ex8
xlsx
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School
Yorkville University *
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Course
BUSI2073
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
xlsx
Pages
7
Uploaded by AgentJaguar3705
students arrive at the help desk at the rate of 4 every 10 minutes. The average service time is 2 minutes
The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed
avg num of arr
average time a student is in the lab
avg num serv
=1/(0.5- 0.4 )
10 mins
average number of students in the lab
0. 4/(0.5-0.4)
4
average number of students waiting to receive service
0.4^2/0.5*(0.5-0.4)
3.2
average time a student is in the queue
0. 4/0.5*(0.5-0.4)
0.08 mins
What is the probability that there are no students at the computer lab 1-0.4/0.5
20%
What percentage of the time is the help desk busy
0.4/0.5
80%
What is the probability that there are exactly 2 students in the lab? p2
e
0.6703
5% ((e0.4*(0.4^2))/2)
By how much would your answer to part (a) be reduced if a second help desk, which could do the same p0=
m=2
1/
1+0.4/0.5
1/2*(0.4/0.5)^2 x
(0.4*0.5)/((0.4*0.5)-2)
1.8
0.32 -0.11111111
=
0.56675062972
ls
0.128 =0.4*0.5*(0.4/0.5)^2
0.36 =1*(1-0.4)^2
+0.36/0.57
0.201511
0.128/0.36
0.35555555556 + 0.4/0.5
0.8 =
1.001511
ws
2.50377834 2.5 mins
ls/0.4
reduced by 7.5 mins 10 mins -2.5mins
d. rival /min
0.4
ved/min
0.5
work, were added
ls
8.2
5 weaving machines in use
need repair after about 20 hours of use
the maintenance worker can service a weaving machine in an average of 2 hours
Weaving machine downtime costs $120 per hour. Jim is paid $25 per hour
aver arr rate /hr
0.25 5/20
avg ser rate/hr
c) What is the total hourly costs? 0.5 1/2
n
5
a) What is the average time a weaving machine is waiting to be repaired? 1 hr
=+aver arr rate/((2*avg ser rate)*(avg ser rate-aver arr rate))
b) What is the average number of weaving machines in the repairing area?
lq
0.25
=+aver arr rate^2/((2*avg ser rate)*(avg ser rate-aver arr rate))
ls
0.75 per hr lq+aver arr rate /avg ser rate
c) What is the total hourly costs? 145 per repair average time a weaving machine is waiting to be repaired*(Weaving machine downtime costs $120 per hour
+Jim is paid $25 per hour)
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William consider price and reputation as the most important criteria
He considers reputation to be four times more important than price
choices to two suppliers
On a 10-point scale, he has assigned Rideau’s Windows Supply a score of 9 on price and 4 on reputation.
He has assigned Ian and Family a score of 3 on price and 6 on reputation.
Rideau’s Windows Supply
crtterion weight score(1-10)
weight X score
reputation
0.8
4
3.2
price
0.2
9
1.8
tatal
1
13
5
Ian and Family
reputation
0.8
6
4.8
price
0.2
3
0.6
tatal
1
9
5.4
.
its engines valued at $500,000
The engines need to be shipped to the Montreal, QC, plant
The annual holding cost rate for auto engine has been estimated at 15%. There are five shipping companies available
Their delivery time and costs are listed in the table below.
Which carrier is most economical? time(days)
cost
shipping day saved
Daily holding cost saved
money saved
a
20
500
0
0
0
b
15
800
5
1027.39726027397 227.397260273972
c
12
1200
8
1643.83561643836 443.835616438356
d
8
1600
12
2465.75342465753 865.753424657534
e
5
2000
15
3082.19178082192 1082.19178082192
Carrier x-carrier a
Daily holding cost Daily holding cost SA
(longest) DAYS
X DAYS SAVED
- COST
annual holding cost rate
15%
product value
500,000
(annual holding cost rate
x product value) /365
Daily holding cost 205.479452054794
: Carrier e saved the most money
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