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The Operational Fixed Interval Scheduling Problem aims to find an assignmentof jobs to machines that maximizes the total weight of the completed jobs. Weintroduce a new variant of the problem where we consider the additional goal ofminimizing the idle time, the total duration during which the machines areidle. The problem is expressed using quadratic unconstrained binaryoptimization (QUBO) formulation, taking into account soft and hard constraintsrequired to ensure that the number of jobs running at a time point is desirablyequal to the number of machines. Our choice of QUBO representation is motivatedby the increasing popularity of new computational architectures such asneuromorphic processors, coherent Ising machines, and quantum andquantum-inspired digital annealers for which QUBO is a natural input. Anoptimization problem that can be solved using the presented QUBO formulation isthe music reduction problem, the process of reducing a given music piece for asmaller number of instruments. We use two music compositions to test the QUBOformulation and compare the performance of simulated, quantum, and hybridannealing algorithms.

Fixed interval scheduling problem with minimal idle time with an application to music arrangement problem