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

Performance impact of constraint variants on a MILP formulated Hearing Scheduling Problem | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Performance impact of constraint variants on a MILP formulated Hearing Scheduling Problem I.M.W. (Ieke) Schrader, E.W. (Erwin) Hans, J.M.J. (Marco) Schutten This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7147493/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract 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. Operations Research Block Scheduling MILP Inventory balance equation Computational impact Judicial System Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7147493","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":486829111,"identity":"4c941377-bfa8-446b-af32-da051448d6d6","order_by":0,"name":"I.M.W. 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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. 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