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

In this article we approach an extended Job Shop Scheduling Problem (JSSP). The goal is to create an optimized duty roster for a set of workpieces to be processed in a flexibly organized workshop, where the workpieces are transported by one or more Autonomous Ground Vehicles (AGV), that are included in the planning. We are approaching this extended, more complex variant of JSSP (still NP-complete) using Constraint Programming (CP) and Quantum Annealing (QA) as competing methods. We present and discuss: a) the results of our classical solution based on CP modeling and b) the results with modeling as quadratic unconstrained binary optimisation (QUBO) solved with hybrid quantum annealers from D-Wave, as well as with tabu search on current CPUs. The insight we get from these experiments is that solving QUBO models might lead to solutions where some immediate improvement is achievable through straight-forward, polynomial time postprocessing. Further more, QUBO proves to be suitable as an approachable modelling alternative to the expert CP modelling, as it was possible to obtain for medium sized problems similar results, but requiring more computing power. While we show that our CP approach scales now better with increased problem size than the hybrid Quantum Annealing, the number of qubits available for direct QA is increasing as well and might eventually change the winning method.