MCM 2018 A: Multi-hop HF Radio Propagation

Background: On high frequencies (HF, defined to be 3-30 mHz), radio waves can travel long distances (from one point on the earth's surface to another distant point on the earth's surface) by multiple reflections off the ionosphere and off the earth. For frequencies below the maximum usable frequency (MUF), HF radio waves from a ground source reflect off the ionosphere back to the earth, where they may reflect again back to the ionosphere, where they may reflect again back to the earth, and so on, travelling further with each successive hop. Among other factors, the characteristics of the reflecting surface determine the strength of the reflected wave and how far the signal will ultimately travel while maintaining useful signal integrity. Also, the MUF varies with the season, time of day, and solar conditions. Frequencies above the MUF are not reflected/refracted, but pass through the ionosphere into space. In this problem, the focus is particularly on reflections off the ocean surface. It has been found empirically that reflections off a turbulent ocean are attenuated more than reflections off a calm ocean. Ocean turbulence will affect the electromagnetic gradient of seawater, altering the local permittivity and permeability of the ocean, and changing the height and angle of the reflection surface. A turbulent ocean is one in which wave heights, shapes, and frequencies change rapidly, and the direction of wave travel may also change.


Part I: Develop a mathematical model for this signal reflection off the ocean. For a 100-watt HF constant-carrier signal, below the MUF, from a point source on land, determine the strength of the first reflection off a turbulent ocean and compare it with the strength of a first reflection off a calm ocean. (Note that this means that there has been one reflection of this signal off the ionosphere.) If additional reflections (2 through n) take place off calm oceans, what is the maximum number of hops the signal can take before its strength falls below a usable signal-to-noise ratio (SNR) threshold of 10 dB?

Part II: How do your findings from Part I compare with HF reflections off mountainous or rugged terrain versus smooth terrain?

Part III: A ship travelling across the ocean will use HF for communications and to receive weather and traffic reports. How does your model change to accommodate a shipboard receiver moving on a turbulent ocean? How long can the ship remain in communication using the same multi-hop path?

Part IV: Prepare a short (1 to 2 pages) synopsis of your results suitable for publication as a short note in IEEE Communications Magazine.

Your submission should consist of:

  • One-page Summary Sheet,
  • Two-page synopsis,
  • Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and synopsis.
  • Note: Reference list and any appendices do not count toward the 23-page limit and should appear after your completed solution.
MCM 2018 B: How Many Languages?

Background: There are currently about 6,900 languages spoken on Earth. About half the world's population claim one of the following ten languages (in order of most speakers) as a native language: Mandarin (incl. Standard Chinese), Spanish, English, Hindi, Arabic, Bengali, Portuguese, Russian, Punjabi, and Japanese. However, much of the world's population also speaks a second language. When considering total numbers of speakers of a particular language (native speakers plus second or third, etc. language speakers), the languages and their order change from the native language list provided. The total number of speakers of a language may increase or decrease over time because of a variety of influences to include, but not limited to, the language(s) used and/or promoted by the government in a country, the language(s) used in schools, social pressures, migration and assimilation of cultural groups, and immigration and emigration with countries that speak other languages. Moreover, in our globalized, interconnected world there are additional factors that allow languages that are geographically distant to interact. These factors include international business relations, increased global tourism, the use of electronic communication and social media, and the use of technology to assist in quick and easy language translation.

Problem: A large multinational service company, with offices in New York City in the United States and Shanghai in China, is continuing to expand to become truly international. This company is investigating opening additional international offices and desires to have the employees of each office speak both in English and one or more additional languages. The Chief Operating Officer of the company has hired your team to investigate trends of global languages and location options for new offices.

Part I:

A. Consider the influences and factors described in the background paragraph above, as well as other factors your group may identify. Based on projected trends, and some or all of these influences and factors, model the distribution of various language speakers over time.

B. Use your model to predict what will happen to the numbers of native speakers and total language speakers in the next 50 years. Do you predict that any of the languages in the current top-ten lists (either native speakers or total speakers) will be replaced by another language? Explain.

C. Given the global population and human migration patterns predicted for the next 50 years, do the geographic distributions of these languages change over this same period of time? If so, describe the change.

Part II:

A. Based on your modeling from Part I, and assuming your client company wants to open six new international offices, where might you locate these offices and what languages would be spoken in the offices? Would your recommendations be different in the short term versus the long term? Explain your choices.

B. Considering the changing nature of global communications, and in an effort to save your client company resources, might you suggest that the company open less than six international offices? Indicate what additional information you would need and describe how you would analyze this option in order to advise your client.

Part III:

Write a 1-2 page memo to the Chief Operating Officer of the service company summarizing your results and recommendations.

Note: In your analysis, ignore unpredictable or high-impact, low probability events such as asteroid collisions that would cause a catastrophic jump in evolutionary trends over time, and possibly render all languages extinct.

Your submission should consist of:

  • One-page Summary Sheet,
  • Two-page memo,
  • Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and memo.
  • Note: Reference list and any appendices do not count toward the 23-page limit and should appear after your completed solution.
MCM 2018 C: Energy Production

Background: Energy production and usage are a major portion of any economy. In the United States, many aspects of energy policy are decentralized to the state level. Additionally, the varying geographies and industries of different states affect energy usage and production. In 1970, 12 western states in the U.S. formed the Western Interstate Energy Compact (WIEC), whose mission focused on fostering cooperation between these states for the development and management of nuclear energy technologies. An interstate compact is a contractual arrangement made between two or more states in which these states agree on a specific policy issue and either adopt a set of standards or cooperate with one another on a particular regional or national matter.

Problem: Along the U.S. border with Mexico, there are four states - California (CA), Arizona (AZ), New Mexico (NM), and Texas (TX) - that wish to form a realistic new energy compact focused on increased usage of cleaner, renewable energy sources. Your team has been asked by the four governors of these states to perform data analysis and modeling to inform their development of a set of goals for their interstate energy compact.

The attached data file "ProblemCData.xlsx" provides in the first worksheet ("seseds") 50 years of data in 605 variables on each of these four states' energy production and consumption, along with some demographic and economic information. The 605 variable names used in this dataset are defined in the second worksheet ("msncodes").

Part I:

A. Using the data provided, create an energy profile for each of the four states.

B. Develop a model to characterize how the energy profile of each of the four states has evolved from 1960 - 2009. Analyze and interpret the results of your model to address the four states' usage of cleaner, renewable energy sources in a way that is easily understood by the governors and helps them to understand the similarities and difference between the four states. Include in your discussion possible influential factors of the similarities and differences (e.g. geography, industry, population, and climate).

C. Determine which of the four states appeared to have the "best" profile for use of cleaner, renewable energy in 2009. Explain your criteria and choice.

D. Based on the historical evolution of energy use in these states, and your understanding of the differences between the state profiles you established, predict the energy profile of each state, as you have defined it, for 2025 and 2050 in the absence of any policy changes by each governor's office.

Part II:

A. Based on your comparison between the four states, your criteria for "best" profile, and your predictions, determine renewable energy usage targets for 2025 and 2050 and state them as goals for this new four-state energy compact.

B. Identify and discuss at least three actions the four states might take to meet their energy compact goals.

Part III:

Prepare a one-page memo to the group of Governors summarizing the state profiles as of 2009, your predictions with regard to energy usage absent any policy changes, and your recommended goals for the energy compact to adopt.

Your submission should consist of:

  • One-page Summary Sheet,
  • One-page memo,
  • Your solution of no more than 20 pages, for a maximum of 22 pages with your summary and memo.
  • Note: Reference list and any appendices do not count toward the 22-page limit and should appear after your completed solution.
ICM 2018 D: Out of Gas and Driving on E (for electric, not empty)

For both environmental and economic reasons, there is global interest in reducing the use of fossil fuels, including gasoline for cars. Whether motivated by the environment or by the economics, consumers are starting to migrate to electric vehicles. Several countries are seeing early signs of the potential for rapid growth in the adoption of electric vehicles. In the US and other countries, the release of the more affordable all-electric Tesla Model 3 has resulted in record numbers of pre-orders and long wait lists ( To further accelerate the switch to electric vehicles, some countries, including China, have announced that they will ban gasoline and diesel cars in the coming years (

Eventually, when a ban goes into effect, there needs to be a sufficient number of vehicle charging stations in all the right places so that people can use their vehicles for their daily business, as well as make occasional long-distance trips. The migration from gasoline and diesel cars to electric vehicles, however, is not simple and can't happen overnight. In a fantasy world, we would wake up one day with every gas vehicle replaced by an electric one, and every gas station replaced with a charging station. In reality, there are limited resources, and it will take time for consumers to make the switch. In fact, the location and convenience of charging stations is critical as early adopters and eventually mainstream consumers volunteer to switch (

As nations plan this transition, they need to consider the final network of charging stations (the number of stations, where they will be located, the number of chargers at the stations, and the differences in the needs of rural areas, suburban areas, and urban areas), as well as the growth and evolution of the network of charging stations over time. For example, what should the network look like when electric vehicles represent 10% of all cars, 30% of all cars, 50% of all cars, and 90% of all cars?

As nations seek to develop policies that promote the migration towards electric vehicles, they will need to design a plan that works best for their individual country. Before they can begin, they would like your team's help in determining the final architecture of the charging network to support the full adoption of all-electric vehicles. Additionally, they would like you to identify the key factors that will be important as they plan their timeline for an eventual ban or dramatic reduction of gasoline and diesel vehicles.

To help your team manage the scope of this problem, we ask that you focus only on personal passenger vehicles (i.e. cars, vans, and light trucks used for passengers). At the end of your report, you may briefly comment on the relevance of your findings and conclusions on commercial vehicles to include heavy trucks and busses.

Your tasks are the following:

Task 1: Explore the current and growing network of Tesla charging stations in the United States. Tesla currently offers two types of charging stations: (1) destination charging designed for charging for several hours at a time or even overnight (; and (2) supercharging designed for longer road trips to provide up to 170 miles of range in as little as 30 minutes of charging ( These stations are in addition to at-home charging used by many Tesla owners who have a personal garage or a driveway with power. Is Tesla on track to allow a complete switch to all-electric in the US? If everyone switched to all-electric personal passenger vehicles in the US, how many charging stations would be needed, and how should they be distributed between urban, suburban, and rural areas?

Task 2: Select one of the following nations (South Korea, Ireland, or Uruguay).

  • 2a. Determine the optimal number, placement, and distribution of charging stations if your country could migrate all their personal passenger vehicles to all-electric vehicles instantaneously (no transition time required). What are the key factors that shaped the development of your plan?
  • 2b. While these countries have already started installing chargers, you get to start with a clean slate. Present a proposal for evolving the charging network of your chosen country from zero chargers to a full electric-vehicle system. How do you propose the country invest in chargers? Should the country build all city-based chargers first, or all rural chargers, or a mix of both? Will you build the chargers first and hope people buy the cars, or will you build chargers in response to car purchases? What are the key factors that shaped your proposed charging station plan?
  • 2c. Based on your growth plan, what is the timeline you propose for the full evolution to electric vehicles in your country? To get started, you may wish to consider how long it will take for there to be 10% electric vehicles, 30% electric vehicles, 50% electric vehicles, or 100% electric vehicles on your selected country's roads. What are the key factors that shaped your proposed growth plan timeline?

Task 3: Now consider countries with very different geographies, population density distributions, and wealth distributions, such as Australia, China, Indonesia, Saudi Arabia, and Singapore. Would your proposed plan for growing and evolving the network of chargers still apply to each of these countries? What are the key factors that trigger the selection of different approaches to growing the network? Discuss the feasibility of creating a classification system that would help a nation determine the general growth model they should follow in order for them to successfully migrate away from gasoline and diesel vehicles to all electric cars.

Task 4: The technological world continues to change and is impacting transportation options such as car-share and ride-share services, self-driving cars, rapid battery-swap stations for electric cars, and even flying cars and a Hyperloop. Comment on how these technologies might impact your analyses of the increasing use of electric vehicles.

Task 5: Prepare a one-page handout written for the leaders of a wide range of countries who are attending an international energy summit. The handout should identify the key factors the leaders should consider as they return to their home country to develop a national plan to migrate personal transportation towards all-electric cars and set a gas vehicle-ban date.

Your submission should consist of:

  • One-page Summary Sheet,
  • One-page handout,
  • Your solution of no more than 20 pages, for a maximum of 22 pages with your summary and handout.
  • Note: Reference list and any appendices do not count toward the 22-page limit and should appear after your completed solution.
ICM 2018 E: How does climate change influence regional instability?

The effects of Climate Change, to include increased droughts, shrinking glaciers, changing animal and plant ranges, and sea level rise, are already being realized and vary from region to region. The Intergovernmental Panel on Climate Change suggests that the net damage costs of climate change are likely to be significant. Many of these effects will alter the way humans live, and may have the potential to cause the weakening and breakdown of social and governmental structures. Consequently, destabilized governments could result in fragile states.

A fragile state is one where the state government is not able to, or chooses not to, provide the basic essentials to its people. For the purpose of this problem "state" refers to a sovereign state or country. Being a fragile state increases the vulnerability of a country's population to the impact of such climate shocks as natural disasters, decreasing arable land, unpredictable weather, and increasing temperatures. Non-sustainable environmental practices, migration, and resource shortages, which are common in developing states, may further aggravate states with weak governance (Schwartz and Randall, 2003; Theisen, Gleditsch, and Buhaug, 2013). Arguably, drought in both Syria and Yemen further exacerbated already fragile states. Environmental stress alone does not necessarily trigger violent conflict, but evidence suggests that it enables violent conflict when it combines with weak governance and social fragmentation. This confluence can enhance a spiral of violence, typically along latent ethnic and political divisions (Krakowka, Heimel, and Galgano 2012).

Your tasks are the following:

Task 1: Develop a model that determines a country's fragility and simultaneously measures the impact of climate change. Your model should identify when a state is fragile, vulnerable, or stable. It should also identify how climate change increases fragility through direct means or indirectly as it influences other factors and indicators.

Task 2: Select one of the top 10 most fragile states as determined by the Fragile State Index ( and determine how climate change may have increased fragility of that country. Use your model to show in what way(s) the state may be less fragile without these effects.

Task 3: Use your model on another state not in the top 10 list to measure its fragility, and see in what way and when climate change may push it to become more fragile. Identify any definitive indicators. How do you define a tipping point and predict when a country may reach it?

Task 4: Use your model to show which state driven interventions could mitigate the risk of climate change and prevent a country from becoming a fragile state. Explain the effect of human intervention and predict the total cost of intervention for this country.

Task 5: Will your model work on smaller "states" (such as cities) or larger "states" (such as continents)? If not, how would you modify your model?

Your submission should consist of:

  • One-page Summary Sheet,
  • Your solution of no more than 20 pages, for a maximum of 21 pages with your summary.
  • Note: Reference list and any appendices do not count toward the 21-page limit and should appear after your completed solution.
ICM 2018 F: Cost of Privacy

Pervasiveness of, and reliance on, electronic communication and social media have become widespread. One result is that some people seem willing to share private information (PI) about their personal interactions, relationships, purchases, beliefs, health, and movements, while others hold their privacy in these areas as very important and valuable. There are also significant differences in privacy choices across various domains. For example, some people are quick to give away the protection of their purchasing information for a quick price reduction, but at the same time are unlikely to share information about their disease conditions or health risks. Similarly, some populations or subgroups may be less willing to give up particular types of personal information if they perceive it posing a personal or community risk. The risk may involve loss of safety, money, valuable items, intellectual property (IP), or the person's electronic identity. Other risks include professional embarrassment, loss of a position or job, social loss (friendships), social stigmatization, or marginalization. While a government employee who has voiced political dissent against the government might be willing to pay to keep their social media data private, a young college student may feel no pressure to restrict their posting of political opinion or social information. It seems that individual choices on PI protection and internet and system security in cyber space can create risks and rewards in elements of freedom, privacy, convenience, social standing, financial benefits, and medical treatment.

Is private information (PI) similar to private personal property (PP) and intellectual property (IP)? Once lawfully obtained, can PI be sold or given to others who then have the right or ownership of the information? As detailed information and meta-data of human activity becomes more and more valuable to society, specifically in the areas of medical research, disease spread, disaster relief, businesses (e.g. marketing, insurance, and income), records of personal behaviors, statements of beliefs, and physical movement, these data and detailed information may become a valuable and quantifiable commodity. Trading in one's own private data comes with a set of risks and benefits that may differ by the domain of information (e.g. purchasing, social media, medical) and by subgroup (e.g. citizenship, professional profile, age).

Can we quantify the cost of privacy of electronic communications and transactions across society? That is, what is the monetary value of keeping PI protected, or how much would it cost for others to have or use PI? Should the government regulate this information or is it better left to privacy industry or the individual? Are these information and privacy issues merely personal decisions that individuals must evaluate to make their own choices and provide their own protection?

There are several things to consider when evaluating the cost of privacy. First, is data sharing a

public good? For example, Center for Disease Control may use the data to trace the spread of disease in order to prevent further outbreak. Other examples include managing at risk populations, such as children under 16, people at risk of suicide, and the elderly. Moreover, consider groups of extremists who seek to hide their activities. Should their data be trackable by the government for national security concerns? Consider a person's browser, phone system, and internet feed with their personalized advertisements; how much is this customization worth? Overall, when evaluating cost of privacy we need to consider all of these tradeoffs. What is the potential gain from keeping data private and what is lost by doing so?

As a policy analysis team for a national decision maker, your team's tasks are:

Task 1: Develop a price point for protecting one's privacy and PI in various applications. To evaluate this, you may want to categorize individuals into subgroups with reasonably similar levels of risk or into related domains of the data. What are the set of parameters and measures that would need to be considered to accurately model risk to account for both 1) characteristics of the individuals, and 2) characteristics of the specific domain of information?

Task 2: Given the set of parameters and measures from Task 1, model for cost of privacy across at least three domains (social media, financial transactions, and health/medical records). In your base model consider how the tradeoffs and risks of keeping data protected affect your model. You may consider giving some of the tradeoffs and risks more weight than others as well as stratifying weights by subgroup or category. Consider how different basic elements of the data (e.g. name, date of birth, gender, social security or citizenship number) contribute to your model. Are some of these elements worth more than others? For example, what is the value of a name alone compared with value of a name with the person's picture attached? Your model should design a pricing structure for PI.

Task 3: Not long ago, people had no knowledge about which agencies had purchased their PI, how much their PI was worth, or how PI was being used. New proposals are being put forth which would turn PI into a commodity. With the pricing structure you generated in Task 2, establish a pricing system for individuals, groups, and entire nations. With data becoming a commodity subject to market fluctuations, is it appropriate to consider forces of supply and demand for PI? Assuming people have control to sell to their own data, how does this change the model?

Task 4: What are the assumptions and constraints of your model? Assumptions and constraints should address issues such as government regulations (e.g. price regulations, specific data protections such as certain records that may not be subject to the economic system) and cultural and political issues. Based on your model and the political and cultural issues, consider if information privacy should be made a basic human right when thinking about policy recommendations. Consider introducing a dynamic element to your model by introducing the variations over time in human decision-making given changing personal beliefs about the worth of their own data (e.g. personal data such as name, address, picture), transaction data (e.g. on-line purchases, search history), and social media data (e.g. posts, pictures).

Task 5: Are there generational differences in perceptions of the risk-to-benefit ratio of PI and data privacy? As generations age, how does this change the model? How is PI different or similar to PP and IP?

Task 6: What are the ways to account for the fact that human data is highly linked and often each individual's behaviors are highly correlated with others? Data on one person can provide information about others whom they are socially, professionally, economically, or demographically connected. Therefore, personal decisions to share one's own data can affect countless others. Are there good ways to capture the network effects of data sharing? Does that effect the price system for individuals, subgroups, and entire communities and nations? If communities have shared privacy risks, is it the responsibility of the communities to protect citizens' PI?

Task 7: Consider the effects of a massive data breach where millions of people's PI are stolen and sold on the dark web, sold as part of an identity theft ring, or used as ransom. How does such a PI loss or cascade event impact your model? Now that you have a pricing system that quantifies the value of data per individual or loss type, are agencies that are to blame for the data breach responsible to pay individuals directly for misuse or loss of PI?

Task 8: Write a two-page policy memo to the decision maker on the utility, results, and recommendations based your policy modeling on this issue. Be sure to specify what types of PI are included in your recommendations.

Your submission should consist of:

  • One-page Summary Sheet,
  • Two-page memo,
  • Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and memo.
  • Note: Reference list and any appendices do not count toward the 23-page limit and should appear after your completed solution.