ORIE 4580/5580
Solutions for Homework Assignment 11
Question 1:
Using policy 1, the first machine starts at time 0 with the job that takes the longest processing time and finishes this job at max{T
1
, T
2
, T
3
}.
The second
machine starts at time 0 with the job that takes the second longest processing time and finishes at median{T
1
, T
2
, T
3
}.
The second machine finishes first
and will complete the only remaining job at median{T
1
, T
2
, T
3
} + min{T
1
, T
2
, T
3
}.
Therefore, the time it takes the first policy to complete all three jobs =
max{max{T
1
, T
2
, T
3
}, median{T
1
, T
2
, T
3
} + min{T
1
, T
2
, T
3
}}.
Similarly, under policy 2, the first machine starts at time 0 with the job that takes the shortest processing time and finishes this job at min{T
1
, T
2
, T
3
}.
The
second machine starts at time 0 with the job that takes the second shortest processing time and finishes at median{T
1
, T
2
, T
3
}.
The first machine finishes
first and will complete the only remaining job at min{T
1
, T
2
, T
3
} + max{T
1
, T
2
, T
3
}.
Therefore, the time it takes the second policy to complete all three
jobs = max{median{T
1
, T
2
, T
3
}, min{T
1
, T
2
, T
3
} + max{T
1
, T
2
, T
3
}}.
a)
By using only 10 replications and
no
common
random numbers, a 95% confidence interval for θ
1

θ
2
is [1.259,0.955].
The width of the confidence
interval is 2.214
.
Because 0 is included in the confidence interval, at this level of α (5%), we fail to reject the null hypothesis that the
two systems have
equal means.
Note that you may observe different values due to randomness.
A portion of the worksheet (with formulae) used to obtain these numbers
is shown here (see details in the accompanying spreadsheet):
A
B
C
D
E
F
2
T1
T2
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 '08
 TOPALOGLU
 Statistical hypothesis testing, 5%, Randomness, 15 16 17 18 19 20 21 22 L

Click to edit the document details