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