Optimization and public health

December 21, 2020 News by Cassotis Consulting


A review of optimization opportunities in the healthcare industry has shown many applications for facilities management. However, it is not common to find cases of public health systems using optimization tools in strategic decision-making. What challenges could be tackled within this perspective?


From the health facility management point of view, there are many applied examples of optimization techniques to support their decision-making. Among them, we can list a few:


  • Nurse scheduling [1], which involves finding an optimal way to assign nurses to shifts 
  • Surgery scheduling [2], which involves the selection, allocation, and sequencing of procedures to be performed
  • Hospital/Residents matching [3]: which involves finding a stable match for graduating medical students (residents) to hospital posts  


However, those applications do not seem to help the broad demands of the public, especially the ones arisen during 2020. From all opportunities, we will detail two: medicine distribution and health centers' placement.


The first challenge is very relatable now that recent studies have shown the effectiveness and safety of COVID-19 vaccines. Federal, state, and local governments along with the private sector need to coordinate efforts and to optimize the transportation of the vaccines from the production sites to the citizens. The number of possible distribution routes is vast, and each logistically feasible plan should be investigated. At the same time, it is expected that the chosen plan is the one with minimum cost. Luckily, this type of problem has been studied for a long time in Operations Research and many formulations could help on this mutual effort. One example is the Minimum Cost Flow problem [4]. Its linear construction, combined with network simplex algorithms, can find solutions in polynomial time even considering a large instance to solve.


For the second example, let's imagine a policy that guarantees that none of its citizens should live further than a specific distance from a health center and a hospital. To lower the distances, it is necessary to build new facilities and increase expenses. Is there a way to optimize those investments and guarantee the accessibility of the public? Similar decisions are supported using the Facility Location problem formulations [5]. Specialists agree that finding an optimal solution for the problem becomes increasingly more complex with every potential site. Those very hard-to-solve problems are usually tackled by combining mixed integer programming with decomposition techniques - the most known being Benders' decomposition [6].


In a universe of possibilities and combinations, too big to manually evaluate, support decision models are a tool to benefit the entire population.



[1] Smet, Pieter. "Nurse rostering: models and algorithms for theory, practice and integration with other problems." (2015).

[2] May, Jerrold H., et al. "The surgical scheduling problem: Current research and future opportunities." Production and Operations Management 20.3 (2011): 392-405.

[3] Askalidis, Georgios, et al. "Socially stable matchings in the hospitals/residents problem." Workshop on Algorithms and Data Structures. Springer, Berlin, Heidelberg, 2013.

[4] Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993). Network Flow Problems. In Network flows: Theory, algorithms, and applications. Upper Saddle River, NJ: Prentice-Hall.

[5] Cornuéjols, Gérard, George Nemhauser, and Laurence Wolsey. The uncapacitated facility location problem. Cornell University Operations Research and Industrial Engineering, 1983.

[6] Rahmaniani, Ragheb, et al. "The Benders decomposition algorithm: A literature review." European Journal of Operational Research 259.3 (2017): 801-817.


Author: Guilherme Martino - Senior Consultant at Cassotis Consulting

                                     Co-author Fabio Silva - Senior Manager at Cassotis Consulting