这个作业是统计计算航空公司座位最佳销售策略
ENGSCI / STATS 255 SC Assignment 3

1.空中奥特罗阿舰队人数(25分)
Aotearoa航空公司是一家航空公司,受到新西兰航空公司的重创。
大流行,其航班座位的需求大大减少。运筹学团队已经
负责通过减少机队规模来节省成本。正在考虑三个决定:
D1:维持现有机队(每年提供2,250,000个席位);
D2:适度减少(每年提供1,250,000个席位);
D3:大幅减少(每年提供625,000个席位)。
据估计,机队规模的适度减少将使运营成本减少3,000万美元
每年大幅度减少费用,每年将节省5,000万美元。减少机队
将于2021年初完成。
2021年对空中Aotearoa航班的需求尚不确定,并将取决于许多相关因素
新西兰正在持续应对大流行。运营研究团队已建模
三种情况:
S1:需求严重减少;
S2:适度减少需求;
S3:正常需求。
根据需求,Aotearoa航空公司将设定价格,以便售出足够的机票以维持
平均80%的座位使用率。下表显示了每张机票所需的平均价格
实现这一目标。
机队规模决定
D1 D2 D3
S1 $ 30 $ 40 $ 60
S2 $ 50 $ 80 $ 100
S3 $ 80 $ 100 $ 150
(a)仅考虑门票销售的收益(基于门票的价格和数量)
并通过减少机队规模来节省年度成本,针对这种情况构建回报矩阵,
行是决策,列是自然状态。 (你应该写
您的收益(百万美元)。)
(b)如果航空Aotearoa乐观,最好的决定是什么?解释为什么。
(c)如果航空Aotearoa悲观,最好的决定是什么?解释为什么。
(d)如果Aotearoa航空公司希望最大程度地减少自己的最大遗憾,那是最佳决定?显示所有
加工。
假设根据Aotearoa航空公司的初步分析,估计有0.3
需求将严重减少的概率,需求将适度降低的0.5
降低,并且需求正常的概率为0.2。
(e)针对这种情况绘制并标记决策树,并计算最佳决策,假定
空气Aotearoa是风险中性的。
(f)计算完美信息的期望值。显示所有工作。
2
The Air Aotearoa’s operations research team approaches an epidemiologist to seek advice about the
persistence of the pandemic into 2021. The epidemiologist believes that there’s a probability of 0.2
that the pandemic have a significant impact in 2021, and 0.8 probability that it will have a minor
impact; moreover, the (conditional) probability distributions for the three demand scenarios are given
in the table below.
Pandemic Impact
significant minor
S1 0.800 0.175
S2 0.200 0.575
S3 0.000 0.250
(g) Assuming risk-neutrality, how much would Air Aotearoa be willing to pay to know whether the
impact of the pandemic in 2021 will be significant or minor, prior to making a decision about
reducing the fleet size?
Suppose that Air Aotearoa is risk-averse, with utility function: U(π) = √3 π − 70, where π is the
payoff in $millions.
(h) If making the investment decision, without the additional advise from the epidemiologist, compute Air Aotearoa’s expected utility for each decision on fleet size. Which decision should Air
Aotearoa choose, and why?
(i) What is the CEV associated with the decision determined in (h)?
3
2. New Zealand Electricity Sector (25 marks)
The New Zealand electricity sector comprises a multi-nodal market, with generators, retailers, transmission and distribution. In this question we will be looking at the generation of power in 2018.
Generation data (in kWh) is collected on a half-hourly basis from 64 generation sites across New
Zealand. We wish to use this data to investigate how different generation technologies contribute to
New Zealand’s electrical energy mix.
For this question you need to first install RStudio (or use rstudio.cloud), and download generation.csv,
plants.csv and regions.csv from Canvas. Remember to first load the tidyverse library, and then
import generation.csv and plants.csv into R.
(a) Use the match function to create Fuel, Region and Emissions (in kg CO2e / kWh) attributes
in the generation data set, by matching the nodal information with the plants data set.
Hint: for Fuel you will need to complete this command:
> generation$Fuel=as.factor(plants$Fuel[match( , )])
(b) Filter the data in the generation data set to create a new data set called windgen containing
only data about wind generators.
(c) Create a pairs plot that compares wind generation in different trading periods each day. Since
48 half-hour trading periods are too many to show on a pairs plot, select the trading periods 1,
3, 5, 7, 9, 11 to include in your plot. Comment on any observations.
(d) Use the gather function to reshape the generation data set so that it has a single generation
output attribute kWh for all trading periods, you should set the key to be TP).
Hint: you can use the starts with( ) function, instead of listing all columns to ‘gather’.
(e) Use the group by() and summarise( , ( ,na.rm=TRUE)) functions to display the total
generation (in kWh) by Fuel type.


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