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PROBLEM A:
Managing
The Zambezi River
The Kariba
Dam on the Zambezi River is one of the larger dams
in Africa. Its construction
was
controversial, and a 2015 report by the Institute
of Risk Management of South Africa
included a warning that the dam is in
dire need of maintenance. A number of options are
available to the Zambezi River
Authority (ZRA) that might address the situation.
Three
options in particular are of
interest to ZRA:
(Option 1) Repairing
the existing Kariba Dam, (Option 2) Rebuilding the
existing Kariba
Dam, or (Option 3)
Removing the Kariba Dam and replacing it with a
series of ten to twenty
smaller dams
along the Zambezi River.
There are two
main requirements for this problem:
Requirement 1 ZRA management requires a
brief assessment of the three options listed,
with sufficient detail to provide an
overview of potential costs and benefits
associated with
each option. This
requirement should not exceed two pages in length,
and must be
provided in addition to
your main report.
Requirement 2 Provide
a detailed analysis of Option (3) - removing the
Kariba Dam and
replacing it with a
series of ten to twenty smaller dams along the
Zambezi river. This new
system of dams
should have the same overall water management
capabilities as the
existing Kariba Dam
while providing the same or greater levels of
protection and water
management options
for Lake Kariba that are in place with the
existing dam. Your analysis
must
support a recommendation as to the number and
placement of the new dams along
the
Zambezi River.
In your report for
Requirement 2, you should include a strategy for
modulating the water
flow through your
new multiple dam system that provides a reasonable
balance between
safety and costs. In
addition to addressing known or predicted normal
water cycles, your
strategy should
provide guidance to the ZRA managers that explains
and justifies the
actions that should
be taken to properly handle emergency water flow
situations (i.e.
flooding and/or
prolonged low water conditions). Your strategy
should provide specific
guidance for
extreme water flows ranging from maximum expected
discharges to minimum
expected
discharges. Finally, your recommended strategy
should include information
addressing
any restrictions regarding the locations and
lengths of time that different areas
of
the Zambezi River should be exposed to the most
detrimental effects of the extreme
conditions.
Your MCM
submission should consist of three elements: a
standard 1 page MCM Summary
Sheet, a
1-2 page brief assessment report (Requirement 1),
and your main MCM solution
(Requirement
2) not to exceed 20 pages for a maximum submission
of 23 pages. Note: Any
appendices or
reference pages you include will not count towards
the 23 page limit.
A
题中文翻译：
问题
A
：管理赞比西河
赞比西河上的卡里巴水坝是非洲较大的水坝之一。
它的建设是有争议的，
南非风险管理研究
所的
2015
年报告包括一个警告，大坝是急需维护。赞比西河管理局（
ZRA
）可提供若干选
择，以解决这一问题。
ZRA
特别感兴趣的有三个选项：
<
/p>
（选项
1
）修复现有的
< br>Kariba
水坝（选项
2
）重
建现有的
Kariba
水坝，或（选项
3
）拆除
Kariba
水坝，并更换为
沿赞比西河的一系列十到二十个较小的水坝。
这个问题有两个主要要求：
要求
1 ZRA
管理要求对所列出的三
个选项进行简要评估，并提供足够的详细信息，以提供
与每个选项相关的潜在成本和收益
的概述。
此要求的长度不应超过两页，
除了主要报告之外，
还必须提供此页面。
要求
2
对选项（
3
）进行详细分析
-
删除
K
ariba
水坝，并用赞比西河沿岸一系列十至二十
个较小的水
坝替代。这个新的水坝系统应该与现有的
Kariba
水坝具有
相同的整体水管理能
力，
同时为现有的水坝提供与卡里巴湖相同
或更高水平的保护和水管理选择。
您的分析必须
支持关于沿赞比
西河新坝的数量和位置的建议。
在您的要求
< br>2
报告中，
您应该包括一个策略，
用于调节通过您的新多坝系统的水流，
从而在
安全和成本之间
提供合理的平衡。除了解决已知或预测的正常水循环，您的战略应为
ZRA
经理提供指导，解释和证明应当采取的行动，以正确处理应急水流情况（即洪水和
/
或长期
低水位状况）
。
您的策略应为从最大预期排放到最小预期排放的极端水流提供具体指导。
最
后，
您的建议战略应包括解决对赞比西河不同地区暴露于极端
条件最有害影响的位置和时间
长度的任何限制的信息。
您的
MCM
提交应包括三个要素：标准的
1
页
MCM
摘要表
，
1-2
页简要评估报告（要求
1
）
和您的主要
MCM
解决方案（要求
2
）不超过
20
页，最多提交
23
页面。注意：您加入的任
何附录或参考页面不会计入
23
页的上
限。
PROBLEM B:
Merge After Toll
Multi-lane divided
limited-
access toll highways use “ramp
tolls” and “barrier tolls” to collect
tolls from motorists. A ramp toll is a
collection mechanism at an entrance or exit ramp
to the
highway and these do not concern
us here. A barrier toll is a row of tollbooths
placed across
the highway,
perpendicular to the direction of traffic flow.
There are usually (always) more
tollbooths than there are incoming
lanes of traffic (see former 2005 MCM Problem B).
So
when exiting the tollbooths in a
barrier toll, vehicles mus
t “fan in”
from the larger number
of tollbooth
egress lanes to the smaller number of regular
travel lanes. A toll plaza is the
area
of the highway needed to facilitate the barrier
toll, consisting of the fan-out area
before the barrier toll, the toll
barrier itself, and the fan-in area after the toll
barrier. For
example, a three-lane
highway (one direction) may use 8 tollbooths in a
barrier toll. After
paying toll, the
vehicles continue on their journey on a highway
having the same number of
lanes as had
entered the toll plaza (three, in this example).
Consider a toll highway having L lanes
of travel in each direction and a barrier toll
containing
B tollbooths (B > L) in each
direction. Determine the shape, size, and merging
pattern of
the area following the toll
barrier in which vehicles fan in from B tollbooth
egress lanes
down to L lanes of
traffic. Important considerations to incorporate
in your model include
accident
prevention, throughput (number of vehicles per
hour passing the point where the
end of
the plaza joins the L outgoing traffic lanes), and
cost (land and road construction are
expensive). In particular, this problem
does not ask for merely a performance analysis of
any particular toll plaza design that
may already be implemented. The point is to
determine
if there are better solutions
(shape, size, and merging pattern) than any in
common use.
Determine the performance
of your solution in light and heavy traffic. How
does your
solution change as more
autonomous (self-driving) vehicles are added to
the traffic mix?
How is your solution
affected by the proportions of conventional
(human-staffed) tollbooths,
exact-
change (automated) tollbooths, and electronic toll
collection booths (such as
electronic
toll collection via a transponder in the vehicle)?
Your MCM submission should consist of a
1 page Summary Sheet, a 1-2 page letter to the
New Jersey Turnpike Authority, and your
solution (not to exceed 20 pages) for a maximum
of 23 pages. Note: The appendix and
references do not count toward the 23 page limit.
B
题中文翻译：
问题
B
：收费后合并
高速路的收费站会通过
匝道收费
< br>
和
过卡收费
两种方式来收取驾驶员的高速费。匣道收费
是一种在入口和
出口的回道处设立的收费站，
但是今天这个不在我们的讨论范围之列。
< br>过卡
收费是一排垂直高速路行驶方向设立的的许多收费窗口。
而这些收费窗口通常都会比车道条
数要多
(
详情参见
2005
年
MCM
的
B
题
)
。因此，当汽车驶出收费站之后，车流必须从较宽
的收费站出口呈扇
形快速并入车道较少的常规机动车道。
收费广场是为改善过卡之后的拥堵
状况建立的，
包括收费站之前多车道区域，
收费站本身
以及经过收费站之后的扇入区域。
举
个例子，
< br>一条单向的三车道高速路需要
8
个收费窗口，
在支付过桥费后，
驾驶员可以继续保
持与自己进收
费广场之前的相同数量的车道（在该示例中为三个）的高速公路上继续行驶。
试考虑一个收费高速公路上两个方向都有
L
条车
道，每个方向上有
B
个收费站
(B>L
),
请确
定你设计的收费区域的形状，大小以及当汽车从驶出
B
时如何将车道进行合并至
L
条车道。
在你的设计中请注明一些重要事项如事故预防，
吞吐量
(
即每小时有多少车辆从收费广场驶
出，驶入
L
条车道。
)
成本
(
土地和公路建设的费用很昂贵<
/p>
)
，重点在于并非只是对现有的收
费广
场进行性能分析，请试着探索是否有比现今采用的更好的收费解决方案
(
包括形状，大
小以及收费方式
)
。
请确定你的解决方案在小车流量和大车流量下的性能表现
。
随着更多的私家
(
自驾
)
车进入其
中，你的解决方案会有什么改变昵
?
你的解决方案会如何影响常规收费站
(
需要人员进行收
费
)
，
不找零
(
自动化的
)
收费站以及电于收费站的比例
(
< br>比如通过车内的发射器应答器来收取
费用
) ?
您的
MCM
提交应包括
1
页摘要表，
1-2
页给新泽西州收
费公路管理局的信件，以及您的解
决方案（不超过
20
页），最多
23
页。注意：附录和参考文献不计
入
23
页的限制。
PROBLEM
C:
“
Cooperate and
navigate
”
Traffic
capacity is limited in many regions of the United
States due to the number of lanes
of
roads.
For example, in the Greater
Seattle area drivers experience long delays during
peak traffic
hours
because
the volume of traffic exceeds the designed
capacity of the road networks. This is
particularly
pronounced on
Interstates 5, 90, and 405, as well as State Route
520, the roads of
particular interest
for this problem.
Self-
driving, cooperating cars have been proposed as a
solution to increase capacity of
highways
without increasing
number of lanes or roads. The behavior of these
cars interacting with the
existing
traffic flow and each other is not well
understood at this point.
The Governor
of the state of Washington has asked for analysis
of the effects of allowing
self-
driving,
cooperating cars on the roads
listed above in Thurston, Pierce, King, and
Snohomish
counties. (See
the
provided map and Excel spreadsheet). In
particular, how do the effects change as the
percentage of self-driving cars
increases from 10% to 50% to 90%? Do equilibria
exist? Is
there a
tipping
point where performance changes markedly? Under
what conditions, if any, should
lanes
be
dedicated to these cars? Does your
analysis of your model suggest any other policy
changes?
Your answer should
include a model of the effects on traffic flow of
the number of lanes,
peak and/or
average traffic volume, and percentage
of vehicles using self-driving, cooperating
systems.
Your
model should
address cooperation between self-driving cars as
well as the interaction
between
selfdriving
and non-self-driving
vehicles. Your model should then be applied to the
data for the roads
of
interest, provided in the attached
Excel spreadsheet.
Your MCM submission
should consist of a 1 page Summary Sheet, a 1-2
page letter to the
Governor’s office,
and your solution (not to exceed 20 pages) for a
maximum of 23 pages.
Note: The
appendix and references do not count
toward the 23 page limit.
Some useful
background information:
? On average,
8% of the daily traffic volume occurs during peak
travel hours.
? The nominal
speed limit for all these roads is 60 miles per
hour.
? Milepost
s
are numbered from south to north, and west to
east.
? Lane widths are the standard 12
feet.
? Highway 90 is
classified as a state route until it intersects
Interstate 5.
? In case of
any conflict between the data provided in this
problem and any other so
urce,
use the
data provided in
this problem.
Definitions:
milepost: A marker on the road that
measures distance in miles from either the start
of the
route or a
state
boundary.
average daily traffic: The
average number of cars per day driving on the
road.
interstate: A limited access
highway, part of a national system.
state route: A state highway that may
or may not be limited access.
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