Interactive Job Scheduling with Partially Known Personnel Availabilities

Abstract

When solving a job scheduling problem that involves humans, the times in which they are available must be taken into account. For practical acceptance of a scheduling tool, it is further crucial that the interaction with the humans is kept simple and to a minimum. Requiring users to fully specify their availability times is typically not reasonable. We consider a scenario in which initially users only suggest single starting times for their jobs and an optimized schedule shall then be found within a small number of interaction rounds. In each round users may only be suggested a small set of alternative time intervals, which are accepted or rejected. To make the best out of these limited interaction possibilities, we propose an approach that utilizes integer linear programming and a theoretically derived probability calculation for the users’ availabilities based on a Markov model. Educated suggestions of alternative time intervals for performing jobs are determined from these acceptance probabilities as well as the optimization’s current state. The approach is experimentally evaluated and compared to diverse baselines. Results show that an initial schedule can be quickly improved over few interaction rounds, and the final schedule may come close to the solution of the full-knowledge case despite the limited interaction.