Jayant Rajgopal

Yuwen Yang, Jayant Rajgopal

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, Hoda Bidkhori, Jayant Rajgopal

Vaccination has been proven to be the most effective method to prevent infectious diseases. However, there are still millions of children in low and middle-income countries who are not covered by routine vaccines and remain at risk. The World Health Organization - Expanded Programme on Immunization (WHO-EPI) was designed to provide universal childhood vaccine access for children across the world and in this work, we address the design of the distribution network for WHO-EPI vaccines. In particular, we formulate the network design problem as a mixed integer program (MIP) and present a new algorithm for typical problems that are too large to be solved using commercial MIP software. We test the algorithm using data derived from four different countries in sub-Saharan Africa and show that the algorithm is able to obtain high-quality solutions for even the largest problems within a few minutes.