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Team Control Number
66500
Problem Chosen
A
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2017 MCM Summary Sheet
Joint Force in Managing Zambezi River
Abstract
Owing to the report put forward by the Institution of Risk Management of South Africa, the
Kariba dam badly needs maintenance. The three options Zambezi River Authority provided might
address the problem. Our modeling group make assessments to the three options and provides
feasible plans to replace the former Kariba dam with several smaller dams. The requirements are
satisfied in this paper.
With regard to requirement 1, we list factors of costs and benefits in advance. Then, we
categorize potential cost into two parts, direct cost and indirect cost. With relative profiles, the two
categories are quantized. However, the benefits of the three options can hardly be quantified. So we
take advantage of fuzzy synthetic evaluation method and work out the relative levels of benefits in
the three options. Finally, the return on investment (ROI) is calculated. Based on that, we can safely
draw conclusion that option 1 is more economically efficient in a short period. But in the long term,
option 3 appears to have more potential profits.
When it comes to requirement 2, we establish the water balance equation on both reservoirs
and channels at the basis of analysis on water transference. Afterwards, we divide the water
management capacities into 3 categorizes, the ability against flood, the ability for water supply and
ability for electricity generation. Based on analysis to water management, the multi-dam system of
versatile functions is proposed innovatively. Considering the actual factors in selecting dam sites,
we screen out 29 possible locations. After then, the number and placement of the new dams is
determined using optimization model. In order to lower the cost, we set our goal as the minimum
number of dams. Along with the restraints of water balance equation and greater water management
capacity, we complete optimization. As is shown in our results, 14 dams should be built as
alternative to Kariba dam. Finally, error analysis is attached to our model.
For the sake that the new multi-dam system can function well under various circumstance, we
set our system in three conditions, normal water circles, long-term drought and outburst flood.
Particle swarm optimization (PSO) is adopted repeatedly to optimize the control of water discharge.
Compare the result to the actual adjustments made by Kariba dam, we can conclude that the new
multi-dam system can provide greater level of protection and water management options. Apart
form this, we make thorough evaluations towards optimization scheme and distil general strategy in
each condition. At last, we apply sensitivity analysis to conditions under long-term drought and
outburst flood. The regulation limits are given under extreme conditions.
Last but not least, we take extreme disasters into consideration and use Monte Carlo method to
make assessments. The result suggests the new system have a better resistance against disasters.
Also, we list the overall strengths and weaknesses of our model as well as the further work.
Keywords: return on investment, water balance equation, particle swarm optimization,
Monte Carlo method
