The Traveling Salesman Problem is one of the most intensively studied
combinatorial optimization problems due both to its range of real-world
applications and its computational complexity. When combined with the Set
Covering Problem, it raises even more issues related to tractability and
scalability. We study a combined Set Covering and Traveling Salesman problem
and provide a mixed integer programming formulation to solve the problem.
Motivated by applications where the optimal policy needs to be updated on a
regular basis and repetitively solving this via MIP can be computationally
expensive, we propose a machine learning approach to effectively deal with this
problem by providing an opportunity to learn from historical optimal solutions
that are derived from the MIP formulation. We also present a case study using
the vaccine distribution chain of the World Health Organization, and provide
numerical results with data derived from four countries in sub-Saharan Africa.
Yuwen Yang, Jayant Rajgopal