Assessing the current distribution

[loladekhuijzen]

Lewis suggests to focus on the following to assess the current distribution.

1. Can we reduce travel time with the same number of facilities (all of them can be moved)

2. Can we reduce the number of facilities with low demand without reducing travel time

my thoughts on 1:

Number of facilities stays fixed. We optimally place N facilities, while minimizing travel time. No need to consider facility cost.

We could start from the potential facilities, and contraint LP to keep N of them open, and have the travel time as objective?

my thoughts on 2:

(I'm assuming we can again move around facilities, as otherwise the answer is probably always no)

To determine which facilities are low demand: "we could pick the 10th percentile when ranking locations by their estimated demand from low to high across a large number of countries", but do we then extract some absolute number for a country so we can use the same threshold when considering the potential facilities?
Then, we could constrain the travel time by the travel time in the current situation, and have LP minimize the number of low demand facilities.