Our aim was to minimize the carbon footprint produced when Holy Cross hosts a summit. The emissions we want to minimize are the ones that produced the transit of all the visiting professors. Because all of the professors all travel here individually the total miles traveled by all vehicles is considerably higher, thus increasing the total emissions produced. The plan that we propose is to send one van from Holy Cross to loop through all nearby colleges and pick up all of the professors so not every professor is taking their own car. We used our method to simulate a summit where Holy Cross hosts professors from their most common visitors in the state in the past 5 years: Babson College, Boston University, Bentley, University of Massachusetts Boston, and Boston College.

 

     This hopefully will minimize the total emissions. The challenge of this plan can be aided or solved by some mathematical modeling, more specifically combinatorial graph theory. We began by looking at the optimal vehicle to look at the vehicle’s capacity (how many passengers it can hold) as well as the emissions it produces per mile. After we found the optimal vehicle to carry the professors for our model, we applied certain facets of Hamilton cycles to minimize the distance traveled in the route that picks up the professors and takes them to Holy Cross.

 

     This brings us to the next problem, the traveling salesperson problem, which looks for a way to reach every vertex on the graph (or every stop on the trip) and go back to the original point of departure in the most efficient manner possible. Because this problem does not have a model that solves every scenario, an approximation is necessary. This is due to how time-consuming it would be to sort through every Hamilton cycle possible.

 

     After we find the optimal route, we then must devise a digraph, which is a mathematical model that will allow us to compare the seemingly best routes with the emissions produced if every professor travels on their own. That way, through our weighted digraph, we can account for all of the things that may affect the emissions. This gave us the most accurate representation of the emissions that each route consumes. With this method, we can compare all possible ways to travel to Holy Cross to find the most environmentally friendly way to get there.

 

     To summarize, this essay will utilize, the emissions that each vehicle produces per mile, Hamilton cycles, traveling salesperson problems, approximations to traveling salesperson problems, and finally digraphs, to achieve our goal. We used this method to simulate a summit where Holy Cross hosts professors from their most common visitors in the state in the past 5 years: Babson College, Boston University, Bentley, University of Massachusetts Boston, and Boston College.