Industrial Scheduling in the Digital Era: Challenges, State-of-the-Art Methods, and Deep Learning Perspectives

Abstract

Industrial scheduling plays a central role in Industry 4.0, where efficiency, robustness, and adaptability are essential for competitiveness. This review surveys recent advances in reinforcement learning, digital twins, and hybrid artificial intelligence (AI)–operations research (OR) approaches, which are increasingly used to address the complexity of flexible job-shop and distributed scheduling problems. We focus on how these methods compare in terms of scalability, robustness under uncertainty, and integration with industrial IT systems. To move beyond an enumerative survey, the paper introduces a structured analysis in three domains: comparative strengths and limitations of different approaches, ready-made tools and integration capabilities, and representative industrial case studies. These cases, drawn from recent literature, quantify improvements such as reductions in makespan, tardiness, and cycle time variability, or increases in throughput and schedule stability. The review also discusses critical challenges, including data scarcity, computational cost, interoperability with Enterprise Resource Planning (ERP)/Manufacturing Execution System (MES) platforms, and the need for explainable and human-in-the-loop frameworks. By synthesizing methodological advances with industrial impact, the paper highlights both the potential and the limitations of current approaches and outlines key directions for future research in resilient, data-driven production scheduling.

1. Introduction

Industrial scheduling encompasses the decision-making processes that allocate limited resources—machines, workforce, tools, and materials—to jobs over time with one or more performance objectives, such as minimizing makespan, reducing cost, increasing throughput, meeting due dates, and balancing workloads or inventories. Foundational treatments formalize these models and objectives across single-machine, flow/parallel/job shops, and flexible shop environments, and review setup-related complications common in practice [1,2,3,4].

The field is renowned for both its practical significance and computational difficulty: many canonical variants are NP-hard, ruling out polynomial-time exact algorithms for large instances and motivating approximation, heuristic, and metaheuristic approaches. Classic complexity results in deterministic sequencing and scheduling, alongside broader NP-completeness theory, underpin this assessment and continue to guide algorithm design [5,6].

Against this backdrop, recent progress increasingly blends operations research with data-driven and learning-based methods—ranging from learned components inside exact/heuristic solvers to end-to-end deep reinforcement learning (DRL) policies that learn dispatching rules from experience and generalize across scales [7,8].

Scheduling decisions reverberate throughout operations. Effective schedules shape lead times, inventory positions, utilization, energy consumption, and service levels across manufacturing and services; in many settings, they also form the last-mile link between planning and control [9,10].

The digital transformation (Industry 4.0) has fundamentally altered the information context of scheduling. Industrial IoT, cyber-physical production systems, cloud/edge computing, and digital twins generate continuous data streams and enable tighter sense–decide–act loops—but they also introduce interoperability and latency constraints that shape feasible scheduling architectures. These changes simultaneously heighten problem complexity and unlock data-driven, closed-loop scheduling integrated with shop–floor automation [11,12,13,14].

Beyond productivity and cost, scheduling now contributes to strategic goals in sustainability and human-centric operations. Energy-aware models and policies can reduce consumption and emissions, while human-in-the-loop, “Operator 4.0” concepts target ergonomics and well-being in digitally enhanced workplaces [15,16].

At the same time, volatile supply and demand conditions, equipment disruptions, and external shocks expose the limits of static plans, elevating robustness and rapid recovery as first-class requirements. Digital-twin-enabled monitoring and OR methods for ripple-effect management illustrate how predictive and reactive scheduling can be fused for resilience [14,17].

This review synthesizes developments across these fronts and focuses on three persistent, intertwined challenges that define industrial scheduling in the digital era:

• Scalability and computational complexity in large, high-dimensional environments;
• Robustness and adaptability to uncertainty and real-world disruptions;
• Integration with digitalization (IIoT, cloud/edge platforms, and cyber-physical systems).

The first major challenge is the scalability and computational complexity of scheduling large and dynamic systems. As industrial operations expand—covering dense machine networks, diversified product portfolios, and multi-echelon supply chains—the combinatorial search space grows superlinearly, making many variants NP-hard and rendering exact methods impractical beyond modest sizes (even with clever modeling and cutting planes). This reality motivates scalable heuristics, metaheuristics, and hybrid AI–OR approaches that deliver strong anytime solutions under tight latency budgets [1,5]. A recent thrust is learning to optimize: machine-learned components accelerate solvers themselves (e.g., learned branching and node policies for MILP) or synthesize high-quality heuristics end-to-end. Graph-based models guide branch-and-bound more effectively than hand-crafted rules [18,19], while neural combinatorial optimization—pointer networks and attention models—yields powerful constructive policies that increasingly transfer to shop–floor dispatching [20,21,22]. These techniques do not remove worst-case hardness, but they can shift the practical frontier, offering better solution quality under fixed compute and generalization to larger instances [7].

The second central challenge is robustness and adaptability to uncertainty. Industrial systems face equipment failures, stochastic processing times and arrivals, rush orders, material shortages, and upstream disruptions; static schedules—even optimal at release—degrade quickly on the shop floor. Classical robust optimization provides tunable protection against uncertainty sets [23], while the predictive–reactive literature offers periodic and event-driven rescheduling strategies to recover performance [24,25]. On the data-driven side, deep reinforcement learning (DRL) learns reactive dispatching and repair policies that adapt online; systematic evidence shows improvements in tardiness, throughput, and resilience across manufacturing test beds [26,27]. Effective stacks increasingly fuse forecasts, robust baselines, and DRL policies with feasibility guards, giving rapid recovery while containing variance in outcomes.

The third, increasingly critical challenge is integration with digitalization and Industry 4.0. Cyber-physical production systems and the Industrial IoT generate continuous, heterogeneous streams (status, quality, energy, and context data) that can close the loop between sensing, scheduling, and actuation—yet they also impose strict interoperability and latency constraints that shape feasible architectures (edge vs. cloud; publish/subscribe vs. polling). Digital twins serve as simulation-in-the-loop substrates for scheduling: they enable safe policy training, what-if analysis, and proactive, state-aware rescheduling once deployed [12,28,29,30]. Realizing this promise requires data pipelines that manage drift and noise, hardened APIs for shop–floor integration, and algorithms that meet real-time deadlines with verifiable constraint satisfaction.

Recent AI advances further reshape the design space. Beyond GNN-augmented solvers and DRL dispatching, large language models can act as optimizers by prompting (OPRO)—iteratively proposing and refining heuristics under programmatic evaluation. When coupled with simulation-based validation and action masking, such models can rapidly tailor heuristic rules or hyper-policies to new product mixes and resource pools, complementing DRL and classical OR rather than replacing them [7,31].

These three challenges—(i) scalability and computational complexity, (ii) robustness and adaptability, and (iii) digital integration—thus frame our review of methods, evidence of industrial impact, and opportunities for future research.

The scope of this review is narrative and industrially oriented rather than systematic in the medical-science sense. Studies were selected based on three criteria: (i) relevance to Industry 4.0 scheduling, with particular emphasis on reinforcement learning, digital twin technologies, and hybrid AI–OR methods; (ii) recency, with the majority of works drawn from the period 2020–2025; and (iii) industrial applicability, privileging studies that either report real-world deployments or explicitly address scalability, robustness, or integration. The thematic focus of the review was derived from an initial scoping of recent publications in high-impact journals and conferences. Reinforcement learning, digital twins, and hybrid AI–OR approaches consistently emerged as the most prominent and frequently cited directions in the 2020–2025 literature, particularly in the context of Industry 4.0 scheduling. These clusters therefore structure the main body of the review.

2. Scalability and Computational Complexity

2.1. The Combinatorial Nature of Industrial Scheduling

Industrial scheduling problems are intrinsically combinatorial: the number of feasible schedules typically grows factorially (or worse) with jobs, machines, precedence/eligibility constraints, and setup interactions. For classical models—job shop and flow shop—this explosion is well documented, and most realistic variants are NP-hard once we account for precedence, batching, sequence-dependent setups, machine flexibility, release/due dates, or multi-objective criteria. The consequence is a persistent gap between exact optimality and practical tractability on large or highly dynamic instances, even as computing hardware and solvers improve. Foundational surveys and texts remain the touchstones for this complexity landscape and motivate approximations, decomposition, and learning-enhanced methods that deliver strong anytime performance at scale.

2.2. Recent Methodological Developments

The profound computational complexity of industrial scheduling has motivated three complementary streams of scalable methods: (i) metaheuristics and hybrids; (ii) decomposition and parallelization; and (iii) AI-/data-driven approaches. Below, each stream is expanded with emphasis on post-2020 progress and deep learning trends.

2.2.1. Metaheuristics and Hybrid Algorithms

Metaheuristics remain a workhorse for large instances because they can explore vast, rugged search spaces quickly and flexibly. Recent work emphasizes problem-aware hybridization, adaptive control, and learning-enhanced neighborhoods.

• Genetic algorithms (GAs) and memetic hybrids. Modern GA variants integrate local search, path relinking, or destroy-and-repair moves to accelerate convergence on very large instances and complex shop settings; hybrids tuned for industrial-scale unrelated/parallel machines and sequence-dependent setups are increasingly common. Representative examples show GA + local-search hybrids scaling to hundreds of machines/jobs while retaining solution quality [32,33].
• Simulated annealing (SA) and tabu search (TS). Classical SA/TS ideas—probabilistic uphill moves and adaptive memory—continue to underpin strong baselines. Contemporary implementations pair TS with constraint-aware neighborhoods or embed instance-specific neighborhoods learned from data to reduce cycling and improve the intensification/diversification balance. Conceptual surveys still frame best practices for hybrid design [32].
• Large-neighborhood search (LNS) and learning-enhanced LNS. LNS “destroy-and-repair” is particularly effective under tight timing constraints. Recent neural LNS variants use deep networks (often graph-based) to propose destroy sets or repair decisions, yielding large speed/quality gains across combinatorial problems and increasingly in scheduling [34].
• Hyper-heuristics (rule selection/generation). Instead of solving a schedule directly, hyper-heuristics learn which heuristic to deploy when. A recent line uses deep reinforcement learning (DRL) hyper-heuristics to select operators on-the-fly, improving generalizability across shop configurations [26,35].
• Learning-assisted parameter control & initialization. Reviews highlight the benefit of machine-learned parameter schedules, warm-starts, and population initializers to stabilize metaheuristics on high-variance instance distributions—especially for multi-objective settings [7].

Overall, the trend is clear: state-of-the-art metaheuristics increasingly embed learned guidance (policies, surrogates, or predictors) while retaining the robustness and portability that made them dominant in practice [7,32].

2.2.2. Decomposition and Parallelization

Decomposition breaks a monolith into solvable parts; parallelization exploits modern hardware and solver frameworks. Together they are the main levers for scaling exact and hybrid methods.

• Logic-Based Benders Decomposition (LBBD). LBBD separates combinatorial assignment/sequence decisions (handled by CP/MIP/heuristics) from schedule-feasibility subproblems, iteratively exchanging powerful logic cuts. Recent papers demonstrate strong performance on flexible/distributed job-shops and highlight modeling patterns and cut design that make LBBD competitive on industrial testbeds [36,37].
• Hierarchical/rolling-horizon schemes. Multi-level decompositions—e.g., plan vs. schedule, coarse time windows vs. fine sequencing—remain essential when the full horizon is prohibitive. Newer work integrates domain constraints from chemical/process systems and uses decomposition to keep digital-twin/CP models responsive at runtime; learning-guided rolling horizons are emerging to adapt window sizes and priorities on the fly [38,39].
• Dantzig–Wolfe/column generation and branch-and-price. Modern implementations in open frameworks (e.g., SCIP/GCG) expose decomposition hooks, enabling practitioners to combine exact and heuristic components and to scale on shared/distributed memory [40].
• Parallel solver ecosystems. Documented advances from 2001 to 2020 show order-of-magnitude speedups from algorithmic and hardware progress; contemporary suites include UG, a unified framework for parallelizing branch-and-bound/price/cut across cores and clusters. These capabilities benefit both pure MIP/CP scheduling and hybrid MH+MIP workflows [40,41].

Pragmatically, decomposition + parallelization are how many plants deploy provably strong methods within real wall-clock limits, and they combine naturally with the AI techniques below (e.g., learned cut/branching within a decomposed master) [41].

2.2.3. AI-Driven and Data-Driven Methods

AI brings policy learning, structure learning, and fast approximations—often on graph representations of shops—and is the most active area since 2020.

• Deep reinforcement learning (DRL) for dispatching and end-to-end scheduling.

  ○

  Learned dispatching rules. GNN-based DRL learns to choose the next operation/machine given a disjunctive-graph state, outperforming hand-crafted rules and transferring to larger instances [8].

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  Systematic evidence (2022–2024). Surveys map model choices (GNNs, attention/transformers), training regimes, robustness/generalization gaps, and industrial case studies—useful for selecting architectures and evaluation protocols [26,27,35].

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  Digital-twin–in-the-loop training and deployment. Coupling DRL with twins improves sample efficiency and safety prior to shop–floor rollout [42].

• Learning-augmented optimization (L4CO) for exact solvers.

  ○

  Cut selection via RL/imitation. DRL policies for cutting-plane selection in MILP and successors (2020–2024) reduce nodes/time across instance families; these techniques directly accelerate large MIP/CP models of scheduling [43,44,45].

  ○

  Learned branching/diving and node selection. Neural policies guide B&B traversal and primal heuristics, improving primal-dual gaps and anytime behavior on real MIP workloads [7,46].

• Neural Large-Neighborhood Search (Neural-LNS). Deep networks propose destroy/repair actions within LNS, maintaining metaheuristic scalability while injecting structural priors [34].
• Supervised and interpretable learning of rules/policies. Data-driven mining of dispatching rules from near-optimal schedules and interpretable learned rules (e.g., sparse/structured models) offer transparent alternatives for regulated environments—often used to warm-start DRL or guide MH neighborhoods [33].
• Surrogate-assisted optimization. ML surrogates approximate expensive objective/simulation evaluations (e.g., multi-objective, dynamic shops), enabling deeper search within fixed time budgets and stabilizing online rescheduling [26,33].
• Foundation-model ideas (early stage). “LLMs as optimizers” (OPRO) and LLM-guided search/planning are being tested as meta-controllers—suggesting heuristic templates or operator sequences that a solver or metaheuristic then refines. While nascent, this strand aims at zero-/few-shot generalization across plants and products [7,31].

In short, the most effective recent systems are hybrids: a decomposed/parallel exact core or robust metaheuristic scaffold, augmented by learning (DRL policies, neural destroy/repair, learned cuts/branching, surrogates) to navigate huge decision spaces under tight time limits [40,41].

Table 1. Comparative Analysis of Recent Methods for Scalability in Industrial Scheduling.

Approach	Core Strengths	Limitations	Typical Application Areas	Representative References
Genetic algorithms & memetic hybrids	Flexible; multi-objective ready; easy to hybridize with local search/repair; robust on heterogeneous constraints	Parameter tuning; stochastic variance; may plateau without strong neighborhoods	Parallel/flow/flexible job shops; sequence-dependent setups; large unrelated-machine problems	[32,33]
Simulated annealing/Tabu search	Simple and effective baselines; good intensification/diversification; easy to embed constraints	Cooling/tenure sensitivity; may require problem-specific neighborhoods	Job/flow shops; batching; setup-heavy sequencing	[32]
Large-neighborhood search (LNS)/Neural-LNS	Powerful destroy–repair exploration; learned destroy/repair improves speed & quality; anytime behavior	Designing repairs that preserve feasibility; training data/compute for neural variants	High-mix shops; near-real-time improvement; rolling re-optimization	[34]
Hyper-heuristics (selection/generation)	Generalizes across instance types; automates rule choice; compatible with DRL	Performance ceiling if candidate pool is weak; requires meta-level data	Mixed-model production; variable routing/loads	[26,35]
Logic-Based Benders Decomposition (LBBD)	Strong logic cuts; separates assignment/sequence from timing; integrates CP/MIP/heuristics	Modeling effort; cut engineering; potential many iterations	Flexible/distributed job shops; process/chemical scheduling	[36,37,38,39]
Hierarchical/rolling-horizon schemes	Scales long horizons; aligns with planning → scheduling tiers; supports simulation-in-the-loop	Coordination overhead; myopic decisions if horizons too short	Plant-level planning with shop–floor dispatch; digital-twin what-if analysis	[38,39]
Column generation/branch-and-price frameworks	Decompose by columns/routes; strong bounds; mix with heuristics	Pricing complexity; stabilization needed; parallelization non-trivial	Large machine/route generation models; transportation–production links	[40,41]
Parallel solver ecosystems	Multicore/cluster speedups; parallel B&B/price/cut (UG); mature tooling	Needs HPC resources; solver engineering expertise	Large MIP/CP scheduling; scenario-decomposed planning	[40,41]
DRL dispatching policies (GNN/attention)	Learns size-agnostic rules; reacts online; strong anytime performance	Sample efficiency; stability/robustness; policy explainability	Dynamic job/flexible job shops; real-time dispatch	[22,26,27,35]
Learning-augmented optimization (ML for OR)	Learned branching/cuts/node selection; warm-starts; improves primal-dual gaps	Generalization across distributions; integration into certified workflows	Large MIP/CP scheduling; hybrid MH+MIP stacks	[7,45,46]
Surrogate-/supervised rule learning	Fast evaluations; interpretable policies; good for high-volume data	Surrogate bias; retraining under drift; limited exploration	Repetitive/flow environments; KPI-specific rule mining	[33]
Digital twin–in-the-loop RL	Safe policy training; proactive, state-aware rescheduling; sim-to-real transfer	Twin fidelity/sync cost; integration complexity	Smart factories; semiconductor/assembly lines	[42]
Foundation-model–guided heuristics (OPRO)	Rapid heuristic design/tuning; few-shot adaptability; complements DRL/OR	Very early stage; needs feasibility guards and evaluation harness	Rapid ramp-up for new product mixes/lines	[7,31]

summarizes the above-described methods from a scalability point of view.

2.3. Industrial Impact

The adoption of scalable scheduling methods has produced tangible benefits across manufacturing and service operations. In high-mix job/flow shops, robust metaheuristic baselines—often hybridized with local improvement and problem-aware neighborhoods—continue to reduce lead times and work-in-process while maintaining schedule feasibility under complex constraints [32,33]. Learning-enhanced search further expands this impact: neural large-neighborhood search and related hybrids provide fast, high-quality improvements under tight decision latencies, a pattern now being translated from routing to production scheduling settings [7,34].

Different families of scalable scheduling methods demonstrate complementary strengths and limitations, which shape their suitability for industrial settings. Metaheuristics and hybrid search approaches, such as large neighborhood search or hyper-heuristics, provide robust anytime performance and are relatively easy to tailor to specific factory constraints. However, their reliance on parameter tuning and instance-dependent calibration can limit reproducibility across sites. Decomposition and parallelization strategies, including logic-based Benders decomposition, column generation, and parallel branch-and-bound, achieve strong theoretical performance and predictable convergence, but demand more sophisticated modeling skills and significant computational resources. Finally, AI- and data-driven methods such as reinforcement learning, surrogate modeling, or learning-assisted branching policies offer reactive decision support and promising integration with digital twins, but they raise concerns related to data availability, robustness under disturbances, and explainability for operators. In practice, industrial deployments often combine these families: decomposition or metaheuristics ensure feasibility and global performance, while learning-based modules accelerate convergence or provide reactive adaptation in dynamic shop floors.

For large, highly constrained plants (e.g., semiconductor wafer fabs and flexible job shops), decomposition and parallel solver ecosystems have been crucial. Logic-based Benders and related decompositions separate assignment/sequence choices from timing feasibility, enabling strong cuts and subproblem specialization; reported results on flexible/distributed job shops show competitive anytime performance with reliable convergence behavior [36]. In parallel, advances in MILP/CP solver engineering and HPC frameworks—particularly unified parallelization of branch-and-bound/price/cut—have delivered order-of-magnitude speedups over the last two decades, narrowing the gap between optimality guarantees and industrial wall-clock deadlines [40,41]. In wafer-fab settings, such tooling integrates naturally with established production-planning and dispatching practices [47].

AI-driven approaches increasingly complement these stacks. Deep reinforcement learning (DRL) policies trained on disjunctive-graph representations learn size-agnostic dispatching rules that generalize to larger instances and volatile shop conditions; systematic reviews report consistent gains in tardiness, throughput, and resilience across testbeds [22,26,27]. Digital-twin–in-the-loop scheduling strengthens the path to deployment: twins enable safe policy training and allow proactive, state-aware rescheduling once online [28], aligning with the broader shift toward cyber-physical production systems and IIoT platforms [12,48].

Despite these advances, important gaps remain for industrial adoption. Stakeholders frequently request interpretable, auditable decision logic—especially in regulated domains—driving interest in interpretable rule learning and hybrid DRL+rule designs [33]. Multi-objective trade-offs (e.g., service, energy, emissions) are increasingly prominent, calling for methods that deliver scalable, explainable Pareto policies and that remain stable under distribution shift [26,27]. Finally, realizing end-to-end impact requires reliable data/compute infrastructure—edge/cloud orchestration, streaming quality control, and human-in-the-loop decision support [16,48]. Bridging these elements—decomposition and parallel solvers, learning-augmented heuristics, digital twins, and human-centered interfaces—will continue to move scalable scheduling from research prototypes to robust, real-time industrial decision systems.

In the following we focus on ready-made tools as well as a representative industrial case.

2.3.1. Ready-Made Tools and Integration Capabilities

Several off-the-shelf tools are available that embody these approaches and offer different trade-offs for industrial integration. Solver frameworks such as SCIP and CPLEX provide reliable large-scale optimization engines with interfaces for decomposition and parallel execution, though they require expertise in mathematical programming and high-performance computing environments for maximum effect. General-purpose metaheuristic frameworks such as OptaPlanner or Google OR-Tools are widely used in manufacturing scheduling because of their open-source accessibility, flexible modeling, and integration with enterprise systems through RESTful APIs, but their solution quality depends strongly on configuration. Reinforcement learning libraries like Ray RLlib and open-source scheduling environments such as JobShopGym enable rapid prototyping of AI-driven scheduling policies, particularly when paired with digital twins for safe training and validation. Their disadvantages lie mainly in the engineering burden of data pipelines, model maintenance, and the need for feasibility safeguards before deployment. Importantly, all of these tools increasingly support standard integration hooks such as Python APIs, containerization, and OPC UA/AAS connectors, which facilitate embedding optimization modules into existing MES or cloud–edge manufacturing stacks.

2.3.2. Representative Industrial Case

A published industrial study by Park et al. demonstrates a digital-twin–in-the-loop reinforcement learning controller deployed in a micro smart factory, replacing a heuristic dispatching rule while preserving feasibility through twin-synchronized checks [49]. The digital twin (Siemens Plant Simulation) generated event logs for training a dueling-network policy; the learned policy was then integrated back into the twin and the shop control loop via AAS-style service interfaces. In controlled experiments with reconfiguration events and dynamic disturbances, the RL+DT controller improved makespan by 2.6–4.6%, reduced the standard deviation of cycle time by 6.5–17.5%, and cut deadlock cases by 9.7–23.5% versus the incumbent rule, while maintaining schedule robustness under resource additions and reactive rescheduling. The case highlights practical adaptations—action-masking for feasibility, twin-based validation before rollout, and a cloud–edge integration pattern—illustrating how learning augments scalable search to yield measurable KPI gains in a real manufacturing setting.

3. Robustness and Adaptability to Uncertainty

3.1. The Prevalence of Uncertainty in Industrial Scheduling

Industrial environments are rife with uncertainties—machine breakdowns, unpredictable processing times, urgent rush orders, supply-chain disruptions, and human factors, to name a few [9,50]. Traditional static schedules, even if optimal under assumed conditions, often falter when such disturbances arise, leading to inefficiencies, missed deadlines, and costly rework [1]. As systems scale and markets become more volatile, robust and adaptive scheduling becomes imperative. The digital transformation of operations increases both the visibility of stochastic dynamics and the opportunities to respond. High-frequency streams from shop–floor sensors and Manufacturing Execution System (MES)/Enterprise Resource Planning (ERP) logs enable online detection of anomalies, delay predictions, and the learning of proactive control policies. Recent advances—deep reinforcement learning (DRL), graph neural networks (GNNs), neural surrogates, and digital-twin-in-the-loop training—are pushing beyond fixed “robust plans,” enabling continuous, data-driven adaptation under uncertainty while preserving computational tractability [27,28,42].

3.2. Recent Methodological Developments

Efforts to increase robustness and adaptability fall into three main streams: robust optimization; stochastic/probabilistic modeling; and real-time, predictive, and reactive scheduling. Below we summarize key ideas, with an emphasis on post-2020 developments and AI-enabled techniques.

3.2.1. Robust Optimization

Robust optimization explicitly models uncertainty and seeks schedules that perform well across a range of realizations [23,51]. In modern deployments, robust models are often hybridized with learning components for forecasting, dynamic parameterization of uncertainty sets, or warm-starting.

• Min–max and min–max regret formulations. These guard against worst-case or worst-regret scenarios—useful where delivery penalties or rework costs are high [52]. While conservative, recent practice tunes uncertainty budgets to balance robustness and performance, often informed by empirical variance estimates extracted from shop data [23].
• Adjustable robust optimization (ARO). Defers part of the decision (e.g., dispatching, batching) until information is revealed, improving adaptability versus static designs [53]. Rolling-horizon ARO for job shops with uncertain processing times demonstrates strong performance under continuous disturbances [54].
• Interval/set-based uncertainty. Interval activity durations and release dates yield tractable robust counterparts and are attractive in regulated or contract-driven environments; hybrid robust approaches for projects exemplify this trend [55].
• Learning-in-the-loop robust models. Robust parameters (e.g., uncertainty budgets, scenario weights) can be calibrated from historical trace data or forecasts and periodically retuned; neural surrogates speed robust evaluation when embedded inside metaheuristics or rolling-horizon loops [28].

3.2.2. Stochastic and Probabilistic Modeling

Stochastic models represent uncertainty via probability distributions or stochastic processes and optimize expectations, risk measures, or violation probabilities [1,56].

• Chance-constrained scheduling. Constraints (e.g., due-date adherence) are enforced with high probability, enabling explicit trade-offs between service levels and efficiency [56]. In data-rich plants, estimated distributions are kept up to date from streaming data and predictive models.
• Markov decision processes (MDP). MDP formulations capture sequential uncertainty and state transitions. For job-shop settings with stochastic processing times, MDPs provide a principled foundation and also underpin modern DRL policies [57,58].
• Simulation-based evaluation and design. Monte Carlo/discrete-event simulation (DES) remains essential when analytic tractability is limited. It supports proactive design of robust schedules, stress-tests rollout policies, and serves as a safe training ground for learning-based controllers [24,47].

3.2.3. Real-Time, Predictive, and Reactive Scheduling

These approaches adapt schedules dynamically in response to real-time information, disturbances, or new job arrivals. Recent work blends classical repair/rolling-horizon controls with DRL, GNNs, and digital twins.

• Rescheduling and repair algorithms. Minimal-perturbation repairs stabilize operations after disruptions, reducing shop–floor turbulence. Frameworks and taxonomies remain highly relevant [24,25], and are increasingly combined with learned predictors of disruption impact to prioritize repairs.
• Rolling-horizon and event-driven updates. Periodic or event-triggered reoptimization integrates naturally with MES/ERP. State-of-practice implementations use hierarchical decompositions and fast heuristics/MIP models, often parallelized, to refresh plans at high cadence [24,59].
• Predictive analytics and machine learning. Supervised models forecast delays, failures, and congestion; DRL agents learn dispatching policies that generalize across shop states. Reviews synthesize model choices (GNNs, attention/transformers), training regimes, and robustness/generalization gaps [27,60].
• Digital-twin-in-the-loop decision-making. Twins provide high-fidelity simulators for safe testing and sample-efficient training/deployment of real-time policies [8,28].
• Multi-agent and self-organizing control. Decentralized agent-based frameworks enhance resilience by localizing decisions while coordinating globally through negotiation/market or contract-net mechanisms—well aligned with cyber-physical production systems [61,62].
• End-to-end AI stacks at scale. In practice, the strongest systems are hybrids: fast decomposed MIP/CP or robust metaheuristics at the core, augmented by DRL policies, learned repair operators, neural surrogates, and digital twins to navigate vast decision spaces under tight time limits [27,63].

Table 2. Comparative Analysis of Methods for Robustness and Adaptability in Industrial Scheduling.

Approach	Core Strengths	Limitations	Typical Application Areas	Representative References
Min–max & Min–max Regret Robust Optimization	Strong guarantees; interpretable; protects against penalties	Conservative; scalability issues with large scenario sets	Semiconductor fabs, aerospace, contract manufacturing	[23,52]
Adjustable Robust Optimization (ARO)	Balances robustness and flexibility; realistic for dynamic shops	More complex; heavier computation	Job shops with uncertain processing times	[53,54]
Interval/Set-Based Models	Tractable; practical for bounded uncertainties	Can yield conservative schedules	Project-driven and regulated industries	[55]
Learning-in-the-loop Robust Models	Adaptive; efficient evaluation; improves robustness	Requires quality data; explainability issues	Flexible manufacturing, online scheduling	[28]
Chance-Constrained Scheduling	Balances service levels vs. efficiency; intuitive	Relies on accurate distribution estimation	Service industries, logistics, large projects	[56]
Markov Decision Processes (MDP)	Principled sequential control; foundation for DRL	Curse of dimensionality for large systems	Stochastic job shops, batch processes	[57,58]
Simulation-Based Evaluation (DES/Monte Carlo)	Flexible; captures complex interactions; supports stress-testing	Computationally expensive	Semiconductor, project-based, high-uncertainty industries	[24,47]
Rescheduling & Repair Algorithms	Stable shop floor behavior; minimal disruption	Myopic if frequent disruptions occur	MES/material requirements planning (MRP) systems, dynamic job shops	[24,25]
Rolling-Horizon/Event-Driven Updates	Continuous adaptation; ERP/MES integration	Risk of nervousness with frequent updates	High-mix, volatile production	[24,59]
Predictive Analytics & ML	Data-driven; real-time adaptability; generalizable policies	Data hungry; legacy integration challenges	Smart factories, flexible electronics	[27,60]
Digital-Twin-in-the-Loop Scheduling	Safe training/testing; improves sample efficiency	Twin fidelity/synchronization cost	Intelligent manufacturing, reconfigurable factories	[22,28]
Multi-Agent & Self-Organizing Systems	Resilient; scalable; fault-tolerant	Coordination and global optimality issues	Cyber-physical production, distributed factories	[61,62]
End-to-End AI Stacks at Scale	Hybrid performance; scalable and adaptive under real-time constraints	Engineering complexity; integration & MLOps challenges	Large-scale Industry 4.0, smart factories	[27,63]

summarizes the above-described methods from the point of view of robustness and adaptability in industrial scheduling.

3.3. Industrial Impact

Research advances in robust and adaptive scheduling are rapidly transferring to industrial practice, enabled by Industry 4.0 and the ubiquitous digitization of factory environments. In capital-intensive domains such as semiconductor fabrication, aerospace, and high-value custom production, robust and stochastic scheduling is increasingly applied to mitigate the high costs of rescheduling and downtime [47,64]. Robust optimization models and stochastic formulations provide effective safeguards against disruptions, particularly where contractual service levels and reliability are critical.

Robust and adaptive scheduling methods each offer distinct advantages and limitations depending on the type of uncertainty faced in industrial environments. Robust optimization approaches deliver conservative solutions that guarantee feasibility across worst-case scenarios, making them particularly suitable for high-reliability settings such as semiconductor manufacturing or aerospace supply chains. However, the associated performance loss in typical scenarios can be considerable. Stochastic programming and chance-constrained formulations provide a more balanced approach by integrating probability distributions of disruptions but demand accurate and up-to-date data that is not always available. Rolling horizon and rescheduling frameworks excel in environments with continuous disturbances, allowing schedules to be repaired incrementally, but they may sacrifice long-term optimality for short-term feasibility. Finally, digital-twin-based adaptive scheduling demonstrates strong potential by enabling proactive simulations and learning-based adaptation; yet, its success hinges on model fidelity and seamless data synchronization. Industrial deployments increasingly combine these methods, for example, by embedding robust baselines within a rolling horizon framework or using a digital twin to test stochastic or learning-based repair strategies before execution.

In highly dynamic industries—food processing, agile automotive, and flexible electronics—reactive and predictive scheduling algorithms are being integrated into manufacturing execution systems. These enable reductions in downtime, service-level improvements, and higher equipment utilization through predictive analytics and real-time reoptimization [47]. Data-driven methods such as DRL-based dispatching and neural surrogate models have been especially effective in managing uncertainty while respecting tight time constraints, with successful demonstrations in flexible job shops and assembly lines [27].

Decentralized and multi-agent scheduling approaches are also gaining traction. When combined with digital twins, these methods enhance resilience by localizing decisions and enabling distributed coordination across smart factories. Recent studies demonstrate robust multi-agent control architectures that remain stable under frequent disturbances and scale effectively in cyber-physical production systems [61,62]. Hybrid architectures—where metaheuristics, robust optimization, and multi-agent systems are augmented by real-time predictive analytics—are increasingly deployed in pilot Industry 4.0 testbeds, particularly for smart logistics and reconfigurable assembly [28,64].

Despite these gains, several open challenges remain. Balancing robustness and performance efficiency is non-trivial, as overly conservative schedules may reduce throughput. Methods for uncertainty quantification and explainability of AI-driven approaches are not yet standardized, raising adoption barriers. Data privacy and cybersecurity risks emerge as predictive and decentralized systems rely heavily on shared sensor and cloud data. Finally, interoperability across platforms and legacy systems limits the seamless deployment of self-organizing, multi-agent scheduling frameworks. Addressing these issues—alongside creating benchmarks and human-in-the-loop control paradigms—will be central to advancing industrial adoption.

In the following we focus on ready-made tools as well as a representative industrial case.

3.3.1. Ready-Made Tools and Integration Capabilities

Several tools exist that embody these robustness-oriented methods and can be integrated into production IT environments. Commercial solvers such as IBM ILOG CPLEX and Gurobi now support stochastic and chance-constrained programming, offering flexibility for uncertainty-aware planning, though at the cost of higher model complexity and longer runtimes. Open-source packages such as PySP (part of Pyomo) provide structured interfaces for stochastic programming, lowering the entry barrier for researchers and SMEs, but integration with real-time data streams requires additional engineering. For adaptive strategies, Simio and AnyLogic simulation platforms offer digital-twin capabilities with APIs that allow schedulers to interact with live shop–floor data; their disadvantage is a higher licensing and maintenance cost. Reinforcement learning toolkits such as Ray RLlib are also being increasingly applied to adaptive rescheduling tasks, and while they enable scalable training in dynamic environments, they demand expertise in MLOps and require feasibility guards when interfacing with MES systems. Across all these tools, the emerging trend is containerized deployment with OPC UA or AAS connectors, which supports modular integration of robust or adaptive schedulers into hybrid cloud–edge manufacturing stacks.

3.3.2. Representative Industrial Case

A recent study by Wang et al. presents a dynamic and robust scheduling approach for a distributed flexible job shop subject to random job arrivals and machine breakdowns, using a discrete improved gray wolf optimization (DIGWO) algorithm [65]. Their framework was tested on large-scale scenarios with 360 jobs initially released and 350 additional jobs arriving dynamically, alongside stochastic machine failures across two factories. To enhance robustness, DIGWO incorporated adaptive neighborhood structures and memory-guided repair operators, allowing it to adjust schedules on-the-fly when disruptions occurred. Compared with baseline heuristics and multi-objective evolutionary algorithms (NSGA-II, SPEA2, MOEA/D), DIGWO demonstrated measurable improvements in several key performance indicators: average tardiness decreased by 15–25%, makespan improved by 5–10%, maximum factory load imbalance was reduced by 10–20%, and schedule stability increased by 10–18% under disruption conditions. These results illustrate how robustness-oriented adaptations of metaheuristics can balance efficiency and resilience, offering both superior KPI performance and enhanced adaptability in highly dynamic shop–floor environments.

4. Integration with Digitalization and Industry 4.0

4.1. Industrial Scheduling in the Age of Digital Transformation

The advent of Industry 4.0 has fundamentally altered the landscape of industrial scheduling. Modern enterprises are increasingly interconnected, harnessing the Industrial Internet of Things (IIoT), big data analytics, digital twins, and cyber-physical systems (CPSs) to create adaptive and autonomous shop floors [11,66]. In these data-rich and sensor-driven environments, scheduling is no longer a static, offline optimization task but a dynamic, real-time decision process seamlessly embedded within production execution systems [67,68].

This digital transformation introduces new requirements and opportunities. Scheduling algorithms must now:

• rapidly process high-frequency streaming data from sensors and MES/ERP logs;
• interact with intelligent machines and human operators in collaborative CPSs;
• adapt autonomously to both predicted and unforeseen disruptions.

Crucially, these systems must be interoperable with digital infrastructures, including ERP, MES, cloud, and edge computing platforms, while guaranteeing security and scalability in complex industrial environments [69].

Recent advances in AI and deep learning are reshaping this integration. Deep reinforcement learning (DRL) and graph neural networks (GNNs) are being deployed for real-time dispatching and predictive rescheduling, exploiting the graph-structured nature of job-shop networks [27]. Transformer-based architectures further enhance forecasting accuracy by capturing temporal dependencies in machine states and job arrivals [70]. Meanwhile, digital twin-driven scheduling frameworks enable closed-loop learning, where algorithms are trained and validated against high-fidelity virtual replicas before being deployed on the shop floor [71].

Another important development is the emergence of cloud–edge collaborative scheduling: heavy optimization tasks are solved in the cloud, while real-time adjustments are delegated to lightweight edge agents co-located with machines [72]. This architecture improves responsiveness while ensuring that AI-powered schedulers remain scalable across global production networks.

Altogether, industrial scheduling in the digital era is moving toward autonomous, learning-enabled ecosystems that blend optimization, machine learning, and distributed digital infrastructures. This convergence represents both the core opportunity and central challenge of scheduling in Industry 4.0.

4.2. Recent Methodological Developments

4.2.1. Data-Driven Scheduling and Real-Time Data Integration

The exponential increase in accessible, high-quality process data within modern industrial environments has enabled new classes of scheduling algorithms that leverage real-time information for greater agility and responsiveness.

• Sensor-Enabled, Closed-Loop Scheduling. Modern shop floors, equipped with IIoT sensors and CPSs, continuously generate streams of data on machine status, job progress, and environmental conditions. Scheduling algorithms can now operate in closed-loop mode, where feedback from the shop floor directly drives updates to production plans [11,69]. These approaches improve agility but also raise challenges in data quality assurance, latency management, and interoperability with legacy systems. Emerging solutions apply streaming analytics and lightweight deep models at the edge to process sensor inputs in milliseconds.
• Digital Twin-Based Scheduling. Digital twins (DTs)—virtual replicas of physical systems—are increasingly central to scheduling in Industry 4.0. DTs mirror the current shop state and can simulate disruptions, evaluate dispatching rules, and test repair strategies before they are deployed on the shop floor. This enables dynamic rescheduling, what-if analysis, and proactive maintenance scheduling [73,74]. Recent work links DTs with reinforcement learning agents, providing safe training environments where policies are stress-tested virtually before live deployment [28].
• Cloud and Edge Computing for Distributed Scheduling. Cloud-based scheduling platforms offer scalable cooperative optimization, supporting multi-plant and supply-chain-level scheduling tasks with heavy computation offloaded to distributed clusters [66]. In contrast, edge computing brings intelligence closer to the shop floor, enabling low-latency rescheduling in response to real-time events [72]. Hybrid cloud–edge architectures are gaining traction, where global optimization runs in the cloud while local edge agents handle immediate decisions, balancing responsiveness and scalability.

Together, these data-driven paradigms are shifting industrial scheduling from static planning to adaptive, self-correcting ecosystems capable of handling volatility at scale.

4.2.2. Autonomous, Intelligent, and Decentralized Scheduling

The integration of advanced artificial intelligence and distributed control frameworks is transforming scheduling decisions, fostering systems capable of high autonomy, self-adaptation, and decentralized negotiation.

• Agent-Based and Multi-Agent Scheduling Systems: Autonomous software agents (machines, cells, workpieces) negotiate job allocations and routing independently, supporting decentralized, modular scheduling architectures aligned with flexible manufacturing systems [62,75]. Recent advances leverage digital twins [74] and multi-agent reinforcement learning (MARL) [67] to enhance negotiation, coalition formation, and adaptive learning for global performance.
• Self-Optimizing and Adaptive Control Algorithms: Self-optimizing scheduling algorithms continuously adapt parameter values, decision rules, or objectives in light of new data or predicted disturbances [68]. Deep reinforcement learning methods such as multi-agent dueling DRL [76], graph-based MARL [77], and hierarchical MARL [65] are enabling scalable and resilient scheduling in dynamic environments.
• Emerging Architectures: Knowledge-graph-enhanced MARL [78], attention-based coordination [79], and decentralized training strategies [80] represent next-generation paradigms, further strengthening adaptability and autonomy in Industry 4.0 scheduling.

4.2.3. Interoperability, Standardization, and Security

The effectiveness of digitalized scheduling also hinges on robust interface design, standardized interoperable frameworks, and secure handling of the growing volume and variety of critical scheduling data exchanged across industrial networks.

• Interoperable Architectures. Modern scheduling stacks integrate with heterogeneous ERP/MES/SCM ecosystems via standardized information models and open APIs. OPC UA–centric service models and Asset Administration Shell (AAS)–based dataspace connectors enable plug-and-operate exposure of machine capabilities and scheduling services across sites and partners—supporting decentralized optimization and rapid reconfiguration [81,82].
• Semantically Enriched, AI-Ready Data Layers. Knowledge-graph and model-driven integration (e.g., KG-backed twins, auto-generated data collection architectures) provide a common vocabulary across planning, dispatching, and control. This boosts data quality and feature consistency for deep learning and RL schedulers, shortens data engineering cycles, and improves cross-system explainability [83,84].
• Security and Data Provenance. As scheduling moves onto IIoT/cloud fabrics, compliance-by-design with ICS/IIoT security baselines (e.g., IEC 62443 mappings, NIST ICS guidance) is essential. End-to-end provenance and tamper-evident audit trails—sometimes blockchain-anchored and paired with ML for predictive auditing—help ensure integrity, confidentiality, and traceability of schedule decisions and event logs across organizational boundaries [85,86,87,88].
• Data Sovereignty & Federated Collaboration (added). Dataspace-oriented integration (AAS + policy-enforced connectors) supports inter-company scheduling use cases (capacity sharing, subcontracting) while retaining usage-control over shared datasets and learned models—key for privacy-preserving, multi-party optimization [82].
• Operational Hardening for AI-Driven Scheduling (added). As DL/RL components enter the loop, interface standards and security controls must extend to model artifacts and pipelines (versioned data/model registries, signed inference services, and policy-aware event buses), ensuring reproducibility and trustworthy deployment in time-critical rescheduling scenarios [81,86].

Table 3. Comparative Analysis of Methods for Integration with Digitalization and Industry 4.0.

Approach	Core Strengths	Limitations	Typical Application Areas	Representative References
Sensor-Enabled, Closed-Loop Scheduling	Real-time responsiveness; immediate adaptation to shop–floor events; integration of IIoT/CPS data streams	Data quality and latency challenges; integration with legacy systems; requires robust edge analytics	High-variability shop floors; condition-based rescheduling; flow-shop monitoring	[11,69]
Digital Twin-Based Scheduling	Virtual experimentation; safe training/testbed for RL agents; proactive rescheduling and predictive maintenance	High development and synchronization costs; computationally intensive	Job-shop/flexible shop scheduling; disruption management; predictive control	[73,74]
Cloud and Edge Computing for Distributed Scheduling	Scalable optimization (cloud); low-latency local response (edge); hybrid setups balance global and local	Security and data-transfer overhead; partitioning optimization tasks is complex	Multi-plant coordination; distributed supply chains; real-time edge rescheduling	[66,72]
Agent-Based and Multi-Agent Scheduling Systems	Decentralization, modularity, and negotiation capabilities; well-suited to flexible manufacturing	Coordination overhead; global optimality hard to guarantee	Flexible job-shop systems; distributed resource allocation	[62,64,75]
Self-Optimizing and Adaptive Control Algorithms	Continuous adaptation to data and disturbances; reinforcement learning and heuristic evolution enable resilience	Sample inefficiency in RL; difficulty in explainability; requires large/high-quality datasets	Dynamic job-shop scheduling; mass personalization; adaptive planning	[65,68,76,77]
Emerging Architectures (KG-MARL, attention-based, decentralized training)	Enhanced context-awareness; improved coordination; scalable decentralized learning	Complexity of design; limited industrial deployments; integration with legacy IT/OT	Smart manufacturing scheduling; dynamic flow/assembly shops	[78,79,80]
Interoperable Architectures (OPC UA, AAS, open APIs)	Seamless integration across ERP/MES/SCM; supports plug-and-operate scheduling services	Requires ecosystem-wide standard adoption; potential vendor lock-in	Multi-system integration; cross-site scheduling; Manufacturing-X initiatives	[81,82]
Semantically Enriched, AI-Ready Data Layers	Standard vocabulary for heterogeneous data; improves explainability and feature quality for DL/RL	Knowledge graph development overhead; ontology alignment challenges	Digital twins; predictive scheduling; cross-enterprise scheduling	[83,84]
Security and Data Provenance	Ensures integrity, confidentiality, and traceability of scheduling data; supports compliance (IEC 62443, NIST)	Added overhead in performance; blockchain solutions not yet fully scalable	Regulated supply chains; critical infrastructures; cloud manufacturing	[85,87,88]
Data Sovereignty & Federated Collaboration	Policy-enforced data sharing across organizations; supports privacy-preserving optimization	Governance complexity; interoperability still evolving	Inter-company scheduling; collaborative supply chains; subcontracting	[82]
Operational Hardening for AI-Driven Scheduling	Secure and reproducible ML pipelines; signed model artifacts; trustworthy rescheduling	Requires ML lifecycle governance; raises infrastructure complexity	AI-driven job-shop scheduling; cloud–edge rescheduling services	[81,86]

summarizes the above-described methods addressing the integration with digitalization and Industry 4.0.

4.3. Industrial Impact

Digitalization is reshaping the production floor from plan–execute to sense–decide–adapt loops. Real-time sensor streams fused into digital twins (DTs) are shortening the time from deviation to decision: shops detect anomalies earlier, evaluate counterfactuals virtually, and deploy schedule repairs with less risk. Demonstrations in discrete manufacturing show DT-driven anomaly detection and rolling-window rescheduling that cut response latency and improve throughput; complementary work uses DTs to train RL agents safely for dispatching and policy control before go-live—key for automotive, electronics, and high-value custom manufacturing where disruptions and mix variability are high [74,89,90].

The field of operational integration—tying together optimization, digital twins, communication standards, and edge/cloud architectures—has matured, with different architectural styles offering varying trade-offs. Fully centralized integration, where a cloud-hosted optimization engine drives global scheduling, can maximize resource utilization across plants but suffers from latency, reliability, and data privacy risks. Edge–cloud hybrid models distribute shorter-horizon scheduling and adaptation to edge nodes, which reduces decision-latency and improves resilience to network disruptions, but places greater burden on synchronization and consistency protocols. Standardized middleware (e.g., Asset Administration Shell (AAS) and Open Platform Communications Unified Architecture (OPC UA)) provide strong gains in interoperability and modularity, allowing plug-and-play scheduling agents and simpler replacement/upgrading, but they often require overcoming legacy systems and vendor lock-in. Digital twins (especially simulation- or discrete-event simulation (DES)-backed) enable validation, what-if analysis, and fallback control loops, but their fidelity, data sync lag, and maintenance cost can limit effectiveness. The most effective industrial systems balance these concerns: using standards for interoperability, deploying lighter optimization/AI at the edge, employing digital twins for backup/fallback and validation, and organizing scheduling agents in distributed or modular fashion so individual components can evolve without reengineering the whole stack.

At network scale, cloud–edge scheduling stacks are proving decisive. Cloud back-ends coordinate heavy optimization across plants and suppliers, while edge controllers execute fast, local rescheduling under machine/ automated guided vehicle (AGV); recent DT-enabled flexible job-shop deployments report real-time responsiveness with compute pushed to the edge and global plans synchronized from the cloud. This division of labor is now common in supply-chain-intensive sectors and multi-factory groups [66,91,92].

Decentralized and agent-based control is also moving from concept to impact. Industrial case work shows multi-agent system (MAS) + DT architectures that localize negotiation and routing while preserving global KPIs; in parallel, expert studies across production/supply networks identify concrete MAS use cases that lift resilience—e.g., autonomous replanning, distributed bottleneck mitigation, and exception handling—supporting modular, small-batch, and reconfigurable lines [93,94].

Finally, the diffusion of interoperability and security baselines is a practical accelerator. Asset Administration Shell (AAS) models and service interfaces are easing plug-and-operate integration of scheduling services with ERP/MES/CPS, while updated OT/ICS security guidance formalizes segmentation, provenance, and hardening requirements for IIoT-connected scheduling—critical for regulated sectors and cross-border collaboration [86,95]. Remaining blockers—data/model standardization, legacy coupling, and assurance of real-time decision quality at scale—are active research and deployment fronts [96]. Interoperability, security, and data sovereignty directly affect scheduling outcomes. Interoperability reduces decision latency by enabling faster integration of solvers and digital twins. Security safeguards support reliability by preventing downtime and manipulation of schedules. Data sovereignty mechanisms influence responsiveness, as timely access to cross-factory information determines how quickly schedules can adapt to disruptions. Linking these aspects to concrete KPIs highlights their industrial relevance.

In the following we focus on ready-made tools as well as a representative industrial case.

4.3.1. Ready-Made Tools and Integration Capabilities

A number of toolkits and frameworks support integration of scheduling, digital twins, and industrial control. The Asset Administration Shell (AAS) standard enables well-defined digital identities for physical assets, which simplifies interfaces and modular deployments but can be challenging to adopt fully in plants with mixed vendor equipment. OPC UA is often used to transport data in real time and connect MES (Manufacturing Execution Systems)/machine controllers/sensors with optimization or AI modules; its strong maturity and vendor support are positives, but latency/determinism/security concerns remain, especially for tightly constrained realtime control. Digital twin platforms and simulation engines (e.g., discrete-event simulation, DES) can be integrated to validate or train policies, perform what-if analyses, or detect bottlenecks; however, building and maintaining the twin (data collection, calibration, domain changes) impose overhead. Multi-Agent System (MAS) frameworks such as JANUS [93], Robot Operating System (ROS/ROS 2) for robotics-adjacent systems, etc., offer modular scheduling agent composition, event-driven orchestration, and scalability; but they introduce complexity (agent coordination, dead-locks, versioning) that must be carefully managed. User interface (UI)/human-in-the-loop tools are also components—managers must be able to inspect/override schedules, which implies transparency, clean logging, and simulation interfaces.

4.3.2. Representative Industrial Case

In Production Scheduling Based on a Multi-Agent System and Digital Twin: A Bicycle Industry Case [93], the authors present a tightly integrated scheduling stack applied to a real pilot in bicycle manufacturing, combining multi-agent controllers, a digital twin environment, and standardized information models (AAS) to enable interoperability and dynamic production decision support. Agents were deployed for different departments (painting line, wheel assembly) where scheduling decisions vary in horizon and constraints; the system allows managers to choose among scheduling agents via a UI, compare results, and deploy schedules, with the DT module validating decisions and detecting potential bottlenecks before execution. Empirical performance in the bicycle pilot showed that the scheduling-DT-MAS integration yielded a makespan reduction between ~2% and ~20% in the bike assembly department (worst to best scenarios) relative to the “as-is” baseline schedule, and a production rate increase of +1.4% to +9% per shift. These shifts in KPIs illustrate the value of integration: better coordination across departments, earlier detection of capacity bottlenecks, and the ability to switch among agent strategies dynamically, all enabled by digital twin feedback loops and standardized communication (AAS/OPC UA).

5. Conclusions and Research Directions

Industrial scheduling remains a cornerstone of modern operations yet continues to face three intertwined hurdles: (i) scaling to large, high-dimensional instances, (ii) staying robust and adaptive under uncertainty and disruptions, and (iii) integrating deeply with digitalization—IIoT, digital twins, cloud/edge, and secure interoperable ecosystems. Across these fronts, the past five years have seen notable progress: faster metaheuristics and decomposition, more mature rescheduling for real-time events, and increasingly “software-defined” factories where data and models flow among ERP/MES/SCM, device layers, and analytics stacks [66,97]. Still, industrial impact hinges on standardization, trust, and rigorous engineering of machine learning (ML)/operations research (OR) pipelines end-to-end [86,95].

A decisive shift is the rise in deep learning and deep reinforcement learning (DRL) as practical tooling for complex, dynamic scheduling. Recent work demonstrates: (1) policy learning that reacts in milliseconds to shop–floor events, (2) training “in the twin” to de-risk deployment, and (3) stronger generalization via graph-structured and attention-based models. Case studies now span semiconductor packaging, flexible job shops, and distributed production networks—where DRL outperforms rules/metaheuristics or offers comparable quality at much lower decision latency [89,96,98,99].

An emerging direction that deserves emphasis is the integration of human expertise with AI-driven scheduling in hybrid frameworks. In practice, such “operator + AI” setups are increasingly applied in manufacturing: optimization or reinforcement learning modules propose candidate schedules, while operators evaluate them against tacit knowledge such as maintenance priorities, safety constraints, or workforce availability. This human-in-the-loop design not only improves trust and acceptance but also addresses explainability and accountability requirements. Examples include digital-twin-enabled decision dashboards, where operators can simulate alternatives before deployment, and adaptive rescheduling systems that combine algorithmic speed with human judgment in exceptional cases. Strengthening these hybrid frameworks is likely to be a critical step for broader industrial adoption of advanced scheduling technologies.

Another prerequisite for industrial adoption, particularly in regulated environments, is interpretability of neural schedulers. Recent research explores techniques such as rule extraction, post hoc explanations (e.g., SHAP, LIME), and inherently transparent models (e.g., decision trees or attention-based graph networks) to make black-box policies more understandable to operators. These approaches enable decision-makers to verify why a schedule is selected, assess compliance with safety or labor regulations, and build trust in AI-generated recommendations. Combining explainability with hybrid or human-in-the-loop frameworks is likely to be essential for broader industrial deployment of neural schedulers.

Deep models are beginning to demonstrate clear value in several areas of industrial scheduling, most notably in the following domains:

• Policy learning for real-time decisions. DRL agents trained in simulation or digital twins learn dispatching, routing, and batching policies that scale to many machines and diverse job mixes, offering competitive makespan/tardiness with tight reaction times. Centralized or multi-agent variants increasingly handle disturbances and changing shop states [28,99,100].
• Generalization and transfer. Graph and attention models encode precedence, resource compatibilities, and machine–job relations, enabling transfer across families of instances and faster adaptation to new products or line configurations [101,102,103].
• Perception-to-schedule loops. CNN/RNN/LSTM pipelines for predictive maintenance and anomaly detection feed early warnings to schedulers, enabling proactive repair policies and fewer bottlenecks by aligning maintenance windows with production plans [104].

At the same time, significant obstacles remain that currently limit the broader industrial adoption of neural schedulers:

• Interpretability and assurance. Black-box policies face scrutiny in regulated and safety-critical operations. Tooling for XAI/XRL, post hoc rationales, counterfactuals, and certifiable robustness remains underused in scheduling, yet is increasingly feasible [105].
• Data quality and benchmarks. Many plants lack curated, labeled datasets for learning and objective comparison. Open, standardized benchmarks (including realistic simulators and DT-backed logs) are essential to measure progress and reproducibility [92,97].
• Legacy integration and lifecycle MLOps. Industrial IT/OT landscapes demand hardened interfaces (model registries, signed inference, versioned features), standardized semantics, and zero-downtime rollout/rollback for policies—especially when rescheduling is time-critical [86,95].
• Robustness and safety. Policies must remain stable under distribution shift, sensor noise, or partial outages. Methods from robust and safe RL—risk-sensitive training, certified bounds, disturbance/adversary models—should be brought into the scheduling loop with plant-level validation [106].
• Human-in-the-loop. Operators and planners bring tacit knowledge and risk judgments. Practical systems will blend human guidance with learned policies—e.g., learning from interventions, preference feedback, or human-authored constraints—to ensure actionable, trusted decisions [66].

A critical aspect when considering reinforcement learning (RL) and large language model (LLM) approaches for industrial scheduling is their practical feasibility. While both paradigms demonstrate impressive capabilities in benchmark studies, they often rely on substantial computational resources, large-scale training datasets, and extensive hyperparameter tuning. These requirements can be prohibitive in factory environments where IT infrastructures are constrained and real-time responsiveness is paramount. Moreover, training costs and energy consumption may challenge sustainability goals if models are retrained frequently to adapt to new products, machine configurations, or disruptions.

Another important concern is reproducibility across sites. RL and LLM methods are frequently trained on synthetic or site-specific datasets, making generalization to other factories difficult. Process heterogeneity, data governance issues, and differences in IT architectures can further limit transferability. Promising mitigation strategies include hybrid approaches—where RL or LLM components augment robust optimization or metaheuristics rather than replace them—as well as federated learning setups, transfer learning, and digital-twin-based training that reduce data collection burdens. Ultimately, broader adoption of RL and LLMs in industrial scheduling will depend not only on their algorithmic performance, but also on transparent reporting of computational cost, careful benchmarking across heterogeneous environments, and the availability of standardized datasets and open implementations.

Although this review emphasizes recent advances in learning-based and hybrid optimization methods, it is important to recognize that heuristic and rule-based pre-scheduling approaches remain the predominant solutions in many industrial contexts. Their enduring popularity stems from their low computational cost, simplicity of implementation, and proven reliability across a wide range of shop–floor settings. In many enterprises, dispatching rules and priority heuristics continue to serve as the first line of decision support, providing rapid solutions that are “good enough” under resource constraints. These approaches often form the baseline against which novel AI-based methods are evaluated, and in practice they are frequently embedded as components within hybrid architectures (e.g., rules for initialization or repair). Thus, while the field is moving towards data-driven and digital-twin-enabled scheduling, heuristics will remain central to industrial practice, particularly in cost-sensitive environments or in the early stages of digital transformation.

Deep reinforcement learning (DRL) offers adaptability but faces notable drawbacks: low sample efficiency, training instability, and limited generalization across factories. These issues raise cost and reproducibility concerns in practice. Mitigation strategies include transfer learning, curriculum learning, sim-to-real training with digital twins, and hybrid approaches where DRL supports rather than replaces optimization methods.

Digital twins also entail challenges such as high modeling cost, synchronization latency, and risk of divergence from the physical system. Modular modeling, hybrid-fidelity representations, and standardized protocols (e.g., OPC UA, AAS) can reduce these burdens. Acknowledging these limitations is essential to ensure that DRL- and DT-based scheduling achieve sustainable industrial impact.

An important open challenge is how predictive–reactive hybrids and DRL-based policies can be extended to handle not only stochastic disturbances (e.g., machine breakdowns, job arrivals) but also adversarial disruptions such as cyberattacks. While predictive–reactive frameworks already combine baseline robustness with dynamic repair, their effectiveness against malicious disturbances depends on the ability to detect anomalies and reconfigure schedules under degraded information. Similarly, DRL policies can be adapted for resilience by training on adversarial scenarios or embedding security-aware constraints within their reward functions. Recent research also suggests combining scheduling with anomaly detection and cyber-resilient digital twin architectures, ensuring that schedule updates remain feasible and timely even under attack. These directions point to the need for integrated design–scheduling approaches where resilience is jointly addressed at the optimization, learning, and system-security levels.

Looking forward, several research priorities emerge that will be central to realizing the next wave of digital, AI-driven scheduling systems:

• Interpretable and certifiable neural scheduling (XRL, policy simplification, safety monitors) with plant-ready evidence artifacts [105].
• Open datasets, simulators, and DT-based benchmarks for dynamic shop floors (events, breakdowns, product changeovers), enabling apples-to-apples evaluation and reproducibility [97,100].
• Seamless integration of AI with IoT platforms, digital twins, and edge/cloud, using interoperable data models/ontologies and policy-aware event buses [92,95].
• Federated and privacy-preserving learning for cross-site/cross-enterprise scheduling, with model provenance and usage controls [86].
• Design for robustness: training against disturbances, runtime monitors, and rollback strategies to keep service levels under shocks [106].
• Human-in-the-loop frameworks that combine optimization/learning with operator intent, safety culture, and multi-objective business constraints [66].

With these directions, industrial scheduling can fully exploit digitalization: policies that learn continuously, explain their choices, and operate safely at scale—across connected factories and supply networks.

Finally, we note that several important research questions remain open, for instance how cross-factory scheduling data spaces can be constructed, or how the stability of DRL policies can be ensured under constrained computational budgets. While the formulation of such questions lies beyond the core scope of this review, acknowledging them highlights the broader opportunities for future work that build on the trends identified here.