HiMCM Modeling Challenges: Dandelion Spread, E‑Bus Charging, Olympic Medal Planning

2023 HiMCM / MidMCM Problem Set

Problem A: Dandelion – Friend, Foe, or Neither?

1.1 Background

Dandelion (Taraxacum officinale) is a plant native to Eurasia, now found worldwide. It is recognizable by its bright yellow flowers and the fluffy seed head, each seed equipped with a parachute‑like pappus that aids wind dispersal.

1.2 Questions

Create a mathematical model to predict dandelion spread over 1, 2, 3, 6, and 12 months on a one‑hectare plot, accounting for different climate conditions (temperate, arid, tropical).

Develop a model to determine an “impact factor” for invasive species, integrating plant traits and environmental damage, and compute this factor for dandelion and two other invasive species.

Problem B: Electric Bus Charging

2.1 Background

Electric buses are rapidly expanding in cities worldwide, driven by environmental concerns, falling battery costs, and policy incentives such as the US Infrastructure Law allocating $1.7 billion for e‑bus projects. Challenges include high upfront costs, charging infrastructure, long charging times, and range limits.

2.2 Questions

Build a model to assess the ecological consequences of transitioning to an all‑electric bus fleet.

Apply the model to a metropolitan area with at least 500,000 residents that currently lacks a fully electric fleet.

Develop a financial model for the conversion, considering external funding covering up to 50 % of costs.

Use the financial model to create a ten‑year roadmap for achieving a fully electric fleet by 2033.

Extend the analysis to two additional metropolitan areas.

Draft a one‑page recommendation letter to a transit official.

Problem C: Preparing Olympic Award Ceremonies

3.1 Background

The 2024 Paris Olympics will feature 40 sports, 329 medal events, and 37 venues. The International Olympic Committee needs models to determine the optimal number of medals and flags to order, avoiding both shortages and waste.

3.2 Questions

Choose one of three venues, schedule its award ceremonies, and model the required quantities of gold, silver, and bronze medals.

Model the required flags for that venue, then apply the models to the other two venues.

Combine the results to estimate medal and flag needs for all three venues and discuss scalability to all 37 venues and future Games.

Write a brief letter to the IOC explaining the models and their benefits.