A classical case in optimization: the transportation model.
- Assume we have 4 hospitals: A, B, C, D with excess patients, say 20, 10, 10, 8 [all these numbers are purely illustrative]
- Assume there are 6 hospitals with beds available for outside patients (say: 2, 4, 8, 4, 12, 9)
- Assume there is a “cost” for transferring a patient from any origin to each destination (e.g., km driving for the ambulance, but any other cost will do). Here I used rectilinear diistance on the map. This is the hypotetic situation:
How can we relocate patients?
The easy, standard, way:
- start from A (20 patients) and send them to the closest available locations (2 to a, 4 to b, 2 to d 12 to e)
- then proceed with B (10 patients) and send them the same way: 8 to d, 2 to e
- then C (10 patients): 9 to fand we are done.
Total distance: 311.6
the way Operations Research can do this:
Total distance: 249.5 (a 20% saving in this toy example)
We cannot send more patients than beds available. But we can find a way to do this with less cost. Please notice: distances are real, other numbers as well as node locations are totally random, not just built to make the example work.
We might change this elementary model in many ways:
- assigning patients in a more equitable way (e.g., don’t satisfy 100% of one and almost nothing of another one)
- consider time for transfer, instead of km’s
- taking into account limited ambulance availability
- adding priorities
- adding pair requirements (these patients should be kept together)
- adding probabilistic estimates (tomorrow’s patients)