Quantum computer-aided job scheduling for storage and retrieval systems

In this paper, a quantum computer-aided approach to job scheduling for automated storage and retrieval systems is introduced. The approach covers application cases, where various objects need to be transported between storage positions and the order of transport operations can be freely chosen. The objective of job scheduling is to arrange the transport operations in a sequence, where the cumulative costs of the transport operations and empty runs between subsequent transport operations are minimized. The scheduling problem is formulated as an asymmetric quadratic unconstrained binary optimization (QUBO) problem, in which the transport operations are modeled as nodes and empty runs are modeled as edges, with costs assigned to each node and each edge. An Quantum Approximate Optimization Algorithm (QAOA) is used to solve the QUBO. Evaluations of the quantum computer-aided job scheduling approach have been conducted on the IBM Q System One quantum computer in Ehningen. In particular, the running time for the solution of the QUBO has been investigated, as well as the scalability of the approach with respect to the required number of qubits.