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

Production planning increasingly has to treat workforce capability as a decision variable: certifications lapse when skills are not maintained, new products require skills the current workforce does not hold, and reskilling competes for the same worker hours needed for production. Existing operations benchmarks usually treat labor as exogenous, while workforce-planning models with skills and learning are rarely released as reusable testbeds. We introduce SkillChain-Gym, a benchmark specification for reskilling-aware production-inventory control: a single-site environment with stylized worker skill-state dynamics, hard threshold certification, forgetting, and capacity-consuming training actions constrained by the same per-worker time budget as production. The benchmark includes seed-controlled disruption scenarios, three feasibility modes with projection diagnostics, deterministic replay, and metrics covering operations, resilience, capability growth, and training-access distribution. We evaluate production-only, reactive adaptive, water-filling adaptive, and static-insurance policies with budget variants over 60-shift horizons with paired statistical tests. The results are regime-dependent rather than a ranking. Training-capable policies dominate the production-only baseline, and maintenance training is necessary under forgetting even without disruptions. Among training-capable classes, adaptive training helps when bottlenecks are visible in the forecast, while a lean static cross-training plan, a deliberately favorable comparator whose structure encodes relevant skill contingencies, acts as strong insurance under surprise shocks and absenteeism. Capacity slack and the forgetting rate govern the boundary between these regimes. No policy class dominates across regimes, motivating forecast-driven controllers that decide when to buy skill insurance and when to react.

In skill-constrained production-inventory systems, the qualified human capacity available tomorrow depends on training decisions made today: production requires certified workers, certifications decay unless maintained, and training consumes the same scarce worker hours that production needs now. We study a closed-loop skill-constrained model predictive controller that, at every shift, solves a finite-horizon mixed-integer program over production, inventory, backlog, and training, with binary predicted certification, hard production eligibility, and an interpretable terminal value that prices certified-capacity gaps at the horizon boundary; only the first-period action is applied before replanning. On synthetic, seed-controlled SkillChain-Gym scenarios - announced and surprise new-skill shocks, demand shocks, absenteeism, forecast- and availability-quality modes, capacity-boundary and training-rate sweeps, and negative controls - we evaluate the controller against production-only and maintenance-only ablations, static cross-training insurance plans, and a strong reactive heuristic, under an ex-ante locked configuration and paired statistics. The result is regime dependence, not superiority: no policy class dominates. Predictive control helps when skill or labor bottlenecks are forecastable early enough for training to complete; lean static insurance remains hard to beat under surprise shocks, near the demand-capacity boundary, and wherever pre-shock slack makes insurance cheap. Attribution ablations separate certification maintenance, re-acquisition of lapsed certifications, and greenfield skill acquisition. Forecastability, not adaptivity per se, decides when predictive control pays.

Many social services assign scarce resources, such as housing assistance or hospital interventions, to people who arrive one at a time: each arrival must receive a decision immediately, and the long-run usage of every resource must stay within its capacity. We study how to learn such an assignment policy from logged observational data. The standard pipeline is decision-blind: fit one outcome model per arm by regression, price each capacitated resource from the fitted models, and assign each arrival the arm whose predicted outcome minus price is largest. We instead train the outcome models end-to-end, differentiating an off-policy estimate of the deployed policy's value through the dual prices themselves. We study two formulations: an exact nonconvex one, and a convex relaxation whose optimum always satisfies the capacity constraints in expectation and which is suboptimal by at most a term linear in the smoothing temperature and logarithmic in the number of arms. Every method is evaluated in a queueing simulation with resources replenished at their capacity rates. Across six datasets, the two end-to-end variants take the top slots on a deployment-adjusted value index at every delay cost, including zero; when capacities are binding, decision-blind baselines frequently violate them and incur much longer queueing delays. On the largest dataset, a hospital cohort of seventy thousand patients, end-to-end training also achieves significantly higher policy value, a margin that survives a capacity-matched neural baseline. Flexible decision-blind regression remains the stronger pure predictor where ground truth is measurable; end-to-end training is best suited to settings where resources are genuinely scarce and feasibility matters.