Solving the Extended Job Shop Scheduling Problem with AGVs -- Classical and Quantum Approaches

The subject of Job Scheduling Optimisation (JSO) deals with the scheduling of jobs in an organization, so that the single working steps are optimally organized regarding the postulated targets. In this paper a use case is provided which deals with a sub-aspect of JSO, the Job Shop Scheduling Problem (JSSP or JSP). As many optimization problems JSSP is NP-complete, which means the complexity increases with every node in the system exponentially. The goal of the use case is to show how to create an optimized duty rooster for certain workpieces in a flexible organized machinery, combined with an Autonomous Ground Vehicle (AGV), using Constraint Programming (CP) and Quantum Computing (QC) alternatively. The results of a classical solution based on CP and on a Quantum Annealing model are presented and discussed. All presented results have been elaborated in the research project PlanQK.