Performance impact of constraint variants on a MILP formulated Hearing Scheduling Problem

The Dutch Judicial system faces efficiency challenges due to limited resources and increasing case disposition times. In the literature, operations research is rarely used to improve judicial efficiency. We introduce the Hearing Scheduling Problem (HSP), a tactical planning problem. The HSP concerns the combined decision of scheduling hearing blocks over time and allocating resources (e.g., staff members and courtrooms) to these hearing blocks. Decision-making is under a broad set of limitations, such as staff member skills and desk activity requirements. We focus on civil law in a Dutch Court, but the HSP is generalisable to other law sectors, such as criminal and administrative law. We propose two mixed integer linear program formulations and a relaxation to solve the HSP. Variant 1 employs a strict scheduling approach, while Variant 2 uses a desk time balance equation, and Variant 3 relaxes this equation. The inventory balance equation reduces the number of variables and minimises symmetry compared to the strict approach. When comparing the variants, Variant 3 outperforms Variants 1 and 2 in peak memory usage and the reached integrality GAP. Moreover, Variant 3 obtains a solution up to a schedule horizon of 25 weeks, almost twice as long as for Variants 1 and 2. We conclude that the inventory balance equations in Variants 2 and 3 considerably enhance the computational performance. Given the low infeasibility rate and the better computational performance observed, Variant 3 is suitable for schedule computation for civil law in practice.