Qualified Educational Capacity Planning under Heterogeneous Student Support Needs: A Synthetic Benchmark and Decision-Support Framework

• URL: http://arxiv.org/abs/2606.30650v1
• Date: Mon, 15 Jun 2026 20:28:36 GMT
• Title: Qualified Educational Capacity Planning under Heterogeneous Student Support Needs: A Synthetic Benchmark and Decision-Support Framework
• Abstract summary: We introduce a synthetic benchmark and decision-support framework for qualified educational capacity planning.<n>The model is a stylized single-institution service system with heterogeneous support-demand categories.<n>We compare service-only, reactive, static-insurance, water-filling, and rolling-horizon mixed-integer controllers.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Educational support services often face a qualified-capacity problem: staff time is scarce, qualifications decay, new support needs can appear before anyone is prepared for them, and training consumes the same hours needed by current students. We introduce a synthetic benchmark and decision-support framework for qualified educational capacity planning. The model is a stylized single-institution service system with heterogeneous support-demand categories, backlog-only dynamics, continuous preparation states with hard threshold qualification and decay, and capacity-consuming training. The benchmark includes seed-controlled scenarios for announced and surprise new support categories, staff absences, and demand surges; exact feasibility discipline; declared per-policy information sets; requalification and greenfield-qualification counters; access-dispersion metrics; replay checksums; and paired statistics. We compare service-only, reactive, static-insurance, water-filling, and rolling-horizon mixed-integer controllers, with an attribution chain separating service planning, qualification maintenance, and acquisition, plus a perfect-foresight reference. The central result is a regime map governed by whether a newly required qualification can be acquired within the controller's reaction reach. When it can, the closed-loop controller wins across the core and adversarial suites, with value concentrated in just-in-time qualification acquisition. When the training lag exceeds the horizon, lean static insurance wins structurally, and a reactive trainer that starts after onset can be worse than no training. Backlog perishability shifts this boundary without erasing either regime. EduCapacity Studio reproduces exported scenarios bit-for-bit. All evidence is stylized and synthetic; the framework makes no claims about real student outcomes, compliance, or individual placements.

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