Human-machine interaction for real-time linear optimization

Mixed-Initiative-Systems (MIS) are hybrid decision-making systems in which human and machine collaborate in order to produce a solution. This paper described an MIS system adapted to business optimization problems. These problems can be solved in less than an hour as they show a linear structure. However, this delay is unacceptable for iterative and interactive decision-making contexts where users need to provide their input. Therefore, we propose a system providing the decision-makers with a convex hull of optimal solutions minimizing/maximizing the variables of interest. The users can interactively modify the value of a variable and the system is able to recompute a new optimal solution in a few milliseconds. Four real-time reoptimization methods are described and evaluated.