Innovative mathematical model for planning engine usage in a fighter fleet via stochastic optimization, reducing wear and tear and increasing flight hours.
Summary
Fighter aircraft squadrons must balance training and operational objectives with strict engine life limits. A recent study proposes a multi-stage stochastic optimization model that incorporates uncertainty—such as weather or mission changes—to plan engine usage optimally. At the heart of the solution is a nested decomposition algorithm capable of solving complex, large-scale decisions by breaking the problem down into sub-problems. Compared to traditional manual methods, this approach reduces the number of engines reaching their service limit by 15.3% and adds 465 hours of engine availability for the fleet, demonstrating a significant operational benefit and a breakthrough in optimizing air combat resources.
The operational challenge of modern fighter fleets
Air forces require fighter jet squadrons to meet high monthly flight hour quotas for training and missions. At the same time, each aircraft engine has a defined maximum service life, after which it must undergo major maintenance or be replaced. Engine usage planning is not a trivial matter: it must anticipate uncertainties such as weather conditions, mission reconfigurations, or tactical contingencies that influence the required flight hours.
In this context, classical deterministic approaches—which plan without taking uncertainty into account—often prove ineffective, leading to premature engine wear or reduced operational capabilities. The challenge is to maximize fleet availability while minimizing the risk of exceeding costly maintenance thresholds.
The concept of multistage stochastic optimization
Multistage stochastic optimization is a mathematical method that plans a series of decisions over time, directly incorporating uncertainties in the form of random variables: for example, weather conditions or variations in mission requirements. At each “stage” (period), the model adjusts decisions based on the results observed up to that point.
This approach differs from deterministic models in that it does not simply optimize for a single scenario: it takes into account several possible future trajectories and seeks to find robust decisions regardless of the scenario that materializes. It is particularly well suited to dynamic systems where decisions made today influence future constraints and opportunities.
In the case of fighter fleets, this means that the model can decide when to dismantle or reassemble an engine, redistribute flight hours, or modify maintenance schedules to best respond to operational uncertainties.
The central role of the nested decomposition algorithm
A major obstacle to the application of multistage stochastic optimization is the exponential growth in complexity as the number of periods and uncertainties increases. Each addition of a scenario or phase multiplies the possible combinations and makes the problem difficult to solve directly.
To overcome this obstacle, researchers have developed a nested decomposition algorithm. This type of algorithm breaks down the overall problem into smaller sub-problems, with each sub-problem representing a part of the decision-making process at a given time or under a particular scenario. These sub-problems are then solved in a coordinated manner using tight lower bounds and problem-specific cuts to speed up computation and ensure overall consistency.
In practice, the algorithm works by alternating between global planning phases and detailed resolution phases, gradually refining the optimal decisions without having to exhaustively explore every possible scenario.
Concrete empirical results
The study applied this method to real fleet planning data. The results are striking:
- 15.3% reduction in engines reaching their service life limit compared to usual manual planning;
- 465.66 hours of available engine time gained, representing increased training or mission capacity without additional material investment.
These results demonstrate that not only is the model mathematically robust, but it also provides tangible operational benefits by more effectively aligning maintenance constraints and availability objectives.
Technical constraints and practical limitations
The approach is not without its challenges. From a technical standpoint, modeling requires reliable statistical data on uncertainties—such as weather distributions or mission variations—which can be difficult to obtain with precision. In addition, solving multistage stochastic problems remains computational resource-intensive even with advanced algorithms, especially for very large fleets or long time horizons.
Operationally, integrating this type of model into current air force planning systems requires organizational changes and training planners in advanced optimization tools. Finally, models must be updated regularly to remain relevant in the face of evolving air tactics and technologies.
Opportunities for military and civil aviation
Beyond the management of fighter fleets alone, this approach opens up broader prospects. In military aviation, it can support comprehensive predictive logistics strategies, ensuring that resources are used optimally in peacetime and during operations. It can also be adapted to mixed fleet planning or coalition environments where requirements and uncertainties are even greater.
In civil aviation, similar problems exist for the management of commercial aircraft engines, where companies must balance flight hours, scheduled maintenance, and weather or operational disruptions. Comparable stochastic models can improve the efficiency of civil fleets by reducing costs while maintaining safety and availability.
Underlying technologies and algorithmic research
Multistage stochastic optimization is based on solid foundations in applied mathematics, including stochastic programming, sequential decision theory, and algorithmic decomposition. The most recent work in this area incorporates techniques from artificial intelligence and machine learning to better estimate uncertainty distributions or to accelerate the resolution of subproblems.
Researchers continue to develop hybrid methods that combine approximate and exact approaches to reduce computational load while maintaining solution quality. These advances could make this type of model even more accessible for complex industrial applications.
A gradual transformation of planning practices
This work represents a significant advance in the optimization of aeronautical resources.
By integrating operational variability and providing a robust mathematical framework for managing uncertainty, it pushes the boundaries of military fleet planning.
More broadly, it highlights a fundamental trend: the growing adoption of probabilistic models and sophisticated algorithmic solutions to solve problems traditionally managed by experience and heuristics. Faced with increasingly complex environments, this transition to advanced planning tools is likely to continue, gradually transforming the way aircraft fleets—both military and civilian—are managed to maximize their efficiency and sustainability.
Sources
ScienceDirect – Multi-stage stochastic engine usage optimization for fighter jet fleet using nested decomposition algorithm, Operations Research Perspectives, 2026.
SSRN – Multi-Stage Stochastic Engine Usage Optimization for Fighter Jet Fleet (prepublication).
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