Algorithms, especially the ones used in machine learning, promise to aid people in making decisions. In many scenarios even conceptually simple algorithms can deliver better quality answers than humans, e.g., make less mistakes. Still this promise is far from being realized in its full potential. The main problem is that algorithms are not able to give much insight nor explanation why the returned answer is the correct one. Even if we try to reverse-engineer the reasons why this decision was made by an algorithm, these reasons may still remain incomprehensible to humans. This problem can be best illustrated by the example of Deep Blue, a chess computer developed by IBM. A human has no chance to understand its “reasoning” for a particular move.

In case of games, we might continue the philosophical dispute forever whether Deep Blue understands chess or not. However, this becomes a cornerstone issue when deploying algorithmic solutions in real-world. We need to guarantee that algorithms can be understood by people using them, as otherwise they refuse to follow them. Surprisingly, there exist no good tools to deliver explanations even for the most basic algorithms. For example, some of us often doubt whether GPS found the fastest route, and might be trying alternative ones. This despite the fact that finding the shortest path is a well-studied problem and we can even prove that the algorithm works correctly. The problem is rather about explaining the solution to the user, and not the algorithm itself. Moreover, the algorithm might be used by someone that does not have the right algorithmic background, so explaining its decision becomes even more important. The good news is that one does not need to study algorithms for years to see that they work in the right way. For example, one of the main reasons why Google Maps shows alternative routes, is to explain to the user why the returned solution is the best one. This is because the possible alternatives are worse!

Algorithms are becoming more prevalent in our lives due to ongoing digitalization which is further sped-up by the current pandemic situation. Hence, the need to explain their results becomes more immanent. This research aims to deliver a proof of concept of the tools that would provide explanations for the most basic optimization problems, e.g., assignment problem. Assignments are the cornerstone problem in operational research and are used to describe matching of jobs to workers, jobs to servers, page views to ads, residents to hospitals, students to universities or houses to tenants. Furthermore, all decisions taken by algorithms should be explainable as required by “Ethics guidelines for trustworthy AI’’ that apply to complex ML solutions, but to this case as well.