LLM-Based Exogenous World Modeling for Dynamic Scheduling

1 Introduction

• Reactive dispatching rules consider only currently available operations, while anticipatory optimization depends on a prespecified arrival model and repeated reoptimization can be expensive.Dynamic scheduling is difficult because a locally beneficial decision can delay a later high-priority job beyond its due date, incurring a disproportionate downstream penalty.Source: §1 · p. 1
• AWMP scores feasible actions using afterstate and belief-derived features, then evaluates retained candidates through short rollouts under concrete arrival scenarios.The strategy is discovered offline through meta-evolution.Source: §1 · p. 2
• Online residual self-calibration conditions later LLM prompts on recent prediction outcomes and forecast errors to adapt arrival forecasts to nonstationary patterns.Belief reuse and surprise-triggered refresh reduce LLM calls from one per rollout to a handful per episode.Source: §1 · p. 2
• The afterstate decomposition isolates uncertain future job arrivals from known deterministic scheduling dynamics, allowing the LLM to forecast arrival pressure rather than the full shop transition.The compact belief represents expected job counts in early and late portions of a fixed prediction horizon, without individual job identities or operation-level dynamics.Source: §1 · pp. 1–2
• AWMP reduces total tardiness by 6-21% on dynamic job-shop instances and 22-46% on dynamic flexible job-shop instances versus the best of eight classical PDRs.Experiments cover four arrival distributions, and AWMP runs in seconds.Source: §1 · p. 2

Classical dynamic scheduling methods

• Reactive priority rules rank currently eligible operations without explicitly representing future arrivals, whereas anticipatory optimization evaluates future workloads but depends on an assumed arrival model and repeated solving can be expensive.AWMP occupies a middle ground by augmenting low-latency dispatching with an LLM forecast inferred from arrival history, without requiring a parametric arrival process.Source: §2 · pp. 2–3

Neural dynamic scheduling methods

• Neural dynamic-scheduling policies can capture complex interactions but are generally trained on specific simulated trajectories and may need retraining when the arrival process or objective changes.AWMP trains no neural policy; it uses a frozen pretrained LLM for aggregate arrival pressure and an offline-evolved strategy frozen before evaluation.Source: §2 · p. 3

Learned world models for planning

• Unlike learned world models that estimate substantial environment dynamics, AWMP retains known deterministic shop transitions and isolates future arrivals as the exogenous uncertainty.Its structured world model combines a low-dimensional arrival-pressure predictor with the deterministic scheduling simulator.Source: §2 · p. 3

LLMs for optimization and heuristic discovery

• AWMP uses LLMs in two roles: online forecasting of aggregate arrival pressure and offline evolution of a compact, human-readable planning strategy.The evolved strategy includes a scoring rule, value estimator, and rollout parameters rather than an independent solver program.Source: §2 · p. 3

3.1 Afterstate Decomposition

• AWMP formalizes an afterstate decomposition that separates deterministic shop dynamics from uncertain exogenous job arrivals.Known action-to-afterstate and event-advance transitions are retained exactly, leaving the conditional arrival process as the component requiring forecasting.Source: §3 · p. 3, §3.1 · p. 3

3 Methodology

• The methodology combines exact deterministic shop transitions with a forecasted arrival belief and an offline-discovered strategy for held-out evaluation.The modular design separates forecasting arrivals, planning with the belief, and discovering a compact strategy.Source: §3 · p. 3

3.2 LLM-Based Exogenous World Modeling

• A pretrained LLM forecasts compact early- and late-horizon arrival counts from observed history, with recent forecast residuals used for prompt-level online calibration.The forecast supplies aggregate arrival pressure rather than individual job identities or operation-level dynamics; calibration adapts prompts without updating LLM parameters.Source: §3.2 · pp. 4–5

3.3 Belief-Conditioned Afterstate Planner

• A belief-conditioned scorer screens feasible actions before short rollouts compare retained candidates across generated arrival scenarios.The planner selects the action with the best evaluation averaged across scenarios; cached beliefs are reused, with refresh triggered by sufficient arrival surprise or an expired lookahead horizon.Source: §3.3 · pp. 5–6

3.4 Meta-Evolution of Planning Strategy

• Offline meta-evolution searches compact planning strategies by revising scoring, value, and rollout parameters under predefined safety constraints.A proposer LLM modifies the strategy object, not the arrival predictor or scenario generator; the best strategy is frozen for final evaluation.Source: §3.4 · p. 6

4 Experiments

• The evaluation asks whether AWMP improves scheduling, whether calibration helps forecasts and scheduling, how reuse reduces calls, and whether meta-evolution generalizes to held-out instances.These four questions organize the experiments.Source: §4 · p. 6

4.1 Experiment Setup

• Dynamic JSSP and FJSP benchmarks retain standard shop configurations and processing data, while jobs arrive under four controlled distributions and performance is measured by total weighted tardiness.Baselines include eight classical PDRs and five optimization-based online schedulers.Source: §4.1 · p. 6

4.2 Overall Performance

• AWMP reduces total weighted tardiness by 5.8%–20.7% on dynamic JSSPs and 21.9%–46.3% on dynamic FJSPs versus the best PDR, and beats all five optimization baselines in every setting.The comparison covers eight benchmark-distribution combinations; Table 1 reports average total weighted tardiness, with lower values better.Source: §4.2 · p. 6, Table 1 · p. 7
• One frozen strategy was evaluated across four arrival distributions without per-distribution retuning, covering bursty, increasing, cyclic, and step-changing patterns.The reported scope is the four evaluated arrival distributions.Source: §4.2 · p. 7

4.3 Effect of Residual Self-Calibration

• Forecast correlation rose from r = 0.12 to r = 0.93, while calibrated beliefs reduced the objective from 6771 to 4011, a 41% reduction.Forecast accuracy was evaluated under sinusoidally drifting arrival intensity; the prediction–outcome pairs came from a separate diagnostic run.Source: §4.3 · p. 7

4.4 LLM Call Efficiency

• Inter- and intra-step belief reuse cut LLM calls from 7191 to 18 per episode, approximately 400× fewer, with queries finishing within seconds.Beliefs are shared across candidate actions and rollouts, then refreshed when arrivals deviate sufficiently or the prediction horizon is inadequate.Source: §4.4 · p. 7

4.5 Meta-evolution

• Relative to the initial seed strategy, the evolved strategy reduced the objective by 57% on training instances and 62% on disjoint held-out TA03 and TA04, after being frozen without test-time adaptation.Source: §4.5 · p. 8

5 Conclusion

• AWMP combines exact scheduling dynamics with a pretrained LLM modeling exogenous arrivals and a meta-evolved, belief-conditioned planner using candidate screening and short rollouts.The scenario generator is fixed and non-learned; the paper concludes that this approach can support anticipatory scheduling without learning complete shop transitions or a task-specific neural dispatching policy.Source: §5 · p. 8
• Future work includes richer job-level arrival beliefs, evaluation on real-world and more diverse arrival processes, and more efficient forecasting models to reduce inference latency.The paper also notes possible extension of the structured world-model framework to robust optimization and stochastic programming.Source: §5 · p. 8
• The study uses early–late workload beliefs, four controlled arrival patterns derived from standard benchmarks, and online updates whose runtime remains affected by LLM latency.The authors identify richer job attributes, real scheduling traces, more diverse operating conditions, and faster forecasting models as areas for broader assessment or improvement.Source: §5 · p. 8

A Arrival Distributions

• Each dynamic instance assigns release times to jobs from a static benchmark, with the first job available at t = 0 and remaining releases sampled from one of four families.The arrival window has length H_arr = 0.6H, and β scales the peak arrival rate.Source: A Arrival Distributions · p. 10
• Pulse-train arrivals cluster around four evenly spaced burst centers, with Gaussian temporal jitter scaled by 0.02H_arr.This produces a sequence of short, periodic workload surges.Source: A Arrival Distributions · p. 10
• Late-ramp arrivals increase monotonically over the window, with expected normalized release time 2/3, producing a back-loaded workload.Source: A Arrival Distributions · p. 10
• Cyclic arrivals follow two sinusoidal cycles over the arrival window, alternating between recurring high- and low-intensity periods.Source: A Arrival Distributions · p. 10
• Step-up arrivals release one third of jobs in the first half and two thirds in the second half, doubling the expected arrival rate at the midpoint.Figure 5 plots empirical arrival-rate profiles aggregated over 200 seeds at β = 1.5.Source: A Arrival Distributions · p. 10, Figure 5 · p. 10

• At a refresh, the world model takes arrival history—current time, horizon, released-job count, and release-time log—and returns an arrival belief.Source: B World-Model Interface · p. 10
• The belief estimates early- and late-horizon arrival counts, while a fixed scenario generator supplies concrete release times and job attributes for rollouts.The LLM does not predict individual job identities, exact release times, processing routes, or other job attributes.Source: B World-Model Interface · p. 10
• Each query combines fixed forecasting instructions, arrival history, residual-calibration records, and a predefined JSON schema; these prompt components remain fixed during meta-evolution and evaluation.Source: B World-Model Interface · p. 10

• Total weighted tardiness uses max(0, eCj − dj), imposing no penalty before a due date and a linearly increasing penalty afterward.Source: C Objective · p. 10
• An unfinished job is assigned completion time H, so it contributes a terminal tardiness penalty instead of being omitted.Source: C Objective · p. 10
• Due dates add workload-scaled slack to release time, while weights equal each job's workload relative to mean instance workload.The parameter µ controls due-date tightness; processing-intensive jobs therefore receive proportionally greater importance.Source: C Objective · p. 10