Plan Disruption: Models and Mitigation

• Plan Disruption is a concept describing how plans degrade or change when executed in dynamic environments, using measures like symmetric-difference and deviation in various domains.
• It is formalized through objective functions and real-time execution models in fields such as AI planning, cloud testing, transportation, and operations management.
• Mitigation strategies emphasize redundancy, local flexibility, and targeted guidance to preserve plan integrity and minimize recovery costs across complex systems.

Searching arXiv for papers related to plan disruption across planning, transportation, and operations. Plan disruption denotes a family of concepts concerning how plans degrade, how much they must change, or how much disturbance they themselves induce when deployed in dynamic environments. In classical planning, it is the symmetric-difference distance between the initial state and the final state reached by a solution plan; in robust execution, it is the deviation between the world assumed at planning time and the world encountered at execution time; in live testing of cloud services, it is the extra disturbance attributable to orchestration choices rather than to the intrinsic cost of running tests; and in transportation and operations management, it refers to the operational and behavioral consequences of service interruptions together with the recovery logic used to restore feasible schedules (Pozanco et al., 21 Aug 2025, Lima et al., 2020, Jebbar et al., 12 Nov 2025, Mo et al., 2022).

1. Conceptual scope and domain-specific meanings

The term has no single universal definition. In the planning-theoretic formulation, disruption is a property of the plan outcome: the final state should differ as little as possible from the initial state while still achieving the goals. In robust execution, disruption is a runtime phenomenon caused by unexpected observations or exogenous events that invalidate assumed action orderings. In cloud live testing, the distinction is sharper: “service disruption” is any unacceptable disturbance to production caused by testing, whereas “plan disruption” is the component of that disturbance attributable specifically to orchestration choices such as excessive re-deployments, poor run ordering, or overly aggressive isolation methods. In transit, disruption is usually tied to service interruptions, degraded headways, flow redistribution, crowding, and missed connections rather than to terminal-state deviation (Pozanco et al., 21 Aug 2025, Lima et al., 2020, Jebbar et al., 12 Nov 2025, Mo et al., 2022).

This plurality matters because different domains optimize different objects. A planner minimizing final-state change is not solving the same problem as an operator minimizing recovery time after a blocked track, nor as a cloud engineer minimizing the production footprint of live tests. A plausible implication is that “plan disruption” is best understood as a cross-domain organizing concept for preserving intended structure under disturbance, rather than as a single metric.

2. Formalizations in AI planning and execution

In classical STRIPS planning, the central quantity is the final-state disruption

$$D_{\mathrm{final}}(\pi) := | I \triangle \Gamma(I,\pi) |,$$

where $I$ is the initial state and $\Gamma(I,\pi)$ is the final state reached by plan $\pi$. The paper scalarizes action cost and disruption through

$$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$

with $\omega \in \{10^{-3},1,10^3\}$ in the experiments. Two compilations are proposed. The “lazy” compilation is exact: after achieving the original goals, the plan executes a checking phase that charges $\omega$ for each fluent whose truth value in the final state differs from its value in $I$, yielding $D_{\mathrm{final}}(\pi)=C(\pi')-C(\pi)$ when $\omega=1$. The “eager” compilation changes only action costs by penalizing add-effects on fluents not in $I$0 and delete-effects on fluents in $I$1; it preserves task size but overestimates terminal disruption, satisfying $I$2 (Pozanco et al., 21 Aug 2025).

A different formalization arises in execution under uncertainty. Here the issue is not merely how different the end state is, but whether the next action remains valid after the world changes. The execution framework starts from a totally ordered or partially ordered plan, removes causal edges to obtain an adaptable partially ordered plan, retains interference and duration constraints, and then computes online the complete set of valid totally ordered plans together with the probability of success for each of them. If the current belief state is $I$3, with $I$4 a fuzzy truth assignment over propositions, the executor evaluates candidate linearizations by multiplying precondition-satisfaction probabilities and chooses the next action as the first action of the ordering with maximal $I$5 (Lima et al., 2020).

These two formalisms correspond to different notions of preservation. One minimizes deviation between initial and terminal states; the other preserves plan validity under evolving observations. This suggests that disruption can be encoded either as an objective on outcomes or as an online admissibility condition over execution orderings.

3. Transportation, railways, and passenger systems

In urban public transit, unplanned disruption has been formalized through an incident-based network redundancy index that measures the ability of the integrated bus–rail network to preserve throughput during a specific incident. For incident $I$6, the index is

$I$7

In the Chicago Transit Authority case study, Sedgwick had $I$8 and Jefferson Park had $I$9. During the incidents, service frequency on the incident line was largely reduced: Brown southbound headways changed from about $\Gamma(I,\pi)$0 to $\Gamma(I,\pi)$1 minutes, Blue southbound from about $\Gamma(I,\pi)$2 to $\Gamma(I,\pi)$3 minutes, and passengers redistributed differently depending on redundancy. In the low-redundancy case, most passengers chose nearby buses; in the high-redundancy case, most transferred directly to nearby lines (Mo et al., 2022).

Causal analysis extends this from descriptive redistribution to network-wide effect estimation. In a Hong Kong metro case, treatment is defined at the station-day-interval level by a service interruption of at least five minutes, and synthetic control is used to recover direct and spillover effects on entry ridership, exit ridership, journey time, travel speed, and crowding density. For a 27-minute evening-peak disruption at Chai Wan, the disrupted station experienced exit ridership of about $\Gamma(I,\pi)$4, average journey time of $\Gamma(I,\pi)$5 minutes, and average travel speed of $\Gamma(I,\pi)$6 km/h; inner-city sections reached over $\Gamma(I,\pi)$7 passengers/m$\Gamma(I,\pi)$8, and spillovers propagated into connected lines (Zhang et al., 2023).

Planned transport disruptions exhibit different but equally structured responses. In Amsterdam tram and metro closures, the estimated network-level elasticities were $\Gamma(I,\pi)$9 and $\pi$0, with lower responses among frequent users and during weekday peaks, and stronger responses on weekends; the estimated neural network regression model achieved $\pi$1 and MAE $\pi$2 on OD-level demand prediction during closures (Yap et al., 2022). In Northwest Denver, PureNav treated planned disruptions such as the Central 70 construction as persistent interruptions to local mobility and delivered personalized pre-trip information on road conditions, construction events, PM2.5, weather, and timing. In the second deployment cohort, helpfulness improved from $\pi$3 to $\pi$4 on a $\pi$5 to $\pi$6 scale, weather was rated most useful, and the closer trips were to the highway, the higher the combined usefulness scores (Hammad et al., 2024).

Railway recovery models push the notion of disruption into operational rescheduling. An event-based integer program for Vienna’s subway system jointly reschedules trips and vehicle circulations under a one-direction single-track blockage, allowing trip shifts, cancellations, early turns, and depot replacements; the reduced event-activity graph frequently yields good-quality recovery plans within one minute (Fekete et al., 2011). A separate temporal-planning framework for heterogeneous multi-gauge railways models blocked tracks, blocked trains, slowdowns, and engine failures in PDDL 2.1, generates conflict-free timestamped operational plans, and solved 199 of 200 benchmark instances, with slowdown contributing about $\pi$7 of total delay overall and up to about $\pi$8 at VL3 (Ray et al., 12 Jun 2026).

4. Operational recovery in cloud services, manufacturing, and hospitals

In live testing of cloud services, plan disruption is explicitly endogenous: it is the extra disturbance introduced by orchestration choices. The automated test-plan generation approach therefore minimizes the time and disturbance attributable to setup and teardown rather than to test execution itself. Inputs include the CI call graph, tolerance times on dependency edges, acceptable outage per service instance, isolation cost matrices, TSI precedence, and runtime-framework deployment costs. Outputs include test configurations, a deployment plan, a UTP TestExecutionSchedule, and embedded mitigation strategies such as single step, rolling paths, small flip, and big flip. The optimization target is conceptually

$\pi$9

subject to resource capacity, tolerance time, acceptable outage, and coverage constraints (Jebbar et al., 12 Nov 2025).

In production and supply-chain replanning, the guiding principle is minimal local change. The multi-agent mechanism for Huawei data keeps the released schedule as intact as possible, triggers only directly affected material and capacity agents, and uses local optimization plus negotiation to propagate only necessary adjustments. Supplier material agents solve local allocation problems such as

$$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$0

subject to demand and cumulative supply constraints, while customer agents consolidate reduction proposals and capacity agents reallocate constrained production. Across the reported disruption scenarios, replanning converged in about 1–7 iterations at roughly one minute per iteration, with line stoppage fulfillment around $$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$1–$$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$2 by orders and raw-material stoppage fulfillment around $$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$3–$$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$4 by orders depending on buffer conditions (Tan et al., 2022).

In elective surgical scheduling, disruption-restoration is organized around a nominal schedule plus precomputed back-up schedules for every enumerated emergency and no-show scenario. Emergencies are assigned according to an as-soon-as-possible policy: the model computes whether each operating room is empty at slot $$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$5, calculates each room’s first availability $$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$6, and enforces that the chosen room has minimal first availability. No-show restoration designates a substitute from the next day’s nominal plan, while impacted patients are rescheduled within bounded windows $$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$7 or $$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$8. In the reported computations, the sequential heuristic was more reliable than the warm start on larger instances, and overall time to produce nominal plus back-up schedules was about $$J_\omega(\pi) = C(\pi) + \omega \cdot D_{\mathrm{final}}(\pi),$$9 seconds for the heuristic versus about $\omega \in \{10^{-3},1,10^3\}$0 seconds for the warm start (Doneda et al., 2024).

5. Mitigation strategies and design principles

A first recurring principle is redundancy engineering. In transit, this appears as explicit measurement and exploitation of alternative services: station-level NRUI profiles identify low-redundancy frequent-incident locations where pre-planned bus bridging, shuttle staging, and transfer corridors are appropriate, while high-redundancy frequent-incident locations benefit more from route recommendations and information dissemination (Mo et al., 2022). In Nashville bus operations, proactive reserve-bus stationing based on disruption forecasts and randomized local search reduced left-behind passengers from $\omega \in \{10^{-3},1,10^3\}$1 to $\omega \in \{10^{-3},1,10^3\}$2, a reduction of $\omega \in \{10^{-3},1,10^3\}$3 or about $\omega \in \{10^{-3},1,10^3\}$4 versus the Agency plan, with comparable deadhead miles and minutes (Han et al., 2024). In airline networks, proactively converting 10 regional routes to airside-to-airside bus service under a $\omega \in \{10^{-3},1,10^3\}$5 million investment budget reduced passenger delays by about $\omega \in \{10^{-3},1,10^3\}$6 on disrupted days and about $\omega \in \{10^{-3},1,10^3\}$7 on nominal days (Borrero et al., 30 Jun 2026).

A second principle is local flexibility with bounded perturbation. Partial-order execution preserves only safety-critical temporal structure and defers causal commitment to runtime; manufacturing replanning freezes non-affected portions of the plan and only reoptimizes within a local neighborhood; hospital restoration keeps non-impacted assignments unchanged and forbids anticipation; cloud testing minimizes configuration churn by ordering tests so consecutive configurations are maximally similar, achieving Gray-code-like single-distance transitions under “all boundary environment mixtures paths” coverage (Lima et al., 2020, Tan et al., 2022, Doneda et al., 2024, Jebbar et al., 12 Nov 2025).

A third principle is targeted information and scenario-specific guidance. Transit disruption studies recommend in-station and digital alerts at and upstream of blocked stations, together with simple pre-configured transfer guidance and real-time headway estimates (Mo et al., 2022). PureNav’s redesign from turn-by-turn navigation to personalized pre-trip summaries reflects the same logic: routine commuters often preferred compact metadata on weather, incidents, construction, and PM2.5 over continuous route narration (Hammad et al., 2024). This suggests that disruption mitigation is partly a control problem and partly an information-design problem.

6. Limitations, misconceptions, and open directions

One common misconception is that plan disruption is synonymous with exogenous failure. The cloud-testing formulation shows that disruption can be induced by the plan itself: excessive re-deployments, relocations, or poor test ordering amplify production disturbance even when test cases are intrinsically fixed (Jebbar et al., 12 Nov 2025). A second misconception is that minimizing nominal action cost already yields minimally disruptive plans. The classical-planning experiments contradict this: on 1847 STRIPS tasks, the baseline solved 948 instances, the eager compilation 893, and the lazy compilation 138, and larger $\omega \in \{10^{-3},1,10^3\}$8 values frequently produced solutions with lower disruption than cost-only planning, sometimes at higher action cost (Pozanco et al., 21 Aug 2025).

The empirical and algorithmic limits are domain-specific but structurally similar. Transit analyses are constrained by entry-only AFC, unobserved within-system transfers, shuttle buses that may not require taps, and normality assumptions in significance testing (Mo et al., 2022). Cloud live testing is static rather than runtime-adaptive, and heuristic method selection can be suboptimal in some coverage cases (Jebbar et al., 12 Nov 2025). Surgical disruption-restoration assumes at most one emergency or one no-show per robust day and relies on scenario enumeration with equal likelihoods rather than calibrated probabilities (Doneda et al., 2024). Railway temporal planning assumes a fully observable deterministic environment, known disruption durations, constant speeds, and abstracted signaling layers (Ray et al., 12 Jun 2026).

The current literature therefore distinguishes exactness from tractability, and precomputation from adaptation. Exact terminal-state minimization is available but computationally expensive; proxy costs scale better but can overcount transient changes. Scenario libraries provide immediate deployability but are only as rich as the enumerated contingencies. Online temporal replanning handles evolving states but depends on accurate sensing and feasibility-preserving abstractions. This suggests an emerging research direction toward telemetry-aware, multi-objective, and domain-integrated recovery methods in which disruption is neither purely a cost term nor purely an exogenous shock, but a first-class optimization target spanning state preservation, schedule stability, resource legality, and human response.