A fix-and-optimize approach to preemptive scheduling in audit firms

We study a large-scale multi-project scheduling problem motivated by audit firms, where activities must be assigned to qualified resources over long planning horizons while accounting for workload overload and capacity constraints. The problem is formulated as a mixed-integer programming model with multiple overload-related objectives, including the minimization of maximum and total overload over different horizons. To address the computational challenges posed by real-world instance sizes, we propose a fix-and-optimize matheuristic that decomposes the decision space and enables scalability. Computational experiments are conducted on real industrial data provided by a software company, involving annual planning instances with tens of thousands of activities. We analyze the impact of alternative overload objectives under varying horizons and continuity requirements. Results show that min–max objectives effectively limit extreme overload peaks and promote workload fairness, whereas total-overload minimization concentrates workload on fewer employees and reduces resource usage. Furthermore, allowing limited flexibility in resource-activity assignments leads to substantial performance gains: reassigning only 5–25% of activities nearly eliminates overload. These findings highlight fundamental trade-offs between fairness, flexibility, and efficiency, and demonstrate the value of the proposed framework as a decision-support tool for workload planning in professional service firms.