Optimal Depot location problems
A common operational problem is to find the fewest number of depots needed to service a catchment area. The Minimum Set Cover method is one technique that can be used to solve these kind of problems.
In this example, we identify the minimum number of airbases required to reach all other airbases within a given travel radius for the Australian Royal Flying Doctor Service (RFDS).
The Royal Flying Doctor Service
The Australian Royal Flying Doctor Service operates from 43 airbases and is
“…one of the largest and most comprehensive aeromedical organisations in the world, providing extensive primary health care and 24-hour emergency service to people over an area of 7.69 million square kilometres.”
It has 77 planes of 4 different types , with flying ranges of between 2,700km and 3,610 km.
Fewest Airbase Coverage by Range
The tool below displays the fewest number of airbases required to reach all other airbases, for the specified flying radius. You can adjust the flying radius by using the slider in the top right.
For simplicity, the existing airbases are used as the locations that require service coverage. In a proper planning exercise however, one would use population-weighted or spatially gridded points across the required service area. Moreover, additional requirements would also need to be considered, such as access to specialist staff and equipment that would likely only be available in larger urban areas.
A radius of 1,000km provides the best balance between the coverage of Australia and minimising the size of overlapping coverage areas. Radii smaller than 1,000km tend to create gaps between the coverage circles, whereas radii >1,000km have large overlapping sections and probably start to encroach on the round-trip range limits of their aircraft, once safety contingency is added.
While this simple example focuses on circular flying coverage, the same technique can be applied to any transport depot location problem, including road, rail or shipping logistics.
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