[Submitted on 6 May 2020]

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Abstract: We propose our solution to a particular practical problem in the domain of
vehicle routing and scheduling. The generic task is finding the best allocation
of the minimum number of emph{mobile resources} that can provide periodical
services in remote locations. These emph{mobile resources} are based at a
single central location. Specifications have been defined initially for a
real-life application that is the starting point of an ongoing project.
Particularly, the goal is to mitigate health problems in rural areas around a
city in Romania. Medically equipped vans are programmed to start daily routes
from county capital, provide a given number of examinations in townships within
the county and return to the capital city in the same day. From the health care
perspective, each van is equipped with an ultrasound scanner, and they are
scheduled to investigate pregnant woman each trimester aiming to diagnose
potential problems. The project is motivated by reports currently ranking
Romania as the country with the highest infant mortality rate in the European
Union.

We developed our solution in two phases: modeling of the most relevant
parameters and data available for our goal and then design and implement an
algorithm that provides an optimized solution. The most important metric of an
output scheduling is the number of vans that are necessary to provide a given
amount of examination time per township, followed by total travel time or fuel
consumption, number of different routes, and others. Our solution implements
two probabilistic algorithms out of which we chose the one that performs the
best.