Explainability of Mathematical Models: A Case Study Using a Transportation Problem

In real-world applications of optimization algorithms, users often question decisions made by the algorithm, seeking explanations for why some features were chosen over others. We consider a logistic problem in which we need to allocate vehicles to pick up orders minimizing the total cost. We focus on users' queries regarding allocation decisions in a context where users would formerly create such allocations manually. Users, relying on implicit knowledge, tend to prioritize local cost minimization without considering global implications. Additionally, there are situations where the proposed allocation cannot be used for operational reasons, making it necessary to produce alternative solutions without going over all the optimization process again. To address these challenges, we propose a framework that explains why the user's suggested solution was not chosen and offers a new solution, when feasible, based on the user's suggestion. Furthermore, we present practical results of our framework.