An injector machine goes down roughly 20% of the time (the injector gums up and needs to be cleaned, a quick process). One operator is assigned to service three identical such machines. Each machine can produce 100 parts/h if running properly (i.e., not down). The operator is paid $10/h and each machine costs $20/h to operate. Consider 8hr/shift a) Please fill in the table below: b) How many parts can you produce per shift? c) What is the unit cost fper part for this operation? d) If you hire another operator at the same rate to assist the first operator, what is the unit cost now? e) Is it worth hiring another operator at the same rate to assist the first operator, in case more than one machine goes down at the same time?
An injector machine goes down roughly 20% of the time (the injector gums up and needs to be cleaned, a quick process). One operator is assigned to service three identical such machines. Each machine can produce 100 parts/h if running properly (i.e., not down). The operator is paid $10/h and each machine costs $20/h to operate. Consider 8hr/shift a) Please fill in the table below: b) How many parts can you produce per shift? c) What is the unit cost fper part for this operation? d) If you hire another operator at the same rate to assist the first operator, what is the unit cost now? e) Is it worth hiring another operator at the same rate to assist the first operator, in case more than one machine goes down at the same time?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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An injector machine goes down roughly 20% of the time (the injector gums up and needs to be cleaned, a quick process). One operator is assigned to service three identical such machines. Each machine can produce 100 parts/h if running properly (i.e., not down). The operator is paid $10/h and each machine costs $20/h to operate. Consider 8hr/shift
a) Please fill in the table below:
b) How many parts can you produce per shift?
c) What is the unit cost fper part for this operation?
d) If you hire another operator at the same rate to assist the first operator, what is the unit cost now?
e) Is it worth hiring another operator at the same rate to assist the first operator, in case more than one machine goes down at the same time?
Transcribed Image Text:An injector machine goes down roughly 20% of the time (the injector gums up and needs to be cleaned, a quick
process). One operator is assigned to service three identical such machines. Each machine can produce 100 parts/h if
running properly (i.e., not down). The operator is paid $10/h and each machine costs $20/h to operate. Consider 8hr/shift
a) Please fill in the table below: (please keep three decimal places)
Machine down (m)
Probability
Lost time (hr/shift)
0
1
2
3
b) How many parts can you produce per shift?
c) What is the unit cost for this operation? $
per part (please keep three decimal places)
d) If you hire another operator at the same rate to assist the first operator, what is the unit cost now? $
part (please keep three decimal places)
e) Is it worth hiring another operator at the same rate to assist the first operator, in case more than one machine goes
down at the same time?
parts (please keep an integer)
◆
per
Transcribed Image Text:RANDOM SERVICING
▪ Machine servicing is not regular
▪ Most likely it is random (don't know when)
▪ Use probability theory to estimate % idle time (binomial expansion)
Probability of m (out of n) machines down (P):
=
n!
m!(n-m)!
¡pmqn-m
p = prob of down time
q = prob of up time = 1-p
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