I came across a very interesting but challenging case on road construction in New York. Since I don't know the official solution, it would be great if you can comment on my approach.
Our client is a construction company in the USA. The city wants to rebuild all streets in New York and asked our client about the total cost of such a plan.
To me, this is a traditional market sizing case for which we can use an issue tree.
To calculate the total cost of the plan, I thought of 3 different branches: road surface (in m^3), variable cost (per m^3) and fixed cost.
Branch 1: Road Surface
For simplicity we can think of New York as a rectangle. Since we don't know the ratio of road surface to the total NY surface (interviewer information), we need to dive a little deeper: since we we deal with a block scheme in the city, we can assume that we have streets that run from the North to the South and streets that run from the West to East. Since there are houses, parks etc. between the streets, we would have to calculate the number of streets in each direction. Once we have this number, we could calculate the road surface as follows:
(a) Number of North-South Streets * Length of the City * Width of the Street (PLUS)
(b) Number of West-East Streets * Width of the City * Width of the Street (MINUS)
(c) Road surface of crossings (we counted them twice). How would you do that?
Branch 2: Variable Cost
Now that we have the road surface, we need to multiply it with the associated variable costs, such as:
The resulting figure would give us the total variable cost for the construction.
Branch 3: Fixed Cost
In a last step we would have to add the fixed cost for the road construction such as:
(b) Road closures
(c) Other overhead
1) Do you think this approach is reasonable?
2) How would you calculate the number of North-South streets and West-East streets? Which assumptions would you make?
3) How would you calcuate the road surface of crossings to avoid double counting?
Thanks a million!