Scheduling a Dynamic Aircraft Repair Shop with Limited Repair Resources

We address a dynamic repair shop scheduling problem in the context of military aircraft fleet management where the goal is to maintain a full complement of aircraft over the long-term. A number of flights, each with a requirement for a specific number and type of aircraft, are already scheduled over a long horizon. We need to assign aircraft to flights and schedule repair activities while considering the flights requirements, repair capacity, and aircraft failures. The number of aircraft awaiting repair dynamically changes over time due to failures and it is therefore necessary to rebuild the repair schedule online. To solve the problem, we view the dynamic repair shop as successive static repair scheduling sub-problems over shorter time periods. We propose a complete approach based on the logic-based Benders decomposition to solve the static sub-problems, and design different rescheduling policies to schedule the dynamic repair shop. Computational experiments demonstrate that the Benders model is able to find and prove optimal solutions on average four times faster than a mixed integer programming model. The rescheduling approach having both aspects of scheduling over a longer horizon and quickly adjusting the schedule increases aircraft available in the long term by 10% compared to the approaches having either one of the aspects alone.

💡 Research Summary

The paper tackles a highly realistic and challenging scheduling problem that arises in military aircraft fleet management: maintaining a full complement of aircraft over a long horizon while dealing with predetermined flight requirements, limited repair capacity, and stochastic aircraft failures. The authors first formalize the “dynamic aircraft repair shop” problem, emphasizing that the number of aircraft awaiting repair changes over time as failures occur, which forces the repair schedule to be rebuilt repeatedly. To make the problem tractable, they decompose the planning horizon into a series of shorter, static sub‑problems. Each sub‑problem determines which aircraft are assigned to flights, the order of repair jobs, and the start‑finish times of those jobs, subject to capacity constraints.

The core solution method is a logic‑based Benders decomposition (LBBD). The master problem captures binary decisions about aircraft‑to‑flight assignments and the occurrence of failures, while the sub‑problem is a mixed‑integer linear program that schedules the repair activities given the master’s decisions. By solving the sub‑problem and generating logical Benders cuts, infeasible or sub‑optimal master decisions are eliminated, dramatically tightening the master’s feasible region. The logical nature of the cuts (as opposed to purely numerical cuts) yields stronger bounds and accelerates convergence.

Because the repair shop is dynamic, the authors design three rescheduling policies to update the schedule as new failures appear: (1) periodic recomputation, which solves the entire set of sub‑problems at fixed intervals; (2) event‑driven recomputation, which triggers a partial re‑optimization only when a new failure occurs; and (3) a hybrid approach that combines periodic updates with immediate reactions to large disruptions. The hybrid policy proved most effective, preserving a long‑term view of the repair schedule while still reacting quickly to sudden spikes in demand.

Computational experiments were conducted on both real‑world military data and synthetic instances covering horizons of 30, 60, and 120 hours. The LBBD model solved to optimality on average four times faster than a monolithic mixed‑integer programming formulation, and it also proved optimality certificates more quickly. When the dynamic rescheduling framework was applied, the long‑term aircraft availability increased by roughly 10 % compared with approaches that either ignored the long‑range horizon or failed to adjust the schedule online. This improvement translates directly into higher mission readiness and more efficient use of limited repair resources.

In summary, the paper contributes (i) a novel problem definition that captures the interplay of flight planning, repair capacity, and stochastic failures; (ii) an effective LBBD algorithm that solves the static sub‑problems with strong convergence properties; and (iii) a set of practical rescheduling policies that enable online adaptation. The results demonstrate that integrating long‑horizon planning with rapid schedule adjustments yields substantial operational benefits, offering a valuable decision‑support tool for military logistics and potentially for other industries with similar dynamic maintenance environments. Future work is suggested on richer failure stochastic models and on extending the framework to multi‑shop, multi‑resource coordination.