Maintenance Planning Algorithm (MPA)

• Maintenance Planning Algorithm (MPA) is a family of decision procedures designed to schedule various maintenance tasks by integrating preventive, corrective, and proactive approaches with operational constraints.
• MPA implementations employ bi-level planning, mixed-integer optimization, and real-time heuristics to align maintenance timing with production, logistics, and system health requirements.
• Practical applications of MPAs have demonstrated significant cost savings, enhanced system reliability, and improved resource allocation in manufacturing, rail, energy, and robotic maintenance domains.

Maintenance Planning Algorithm (MPA) denotes a class of decision procedures for scheduling preventive, proactive, corrective, or execution-level maintenance under explicit operational constraints. Across the cited literature, the term is used for bi-level day-ahead proactive-maintenance planning in energy-aware manufacturing, real-time insertion of corrective tasks into idle windows, rolling-horizon mixed-integer models for wind and offshore assets, state-function formulations for rail fleets, and symbolic or agentic planners for robotic and prescriptive maintenance. This suggests that MPA is best understood as a family of maintenance planning architectures rather than a single standardized algorithm (Li et al., 14 Mar 2026, Lin et al., 2017, Mascolo et al., 22 Aug 2025).

1. Terminological scope and problem classes

The literature assigns the label MPA to several distinct but structurally related planning problems. In manufacturing, the algorithm may be the upper-level planner of a hierarchical control framework that decides binary proactive maintenance actions $m_j(t)$ under machine degradation, crew limits, and time windows, while a lower-level scheduler handles production in closed loop (Li et al., 14 Mar 2026). In rail applications, it may denote a 0–1 planning model that selects one maintenance date within a permissible window for each train, subject to maintenance-rate and workshop-capacity constraints (Lin et al., 2017), or a short-term joint train-assignment and maintenance-scheduling model driven by cumulative mileage and depot capacity (Lin, 2017).

In maintenance-task scheduling, MPA can also denote a real-time heuristic. One formulation builds an off-line preventive schedule and then inserts dynamic corrective tasks online into free windows so as to reduce “lost cost” while assigning the most competent available resource to the longest or most demanding tasks (Aboussalim et al., 2010). Another formulation minimizes a weighted sum of flow-time and tardiness for preventive-maintenance tasks with unequal release dates, using a locally optimal pairwise ordering rule and then extending the resulting scheduler to $q$ identical processors in a distributed system (Adjallah et al., 2020).

A further strand treats MPA as a planning layer tightly coupled to execution. In robotic maintenance automation, the planning problem includes symbolic task planning, disassembly-space computation, manipulation and path planning, and runtime interpretation of symbolic manipulation primitives into executable skills under CAD/RGB-D uncertainty (Friedrich et al., 25 Aug 2025, Friedrich et al., 25 Aug 2025). In prescriptive maintenance, the planning layer may begin with condition monitoring and fault classification, continue through retrieval of manuals and external procedures, and output structured recommendations containing immediate actions, inspection steps, corrective measures, parts requirements, and timelines (Harbola et al., 28 Jul 2025).

2. Common mathematical structure

Despite domain heterogeneity, most MPA formulations share four elements: a state model, a maintenance-decision variable, an operational coupling mechanism, and an objective trading intervention cost against deterioration or service loss. In degradation-aware manufacturing, machine health is explicit. A representative state update is

$h(k+1)=h(k)-B_hu(k)+W_hm(k),$

where $u(k)$ is throughput and $m(k)$ is a binary maintenance decision. Capacity and energy intensity are then made health dependent, so maintenance simultaneously restores feasible production capacity and reduces energy intensity (Li et al., 14 Mar 2026).

In usage-driven fleet problems, the core state is cumulative mileage rather than a continuous health index. The short-term train-assignment model updates mileage through

$$l_m(t)=\Bigl[l_m(t-1)+\sum_{r\in R}L^{\text{Route}}_r x_{mr}(t)\Bigr]\Bigl[1-\sum_{p\in P}y_{mp}(t)\Bigr],$$

so route assignment increases cumulative mileage and a maintenance start resets the counter (Lin, 2017). The long-term EMU model instead selects a maintenance start day $x_m^t\in\{0,1\}$ within a train-specific window and uses a state function $f_m(t)$ to determine whether the train is under maintenance on each day, including carry-over and next-horizon effects (Lin et al., 2017).

In task-scheduling formulations, the key state is the release/due-date structure. A canonical objective is

$$\min \sum_i \left[ W_f(c_i-r_i)+W_t\max(0,c_i-d_i)\right],$$

which interprets flow-time as time spent in a critical state and tardiness as delay beyond a due threshold (Adjallah et al., 2020). In the real-time insertion heuristic, the corresponding cost aggregates task penalties and idle-window loss,

$$F_{OG}=\sum_{i=1}^{n}(W_iO_i^+ + h_iO_i^-)+\sum_i C_{i0}+\sum_k C_k^{perdu},$$

with $q$0 derived from the gap between consecutive tasks (Aboussalim et al., 2010).

A broader abstraction appears in reinforcement-learning formulations, where maintenance planning is cast as an MDP $q$1 and the policy objective is

$q$2

or an average-cost analogue. Here state typically includes health, RUL, buffer levels, and resource status, while reward is the negative of aggregated maintenance, downtime, and production costs (Ogunfowora et al., 2023).

3. Algorithmic realizations

MPA implementations range from exact mixed-integer optimization to heuristics, decomposition methods, dynamic programming surrogates, and learning-based policies. A prominent optimization architecture is the bi-level scheme in which the upper level chooses maintenance times and the lower level computes operational consequences. In the energy-aware manufacturing formulation, the upper-level problem minimizes

$q$3

subject to maintenance-window, crew, and end-of-horizon health constraints, while the embedded lower level is a convex QP model predictive control problem for production scheduling. The resulting mixed-integer bi-level program is solved by generalized Benders decomposition, with a master MILP in $q$4 and a lower-level convex subproblem supplying Benders cuts through dual multipliers (Li et al., 14 Mar 2026).

A second family uses rolling-horizon MILP. In offshore wind, the HOST framework solves a day-ahead hourly short-term model coupled to a daily long-term model, then rolls the horizon one day forward and re-solves using updated weather and production forecasts (Papadopoulos et al., 2020). Wind-turbine maintenance under condition monitoring likewise re-solves every 3 months, updating each component’s Weibull scale parameter through a Cox proportional hazards term and then solving a mixed-integer optimization for the next preventive-maintenance epoch and affected turbines (Yu et al., 2021). Distributed maintenance in geo-distributed production systems separates long-term predictive planning from routing: an MPA determines the number and timing of preventive replacements at each site, and a Long-term Heuristic Scheduling Algorithm then solves a CVRPTW-type routing problem for mobile workshops (Mascolo et al., 22 Aug 2025).

Other MPAs are intentionally heuristic. The real-time maintenance scheduler with preventive and corrective tasks uses window fitting: upon arrival of a dynamic task, it computes all free windows $q$5, chooses the smallest admissible window, inserts the task, reassigns the best available resource, and recomputes lost cost (Aboussalim et al., 2010). The preventive-maintenance scheduler for unequal release dates derives a pairwise local-optimality rule, FTR, such that task $q$6 dominates task $q$7 at time $q$8 iff $q$9, and builds an $h(k+1)=h(k)-B_hu(k)+W_hm(k),$0 single-processor algorithm from this dominance structure before extending it to parallel processors with an urgency filter (Adjallah et al., 2020).

Metaheuristics and matrix-algorithmic approaches appear in other settings. The EMU high-level maintenance planner uses simulated annealing on a 0–1 nonlinear model with penalty functions for maintenance-rate, acceptance, and workshop-capacity violations (Lin et al., 2017). Multi-state systems with vacations and preventive maintenance are built as MMAP/PH continuous-time Markov chains, and optimization is performed on the net reward per unit time using stationary distributions and event-rate matrices, with Matlab and R used computationally (Ruiz-Castro et al., 14 Jan 2025).

4. Coupling with operations, logistics, and execution

A defining feature of many MPAs is that maintenance is not optimized in isolation. In the manufacturing bi-level formulation, maintenance decisions alter the lower-level feasible region through

$h(k+1)=h(k)-B_hu(k)+W_hm(k),$1

so downtime, degradation recovery, bottleneck effects, and energy prices are jointly internalized (Li et al., 14 Mar 2026). In the integrated multi-product process and maintenance planning model, preventive maintenance consumes production capacity, while expected corrective-maintenance time and cost are age dependent through an NHPP failure model; the full formulation is a MILP minimizing production, inventory, backorder, setup, PM, and expected CM costs on a single capacitated machine (Arani et al., 2020).

Logistical coupling is explicit in offshore and distributed-maintenance formulations. HOST defines opportunity not only through residual life but also through crew dispatch, projected production, and turbine accessibility. Vessel-rental variables, crew-hour constraints, overtime, and access indicators $h(k+1)=h(k)-B_hu(k)+W_hm(k),$2 or $h(k+1)=h(k)-B_hu(k)+W_hm(k),$3 turn maintenance into a joint timing-and-logistics decision (Papadopoulos et al., 2020). The OMCR framework goes further by decoupling predictive maintenance timing from routing only temporarily: its MPA produces maintenance jobs and time windows, and an LHSA solves a capacitated vehicle-routing problem with time windows; CMW location is then explored through a weighted barycentre of site failure probabilities and MMW capacity through discrete choices $h(k+1)=h(k)-B_hu(k)+W_hm(k),$4 (Mascolo et al., 22 Aug 2025).

Execution-level MPAs introduce an additional coupling between symbolic plans and physical skills. In robotic maintenance automation, task planning builds a relational graph $h(k+1)=h(k)-B_hu(k)+W_hm(k),$5, derives disassembly spaces

$h(k+1)=h(k)-B_hu(k)+W_hm(k),$6

and generates manipulation primitives $h(k+1)=h(k)-B_hu(k)+W_hm(k),$7 linked by a transition function $h(k+1)=h(k)-B_hu(k)+W_hm(k),$8. Runtime interpretation then decomposes each symbolic primitive into skill primitives using position control, force/torque control, or image-based visual servoing (Friedrich et al., 25 Aug 2025). A related system combines symbolic task planning, a novel sampling-based computation of disassembly space with complexity $h(k+1)=h(k)-B_hu(k)+W_hm(k),$9, and path planning with adaptive exploration step size based on octree occupancy (Friedrich et al., 25 Aug 2025).

In LLM-based prescriptive maintenance, the planning layer sits downstream of diagnosis. PARAM serializes vibration-derived features such as BPFO, BPFI, BSF, and FTF into natural language, classifies fault type and severity, retrieves manuals and external procedures through a RAG pipeline, and then synthesizes a structured plan with immediate actions, inspection checklists, corrective measures, parts requirements, and timeline specifications (Harbola et al., 28 Jul 2025).

5. Representative domains and empirical behavior

Manufacturing results show how an MPA can change both maintenance timing and operating cost. In a lithium-ion battery pack assembly line with 6 buffers and 7 machines, the bi-level GBD framework strategically shifted preventive maintenance away from bottlenecks and high-value low-price production windows. Over a 5-day horizon, the reported changes relative to a fixed calendar PM baseline were: energy cost $u(k)$0, PM cost $u(k)$1 (from \$u(k)$21300), total cost $u(k)$3, PM hours $u(k)$4 (from 20 to 13 hours), and average health $u(k)$5 (from 0.87 to 0.90), while all production targets were met in both policies (Li et al., 14 Mar 2026).

In real-time task scheduling, the heuristic MPA reduced idle-window loss by inserting dynamic jobs into best-fitting gaps. In the reported experiment with 10 preventive tasks, lost cost decreased from $u(k)$6 DHS before optimization to $u(k)$7 DHS after inserting 3 dynamic tasks, a reduction of about 37%, and to $u(k)$8 DHS after inserting 9 dynamic tasks, a reduction of about 54% (Aboussalim et al., 2010). In preventive-maintenance scheduling with flow-time and tardiness on parallel processors, the urgency-enhanced real-time algorithm produced much lower average cost over all tasks needed in the horizon than the version without urgency, and processor utilization remained near full capacity until almost all required tasks were processed (Adjallah et al., 2020).

Wind and fleet applications emphasize the value of explicit aging and rolling re-optimization. For a four-component wind-turbine model, the renewal-reward/virtual-maintenance planner produced about 8.5% lower maintenance cost than a pure corrective-maintenance strategy, and in comparison with an earlier state-of-the-art model it obtained similar scheduling with much faster CPU time (Yu et al., 2020). In the offshore HOST formulation, extensive numerical experiments on actual wind, wave, and power data yielded total-cost improvements of 6.8% over BESN, 8.9% over PBOS, 24.9% over TBS, and 67.4% over CMS in one case study, with similarly large margins in a second case study (Papadopoulos et al., 2020). In distributed maintenance for geo-distributed production systems, the OMCR framework was reported to reduce lifecycle maintenance costs by up to 50%, with increased scalability for systems exceeding 30 GDPS (Mascolo et al., 22 Aug 2025).

Robotic and LLM-based MPAs report different performance indicators because the planning target is execution quality rather than fleet-wide cost alone. In robotic maintenance automation, success rates of $u(k)$9 were reported for peg-in-hole, panel assembly, and valve assembly, and $m(k)$0 for cooling lubricant exchange, with no planning errors observed and failures attributed instead to sensing/control noise or device limitations (Friedrich et al., 25 Aug 2025). In the prescriptive-maintenance system, GPT-4-judged evaluations rated Gemini-1.5-Flash and Gemini-2.0-Flash-Exp at 5.0 overall with latency 2.4–2.5 s and cost \$0.00006, while simulations reported rapid anomaly-to-action cycles with 40–60% reductions in MTTR (Harbola et al., 28 Jul 2025).

6. Limitations, misconceptions, and research directions

The literature does not support identifying MPA with a single paradigm such as periodic preventive scheduling. Some formulations are exact mixed-integer programs, some are heuristic event-driven insertion rules, some are receding-horizon controllers, some are MDP policies, and some are symbolic or agentic execution planners. This suggests that “MPA” functions primarily as a role in a maintenance architecture—the component that converts degradation, operational context, and constraints into actionable maintenance decisions—rather than as a canonical solver or model class (Ogunfowora et al., 2023, Friedrich et al., 25 Aug 2025).

Several limitations recur. Deterministic degradation and price assumptions are common at the planning stage: the energy-aware manufacturing framework does not model stochasticity, sudden failures, or intra-day maintenance replanning (Li et al., 14 Mar 2026). The real-time insertion heuristic assumes a single maintenance capacity, equal priority within categories, no explicit precedence constraints, and no stochastic task-arrival model (Aboussalim et al., 2010). The rail and wind rolling-horizon models are strongly dependent on parameterized thresholds, cycle windows, or prognostic models, so poor calibration can distort the maintenance trigger (Lin et al., 2017, Yu et al., 2021). The OMCR framework assumes one critical equipment item per site and perfect repair, and its planning/routing interaction remains iterative rather than fully integrated (Mascolo et al., 22 Aug 2025). Robotic systems are presently limited to linear, monotonous plans or single-arm execution, and uncertainty modeling is still narrow relative to severe wear, corrosion, or major structural deviations (Friedrich et al., 25 Aug 2025, Friedrich et al., 25 Aug 2025). LLM-based prescriptive maintenance inherits risks tied to hallucination, documentation coverage, and safety-critical recommendations, which is why human-in-the-loop review and source traceability remain central (Harbola et al., 28 Jul 2025).

Current research directions therefore move along three axes. One is richer uncertainty handling: stochastic degradation, random failures, robust or chance-constrained formulations, and safe RL for critical assets (Li et al., 14 Mar 2026, Ogunfowora et al., 2023). A second is tighter cross-layer integration, such as combining maintenance planning with routing, production, inventory, access windows, or low-level execution without relying on loose sequential coupling (Papadopoulos et al., 2020, Mascolo et al., 22 Aug 2025). A third is scalability and autonomy: hierarchical decomposition, multi-agent RL, transfer learning, rolling replanning, dual-arm or alternative robotic plans, and LLM/SLM systems that remain grounded in manuals, standards, and sensor evidence (Ogunfowora et al., 2023, Friedrich et al., 25 Aug 2025, Harbola et al., 28 Jul 2025).