JNB535 Business Analytics and Operations Research

UTAS学生证号，如下表所示：

0 1 2 3 4 5 6 7 8 9

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75

a）定义您选择的连续随机变量，包括其名称，单位

b）定义一个与变量范围相对应的误差等级Δ

c）用文字写出完整的对话框以评估不确定性区间

i）对话的初始阶段
ii）启发下界
iii）启发上限
iv）确定所选α-分位数和

[1 + 0.5 +（3 + 2 + 2 + 0.5）= 9分]

FinancialG Ltd.有三种可供选择的投资选择– a1，a2，a3。的

θ1θ2θ3
a1 \$ 100 000 \$ 25 000 \$ 0
a2 \$ 75 000 \$ 50 000 \$ 25 000
a3 \$ 50 000 \$ 50 000 \$ 50 000
a）如果未来经济条件的概率为P（θ1）= 45％，
P（θ2）= 20％，P（θ3）= 35％，确定并激发最佳选择

FinancialG Ltd.的两名财务经理被赋予选择最佳职位的任务

\$ 75000 [0.77; 0.83] [0.58; 0.62]
\$ 50000 [0.58; 0.62] [0.28; 0.32]
\$ 25000 [0.27; 0.33] [0.13; 0.17]

θ1[0.32； 0.42] [0.48; 0.62]
θ2[0.22； 0.28] [0.14; 0.20]
θ3[0.27； 0.39] [0.29; 0.34]

b）应用预期效用原理，对效用进行点估计

c）假设每个不确定区间的概率和效用值为

“次优”选项优先于“最差”选项）。
d）讨论并激发在推荐排名中观察到的差异

e）讨论经理A和经理B在考虑中的其他因素
b部分中的排名与a部分中的决定相比。
[2 + 3 + 7 + 3 + 3 = 18分]

Question 3
Gadgets&Co sells refrigerators. Any refrigerator that malfunctions within 3 years
of purchase is replaced with a new one for free. Of all refrigerators, 3% fail during
their first year of operation; 5% of the one-year-old refrigerators fail within their
second year of operation, and 7% of the two-year-old refrigerators fail within their
3
rd year of operation.
a) Estimate analytically the fraction of all refrigerators that will have to be
replaced under the 3-year warranty scheme.
b) Construct and execute a simulation model (with 120 pseudo-realities) to
estimate the fraction of all refrigerators that will have to be replaced under
the 3-year warranty scheme. Explain and motivate your approach.
Continued …
Distance and Attending 1-2020 JNB535 Business Analytics and Operations Research

c) Assume that it costs \$650 to replace a refrigerator, and Gadgets&Co sells
15,000 refrigerators per year. Estimate analytically the replacement cost
savings per year that Gadgets&Co would achieve if they decreased their
warranty period to 2 years. Explain and motivate your approach and results.
d) Use the results from part b to find a simulation-based estimate of the
replacement cost savings per year that Gadgets&Co would achieve if they
decreased their warranty period to 2 years. Explain and motivate your
approach.
[3+4+3+3=13 marks]
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