to
the one used in class, which may lead to a slightly different answer than a detailed
analysis based on a Gantt chart.)
d)
Profs. Corbett and Roels would like to increase potential demand by offering pizza
delivery direct to the customer. Demand in the past has been 20 pizzas per hour, but
they are concerned that the current production process will not be able to support
this demand increase. What (if any) changes will be needed in the cooking process to
support a demand of 40 pizzas/hour (after the first hour startup period)? Assume that
pizza shells are made to inventory as indicated in question (c).
Q
UESTION
3
A five-stage process is depicted below. Each task must be performed in the order given.
Assume one employee can only work on one unit at any point in time.
A
B
C
D
E
Employees assigned
1
1
1
1
2
P
AGE
2
Task time (or processing time) in seconds
15
30
20
10
45
a)
What is the minimal possible throughput time of this process?
A)
30 seconds
B)
45 seconds
C)
97.5 seconds
D)
120 seconds
E)
165 seconds
b)
If the process operates at 100% capacity utilization, i.e., the bottleneck operates at
100% capacity utilization, what is the capacity utilization at step E?
A)
1
B)
more than 0.8 but less than 1
C)
more than 0.6 but less than 0.8
D)
more than 0.4 but less than 0.6
E)
0.4 or less
c)
Which of the following alternatives is best in terms of efficiency?
A)
Add a third worker to E
B)
Combining tasks A and B into one work station and eliminating one worker
C)
Combining tasks C and D into one work station and eliminating one worker
D)
Indifferent between b and c
E)
Indifferent between a, b, and c
d)
What is the capacity of the process?
A)
100 or more per hour
B)
more than 75 but less than 100 per hour
C)
more than 55 but less than 75 per hour
D)
more than 30 but less than 55 per hour
E)
30 or fewer units per hour
Q
UESTION
4
The New Cola Company utilizes five tasks to produce 12-ounce bottles of soft drinks:
Task
Dscription
Task Time
per 100 bottles
Number of Machines
Cycle Time
per
100 bottles
1
Clean bottles
60 seconds
3
2
Fill bottles
40 seconds
1
3
Check fill
heights
20 seconds
2
4
Cap bottles
30 seconds
4
5
Package
bottles
60 seconds
5
a)
What is the cycle time per 100 bottles for bottle packaging? A)
12 seconds
B)
20 seconds
P
AGE
3
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C)
60 seconds
D)
210 seconds
E)
300 seconds
b)
What is the cycle time per 100 bottles for the process as a whole?
A)
7.5 seconds
B)
20 seconds C)
40 seconds
D)
60 seconds
E)
89.5 seconds
c)
What is the bottleneck operation in the New Cola Company production process?
A)
Bottle cleaning
B)
Bottle filling
C)
Fill height checking
D)
Bottle capping
E)
Bottle packaging
d)
Assuming management allows no inventories to accumulate between tasks, what is
the throughput time for each batch of 100 bottles?
A)
89.5 seconds
B)
40 seconds
C)
60 seconds
D)
200 seconds
E)
none of the above
Q
UESTION
5
Consider the following process. All Steps (A, B, C, D, and E) are necessary to create each
finished unit. Each step employs a single worker. Task times are shown for each step.
a)
What is the fastest a rush order for one unit can go through the process? b)
Working eight hours a day, what is the daily capacity of the process?
For the next two problems, consider hiring another worker and duplicating Operation D as
shown in the diagram below (no buffers). The two workers work on Successive products;
they never work on the same product at the same time. The product still requires the five
Steps (A, B, C, D, E).
P
AGE
4
c)
What is the fastest a rush order of one unit can go through the process?
d)
Working 8 hours a day, what is the daily capacity of the process? P
AGE
5
Q
UESTION
6
Consider a five-workstation, worker-paced line, with five manual tasks to be performed
before the product is completed, as diagrammed below: The times shown are the times, in minutes, that it takes one worker to perform that task for
one unit of product. This line is staffed with six workers, two of whom are assigned to Workstation D. For the
next question, assume that each of the Tasks A through E are never split among multiple
workers. Thus, the two workers doing Task D work on every other unit, each doing all of
Task D on the particular unit on which he or she is working. (Assume there is ample
equipment so that all workers can perform their tasks).
a)
What is this line’s capacity in an eight-hour day?
time to go from one step to another, and doing their tasks in the allotted time without
getting in each other’s way. Assume that ample equipment is available.
b)
One of the two workers assigned to Task D is equally competent at Task C, and it is
decided that this worker will work on both Tasks C and D. (i.e., one worker is
assigned to C, one worker is assigned to D, and one worker moves between C and D.)
This third worker moves between C and D so as to maximize the output of the
process. What is this line’s maximum output rate, in units per eight-hour day?
Q
UESTION
7
At a local business school, there is a toasted submarine sandwich process that uses a
conveyor-fed oven. Zeynep is the sole operator of the sub making process. In the first step
of the process, she spends 2 minutes putting various ingredients in the sub. Then, she puts
the sub on a conveyor belt and, over a period of 12 minutes, the conveyor moves the sub
from the beginning of the oven to the end of the oven, fully toasting it. After the sub comes
out of the oven, Zeynep spends 1 minute slicing the sandwich and putting it in a box. At
most, 5 subs can fit in the oven at once. The toasting time in the oven does not depend on
the number of subs in the oven.
a)
What is the hourly capacity of this sub making process?
b)
What is the labor utilization?
Suppose another employee is hired to do the slicing and boxing, and Zeynep now only loads
the subs with the right ingredients:
P
AGE
6
2 min/sub
(Zeynep)
12 min (oven)
1
min/sub
(Zeynep)
load
ingredien
ts
slice and
box
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c)
What is the hourly capacity of this process with the additional employee?
P
AGE
7