📈 economics

Optimization of Maintenance Strategies for Leased Equipment Considering Learning Effects and Spare Parts Inventory

This study proposes Uptime Target Bonus and Failure Limitation strategies to coordinate maintenance decisions between lessors and lessees in a leasing supply chain, demonstrating that integrating learning effects and spare parts inventory enhances system-wide optimality, profits, and operational stability.

Original authors: Chunliu Zhou, Lisha Liu, Jianhua Cao

Published 2026-10-12

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Chunliu Zhou, Lisha Liu, Jianhua Cao

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the modern world of heavy industry and construction, massive machines like excavators and cranes are often too expensive to buy outright. Instead, companies rent them, creating a partnership between the owner of the machine and the company that uses it. This arrangement works well only if the equipment keeps running. When a machine breaks down, the user loses money because their work stops, while the owner loses money because they must pay for repairs. The central challenge in this relationship is deciding how often to service the machine before it breaks. If the owner services it too rarely, the machine fails often, angering the user. If they service it too often, the machine sits idle too much, wasting time and money for both sides. Furthermore, when a repair is needed, the speed of the fix depends on whether the right spare parts are on hand and how skilled the repair crew has become through experience.

Researchers at Anhui University of Technology set out to solve this complex puzzle by building a detailed model of how these rental relationships work. They focused on two specific factors that are often overlooked in traditional planning: the "learning effect" and the management of spare parts inventory. The learning effect describes how a repair crew becomes faster and more efficient the more times they fix the same type of machine, simply because they gain experience. Spare parts inventory refers to the stock of replacement components that a lessor keeps ready to ensure a broken machine can be fixed immediately without waiting for a shipment. The researchers wanted to know how these two factors interact and how they could be used to align the interests of the machine owner and the renter, ensuring that both parties make decisions that benefit the entire system rather than just themselves.

The study began by mapping out the financial realities for both sides. The machine owner wants to minimize the cost of repairs and the time spent fixing things, while the renter wants to maximize the time the machine is actually working to generate revenue. In a typical rental agreement, these goals clash. The owner might delay maintenance to save money, but this increases the risk of breakdowns that hurt the renter. To understand the best approach, the researchers created two different scenarios. In the first, the owner and renter make decisions independently, each trying to maximize their own profit. In the second, they act as a single team, making decisions to maximize the total profit of the partnership.

When the researchers simulated the independent scenario, they found that the two parties naturally chose different maintenance schedules. The renter, concerned with minimizing the time consumption and cost burden associated with maintenance, tended to choose a significantly lower maintenance frequency. In contrast, the owner, balancing maintenance costs against reliability gains, opted for a much higher frequency. This misalignment meant the machine was not being serviced at the optimal level for the whole system; specifically, the renter's preferred frequency was far below the system optimum, while the owner's was far above it. However, when the researchers introduced the learning effect into the model, the picture changed. As the repair crew gained experience, the time and cost required for each maintenance task dropped. This improvement made it more attractive for the owner to perform maintenance more frequently, which in turn improved the machine's reliability and increased the renter's profits. The study showed that as the crew's skill level grew, the optimal number of maintenance checks increased, and the total profit for everyone involved went up.

The researchers also examined the role of spare parts. They found that having a stock of spare parts on hand significantly reduced the risk of long delays when a machine broke. This availability allowed for faster repairs, which meant less downtime for the renter and higher operational continuity. Interestingly, the presence of spare parts changed the maintenance strategy. With parts readily available, the renter felt less pressure to demand frequent preventive checks, leading to a slight reduction in the number of scheduled maintenance events. However, the owner, knowing that parts were ready to go, was more willing to increase the frequency of maintenance to keep the machine in top condition. This shift created a new dynamic where the benefits of having parts on hand were shared, but the costs of holding that inventory were initially borne only by the owner.

To fix the misalignment of interests, the study proposed two specific strategies to bring the owner and renter back into agreement. The first strategy, called the failure limitation policy, sets a strict cap on the number of times a machine can break down during the rental period. If the machine exceeds this limit, the owner pays a penalty. This forces the owner to invest more in maintenance to avoid the penalty, aligning their actions with the renter's need for reliability. The second strategy, the uptime target bonus, works in the opposite direction. Here, the renter promises a cash bonus to the owner if the machine stays running for a certain amount of time. This rewards the owner for keeping the machine operational, encouraging them to perform maintenance proactively.

The simulations revealed that both strategies could successfully coordinate the supply chain, bringing the independent decisions of the owner and renter in line with the optimal outcome for the whole system. The choice between the two depends on the specific situation. If the machine is prone to frequent failures and the cost of a breakdown is high, the failure limitation policy works best. If the machine is used heavily and the cost of downtime is the primary concern, the uptime target bonus is more effective. The study also highlighted that the renter should share the financial burden of the spare parts inventory. By providing a subsidy to the owner for stocking parts, the renter ensures that the owner has the resources to maintain high availability, which ultimately leads to higher profits for both parties.

The researchers tested their model with various scenarios, changing factors like how hard the machine was used and how long the rental period lasted. They found that longer rental periods generally led to higher profits for everyone, as the benefits of learning and maintenance accumulated over time. Conversely, if the machine was used very intensely, the failure rate rose sharply, and profits began to drop for both sides unless maintenance was increased significantly. The study confirmed that the learning effect and spare parts inventory are not just minor details; they are powerful levers that, when managed correctly, can turn a conflicting rental relationship into a highly efficient partnership. By understanding how experience and inventory interact, companies can move away from rigid, one-size-fits-all maintenance rules and adopt dynamic strategies that adapt to the real-world performance of their equipment.

Technical Summary: Optimization of Maintenance Strategies for Leased Equipment Considering Learning Effects and Spare Parts Inventory

Problem Statement
This study addresses the coordination challenges within a leasing equipment supply chain consisting of a lessor (who provides maintenance) and a lessee (who operates the equipment). In decentralized decision-making environments, the divergent objectives of the two parties—where lessors aim to minimize maintenance costs and lessees prioritize equipment availability and production continuity—often lead to suboptimal system-wide performance. Existing literature frequently treats maintenance efficiency as static and overlooks the simultaneous influence of two critical operational factors: (1) Learning Effects, where lessors accumulate experience over repeated maintenance cycles, reducing time and costs; and (2) Spare Parts Inventory, which ensures repair continuity but incurs holding costs. The paper investigates how to optimize preventive maintenance (PM) strategies and coordinate supply chain interests when these two factors interact, a gap identified in current research which typically examines them in isolation or assumes constant maintenance efficiency.

Methodology
The study develops a unified analytical framework incorporating a Weibull-based failure rate function that accounts for equipment utilization, operating time, and the lessee's effort level. The core of the methodology involves:

Modeling Learning Effects: The duration and cost of the $i$ -th preventive maintenance action are modeled as decreasing functions of the maintenance sequence number, governed by a learning level parameter ( $\theta$ ). Minimal repair (MR) is assumed to be independent of learning effects.
Incorporating Spare Parts Inventory: A spare parts inventory level is introduced to mitigate stockout risks, defined by an operational continuity improvement factor ( $x$ ). This reduces downtime but introduces holding costs, which are shared via a subsidy mechanism where the lessee bears inventory holding costs while the lessor manages stocking.
Decision Frameworks:
- Decentralized Model: The lessor and lessee independently maximize their respective profit functions, subject to penalty costs for repair delays and failure frequency.
- Centralized Model: A single objective function maximizes the total supply chain profit.
Coordination Mechanisms: To align decentralized decisions with the centralized optimum, two strategies are proposed and mathematically analyzed:
- Failure Limitation (FL) Strategy: Sets a maximum allowable failure threshold; the lessee rewards the lessor for avoided failures or penalizes excess failures.
- Uptime Target Bonus (UTB) Strategy: Provides a bonus to the lessor if the equipment's actual uptime exceeds a predefined target level.

Key Contributions
The paper makes three primary contributions to the literature:

Integrated Framework: It constructs a maintenance decision-making framework that simultaneously incorporates learning effects and spare parts inventory, analyzing their interactive impacts on failure dynamics, maintenance efficiency, and cost structures.
Game-Theoretic Analysis: It establishes optimization models for both decentralized and centralized settings, revealing how learning levels and inventory configurations influence the profit distribution and optimal PM frequencies of the lessor and lessee.
Coordination Mechanisms: It designs and validates specific coordination mechanisms (FL and UTB) that achieve supply chain coordination (incentive compatibility) and allow for the fair allocation of additional profits generated by coordination.

Results and Findings
Numerical experiments and sensitivity analyses yield the following key results:

Impact of Learning: As the learning level ( $\theta$ ) increases, the lessor's optimal PM frequency increases because the reduced time and cost of PM make frequent maintenance more attractive. This leads to higher equipment reliability and increased profits for all parties. However, under decentralized decision-making, the gap between the lessor's optimal frequency and the lessee's (who prefers fewer interruptions) widens as learning improves.
Impact of Spare Parts: The introduction of spare parts inventory significantly enhances operational continuity. While it reduces the lessee's need for frequent PM (lowering their optimal frequency), it encourages the lessor to increase PM frequency to leverage the improved repair capability. This creates a cost-benefit mismatch where the lessor bears the inventory cost while the lessee reaps the continuity benefits, necessitating a subsidy mechanism to align incentives.
Impact of Operational Continuity: As the operational continuity improvement factor ( $x$ ) increases, the lessee's PM frequency decreases significantly, indicating a reduced need to rely on frequent PM to compensate for potential repair interruptions. In contrast, the lessor's PM frequency remains unchanged throughout the entire range of $x$ , as their maintenance decisions are primarily determined by their own cost structure and responsibilities rather than changes in equipment availability. At the supply chain level, PM frequency exhibits only a slight decline.
Coordination Effectiveness: Both the FL and UTB strategies successfully coordinate the supply chain, aligning decentralized decisions with the centralized optimum.
- The FL strategy is particularly effective for failure-sensitive equipment, as it directly constrains failure rates.
- The UTB strategy is more suitable for high-utilization scenarios or where downtime costs are substantial, as it directly incentivizes uptime.
Sensitivity: Profitability follows an inverted U-shaped curve relative to equipment utilization rate and PM time. Extending the lease duration consistently increases profits for all parties.

Significance and Claims
The paper claims that its significance lies in moving beyond static maintenance models to capture the dynamic nature of maintenance efficiency (learning) and the critical role of inventory in repair responsiveness. It demonstrates that learning effects and spare parts inventory are not merely operational details but are coupled factors that fundamentally alter optimal maintenance strategies and profit distribution.

The study concludes that without coordination, decentralized decision-making leads to inefficiencies due to misaligned incentives. However, by implementing the proposed FL or UTB strategies, the supply chain can achieve system-wide optimality. The authors assert that firms should transition from fixed-interval maintenance to dynamic strategies that leverage accumulated experience and optimized inventory levels. Furthermore, they emphasize that the choice of coordination mechanism should depend on specific equipment characteristics (e.g., failure sensitivity vs. high downtime costs) and operational contexts to ensure the feasibility and effectiveness of incentive schemes.

A scientific accuracy reviewer checked the draft against the paper and flagged these problems:

Summary claims lessor's PM frequency remains unchanged with operational continuity; paper states it remains unchanged, but summary implies a general trend or misattributes the lack of change. (the paper says: "the lessor's PM frequency remains unchanged throughout the entire range of x")

Produce a corrected version of the draft. Fix ONLY what the reviewer flagged (verify each point against the paper) and keep everything else — the structure, the level of detail, the terminology — unchanged. Output ONLY the corrected summary.

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