Towards Explainable Optimization of Production System Configurations

The critical decisions related to production system configuration are often supported by mathematical optimization tools, such as mixed-integer linear programming (MILP) models built into automated system design software. However, users may have concerns about the computed optimal solution-or about the absence of a solution-arising from discrepancies between the mathematical model and their understanding of the problem, or from the flexibility of input parameters. Thus, to support the decision-making process, it is crucial to make optimization explainable, i.e., to reinforce the understanding of the user why a given solution is recommended. This paper proposes an interactive procedure to solve this problem, where the decision-maker asks consecutive “why not c” type questions, where c is a feature of the solution encoded in a set of constraints on the decision variables of the MILP. Special focus is given to the case where infeasibility must be explained. Two alternative search procedures were implemented to find all possible explanations of infeasibility. The proposed approach was validated on a medium-scale sample instance of the system configuration problem with 17 tasks requiring 13 resources for their execution. The gained explanations can help identify the parameters and constraints that require special attention by the user.