An industrial engineer is conducting an experiment using a Monte Carlo simulatio
ID: 371700 • Letter: A
Question
An industrial engineer is conducting an experiment using a Monte Carlo simulation model of an inventory system. The independent variables in her model are the order quantity (A), the reorder point (B), the setup cost (C), the backorder cost (D), and the carrying cost rate (E). The response variable is average annual cost. To conserve computer time, she decides to investigate these factors using a design with I = ABD and I = BCE.
The results she obtains are:
A
B
C
D
E
y
-1
-1
-1
1
1
95
1
-1
-1
-1
1
134
-1
1
-1
-1
-1
158
1
1
-1
1
-1
190
-1
-1
1
1
-1
92
1
-1
1
-1
-1
187
-1
1
1
-1
1
155
1
1
1
1
1
185
1.Verify that the estimated effects are indeed correct, given the defining relationship
Assume another experiment was added. The results for the new experiment were
A
B
C
D
E
y
1
-1
-1
1
1
136
-1
-1
-1
-1
1
93
1
1
-1
-1
-1
187
-1
1
-1
1
-1
153
1
-1
1
1
-1
139
-1
-1
1
-1
-1
99
1
1
1
-1
1
191
-1
1
1
1
1
150
2.How was the second fraction factorial experiment obtained. Give the defining relationship.
3.When this second fraction is added to the original fraction factorial experiments, what are the main effects estimated.
A
B
C
D
E
y
-1
-1
-1
1
1
95
1
-1
-1
-1
1
134
-1
1
-1
-1
-1
158
1
1
-1
1
-1
190
-1
-1
1
1
-1
92
1
-1
1
-1
-1
187
-1
1
1
-1
1
155
1
1
1
1
1
185
in inventery system. The independent variables in her model are the order qanatity (A).the reorder peut (B), the setup cost (C), the backorder cost (D)and the camymp cost mt2 (E). The response moble is avene nnual cost To conserve computer tre she decides to esnete hese Esctocs using a design withI-ABD and-BCE (a) Verity at tte etooted effects are indeed coreet gven the defning relarionship 136 150 rained retonship When this second Ernction is odded to the eiinal fraction factorial experianents what areExplanation / Answer
Let’s simplify the results first as per the results obtained:
(i)
The design is now as follows:
A
B
C
D
E
de
-
-
-
+
+
ae
+
-
-
-
+
b
-
+
-
-
-
abd
+
+
-
+
-
cd
-
-
+
+
-
ac
+
-
+
-
-
bce
-
+
+
-
+
abcde
+
+
+
+
+
It is easy to verify that D = AB and E = BC; that is the defining relations are I = ABD and I = BCE. The scaled estimates of the effects are:
a
b
ab
c ac
bc abc
49
45
-18 10.5 13.5 -14.5 -14.5
From the complete defining relation I=ABD = BCE = ACDE, the alias structure are identified as follows:
A = BD = ABCE = CDE
B = AD = CE = ABCDE
AB = D = ACE = BCDE
C = ABCD = BE = ADE
AC = BCD = ABE = DE
BC = ADC = E = ABDE
ABC = CD = AE =BDE
Ignoring three-factor and higher interactions, the following effects are estimated:
A + BD = 49
B+AD + CE = 45
AB + D = -18
C +BE = 10.5
AC + DE = 13.5
BC + E = -14.5
CD + AE =-14.5
(ii)
Suppose the following second faction is added to the first:
ade=136
e=93
ab=187
bd=153
acd=139
c=99
abce=191
bcde = 150
The design is as follows:
A
B
C
D
E
e
-
-
-
-
+
ade
+
-
-
+
+
bd
-
+
-
+
-
ab
+
+
-
-
-
c
-
-
+
-
-
acd
+
-
+
+
-
bcde
-
+
+
+
+
abce
+
+
+
-
+
The design is generated by I = ABD = BCE. Putting the two fractions together, re-arrange the runs, we have the following design:
A
B
C
D
E
e
-
-
-
-
+
ae
+
-
-
-
+
b
-
+
-
-
-
ab
+
+
-
-
-
c
-
-
+
-
-
ac
+
-
+
-
-
bce
-
+
+
-
+
abce
+
+
+
-
+
de
-
-
-
+
+
ade
+
-
-
+
+
bd
-
+
-
+
-
abd
+
+
-
+
-
cd
-
-
+
+
-
acd
+
-
+
+
-
bcde
-
+
+
+
+
abcde
+
+
+
+
+
The design is a 251 design generated by I = BCE. The scaled estimates of the effects are:
a
b
ab
c ac
bc abc d ad bd abd cd acd bcd abcd
88.5 98.5
-20
13 14.5 -16.5 -12 -16 -8.5 9.5 12 -17 -12.5 12.5 8
(iii)
Suppose the following faction is added to the first:
abc=189
ce=96
bcd=154
acde =135
abe=193
bde=152
ad=137
(1) = 98
The design of this fraction is as follows:
A
B
C
D
E
(1)
-
-
-
-
-
ad
+
-
-
+
-
bde
-
+
-
+
+
abe
+
+
-
-
+
ce
-
-
+
-
+
acde
+
-
+
+
+
bcd
-
+
+
+
-
abc
+
+
+
-
-
The design is obtained by I = ABD = BCE. Putting two fractions together:
A
B
C
D
E
(1)
-
-
-
-
-
ae
+
-
-
-
+
b
-
+
-
-
-
abe
+
+
-
-
+
ce
-
-
+
-
+
ac
+
-
+
-
-
bce
-
+
+
-
+
abc
+
+
+
-
-
de
-
-
-
+
+
ad
+
-
-
+
-
bde
-
+
-
+
+
abd
+
+
-
+
-
cd
-
-
+
+
-
acde
+
-
+
+
+
bcd - + + +
-
abcde
+
+
+
+
+
The above is a 251 generated by I = ACDE. The scaled estimates of the effects are:
a
b
ab
c
ac
bc
abc
d
ad bd abd
cd
acd
bcd
abcd
87.5
100.5
-18.5
9
12
-14
-16
-17.5
-10.5 10.5 10.5
-13
-15
15
12
A
B
C
D
E
de
-
-
-
+
+
ae
+
-
-
-
+
b
-
+
-
-
-
abd
+
+
-
+
-
cd
-
-
+
+
-
ac
+
-
+
-
-
bce
-
+
+
-
+
abcde
+
+
+
+
+