Workforce-constrained maintenance scheduling for military aircraft fleet: a case study

The problem is related to a fleet of military aircraft with a certain flying program in which the availability of the aircraft sufficient to meet the flying program is a challenging issue. During the pre- or after-flight inspections, some component failures of the aircraft may be found. In such cases, the aircraft are sent to the repair shop to be scheduled for maintenance jobs, consisting of failure repairs or preventive maintenance tasks. The objective is to schedule the jobs in such a way that sufficient number of aircrafts is available for the next flight programs. The main resource, as well as the main constraint, in the shop is skilled-workforce. The problem is formulated as a mixed-integer mathematical programming model in which the network flow structure is used to simulate the flow of aircraft between missions, hanger and repair shop. The proposed model is solved using the classical Branch-and-Bound method and its performance is verified and analyzed in terms of a number of test problems adopted from the real data. The results empirically supported practical utility of the proposed model.     

Loading aircraft for military operations

In this paper, we describe an aircraft loading problem submitted by the French military agency (DGA) as part of a more general military airlift planning problem. It can be viewed as a kind of bi-dimensional bin-packing problem, with heterogeneous bins and several additional constraints. We introduce two-phase methods for solving this NP-hard problem. The first phase consists in building good initial solutions, thanks to two fast algorithms: a list-based heuristic and a loading pattern generation method. Both algorithms call a constraint-based subroutine, able to determine quickly if the items already loaded can be reshuffled to accommodate a new object. The second phase improves these preliminary solutions using local search techniques. Results obtained on real data sets are presented.     

Multiaxial constitutive modeling of aircraft engine materials

Based on a newly developed theory (Lu and Weng, Acta Mech., in press) the high temperature behavior of an aircraft engine material is studied under combined stress state. Both monotonic and cyclic deformations are examined to uncover its stress-strain response, as well as its cyclic hardening and strain-ratchetting characteristics. Under a biaxial loading it is disclosed that tensile cyclic hardening is greatly magnified with a superimposed lateral tension, whereas the strain-ratchetting process is led to an enhanced, unsettling state with a superimposed lateral compression. The biaxial transient and steady-state creep strains have also been calculated. The results suggest that while a superimposed lateral tension will inhibit the creep deformation, a lateral compression can greatly promote the inelastic flow. To reflect the practical service conditions of an aircraft engine, the theory is further applied to examine the effect of loading frequency on the development of inelastic strains under concurrent thermal and mechanical loading. It is found that a more frequently flying aircraft will have a greater accumulation of creep strains and, consequently, a greater possibility of material damage in its engine components over the same total flying time.     

A fully adaptive hybrid optimization of aircraft engine blades

A new fully adaptive hybrid optimization method (AHM) has been developed and applied to an industrial problem in the field of the aircraft engine industry. The adaptivity of the coupling between a global search by a population-based method (Genetic Algorithms or Evolution Strategies) and the local search by a descent method has been particularly emphasized. On various analytical test cases, the AHM method overperforms the original global search method in terms of computational time and accuracy. The results obtained on the industrial case have also confirmed the interest of AHM for the design of new and original solutions in an affordable time.     

A branch-and-price approach for operational aircraft maintenance routing

In recent years, considerable effort in the field of operations research has been paid to optimizing airline operations, including the logistics of an airline’s fleet of aircraft. We focus on the problem of aircraft routing, which involves generating and selecting a particular route for each aircraft of a sub-fleet that is already assigned to a set of feasible sequences of flight legs. Similar studies typically focus on long-term route planning. However, stochastic events such as severe weather changes, equipment failures, variable maintenance times, or even new regulations mandated by the Federal Aviation Administration (FAA) play havoc on these long-term plans. In addition, these long-term plans ignore detailed maintenance requirements by considering only one or two of the primary maintenance checks that must be performed on a regular, long-term basis. As a result, these plans are often ignored by personnel in airline operations who are forced on a daily basis to develop quick, ad hoc methods to address these maintenance requirements and other irregular events. To address this problem, we develop an operational aircraft maintenance routing problem formulation that includes maintenance resource availability constraints. We propose a branch-and-price algorithm for solving this problem, which, due to the resource constraints, entails a modification of the branch-on, follow-on branching rule typically used for solving similar problems. Through computational testing, we explore the efficiency of this solution approach under a combination of heuristic choices for column (route) generation and selection.     

Diagnostics of a combustion process in the aircraft radial engine

We present the statistical nonlinear analysis of time series applied to indicated combustion pressure. Using nonlinear methods we analyzed dynamics of a multi cylinder aircraft radial engine in the presence of cyclic perturbations in a single cylinder. The perturbations have been caused by variation of an air/fuel ratio via injection timing. Identification of the disturbed cylinder has been done successfully by adopting wavelet and multifractal analysis. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heuristics for flight and maintenance planning of mission aircraft

Flight and Maintenance Planning (FMP) of mission aircraft addresses the question of which available aircraft to fly and for how long, and which grounded aircraft to perform maintenance operations on, in a group of aircraft that comprise a unit. The objective is to achieve maximum fleet availability of the unit over a given planning horizon, while also satisfying certain flight and maintenance requirements. The application of exact methodologies for the solution of the problem is quite limited, as a result of their excessive computational requirements. In this work, we prove several important properties of the FMP problem, and we use them to develop two heuristic procedures for solving large-scale FMP instances. The first heuristic is based on a graphical procedure which is currently used for generating flight and maintenance plans of mission aircraft by many Air Force organizations worldwide. The second heuristic is based on the idea of splitting the original problem into smaller sub-problems and solving each sub-problem separately. Both heuristics have been roughly sketched in earlier works that have appeared in the related literature. The present paper develops the theoretical background on which these heuristics are based, provides in detail the algorithmic steps required for their implementation, analyzes their worst-case computational complexity, presents computational results illustrating their computational performance on random problem instances, and evaluates the quality of the solutions that they produce. The size and parameter values of some of the randomly tested problem instances are quite realistic, making it possible to infer the performance of the heuristics on real world problem instances. Our computational results demonstrate that, under careful consideration, even large FMP instances can be handled quite effectively. The theoretical results and insights that we develop establish a fundamental background that can be very useful for future theoretical and practical developments related to the FMP problem.     

A minimum-exposure,minimum-elevation military aircraft heuristic route selection model

An heuristic route selection model is presented for developing military aircraft routes through hostile terrain. The capability of modern air defence systems has forced military aircraft to utilize low level flight to avoid detection and increase survivability. By identifying the high and low elevation points within an area, the model determines their exposure values, which are used with their height and internode distance to calculate a penalty for flying to a point from the current position. In developing a route, the model utilizes basic information concerning air defence deployment, initial and destination points, and terrain data, to specify a minimum-exposure, minimum-elevation route. The results include the development of eight routes for 10 by 10 km areas, and six larger terrain areas varying in size from 20 by 20 km to 35 by 35 km. Validation shows the heuristic to be extremely competitive with visual procedures, and to require considerably less time.     

Reliability-centred maintenance analysis for a complex military system

The preventive-maintenance (PM) programme is a very importantdocument in the life cycle of a piece of equipment or system.The traditional method used within China to determine PM programmeshas many disadvantages, and some tasks in old programmes haveproved to be unnecessary. Through analysing a complex militarysystem (X system) by means of the reliability-centred maintenance(RCM) analysis, it is found that RCM analysis is more successfulthan the traditional method in deciding the PM programme. Thenew PM programme does not include unnecessary PM tasks includedin the old programme. Thus the performance of the X system isenhanced, because the cost is reduced without compromising availability.It is believed that RCM analysis in military industry will makea valuable contribution to the maintenance of weapon systemsand equipment.     

Operational aircraft maintenance routing problem with remaining time consideration

The aircraft maintenance routing problem is one of the most studied problems in the airline industry. Most of the studies focus on finding a unique rotation that will be repeated by each aircraft in the fleet with a certain lag. In practice, using a single rotation for the entire fleet is not applicable due to stochasticity and operational considerations in the airline industry. In this study, our aim is to develop a fast responsive methodology which provides maintenance feasible routes for each aircraft in the fleet over a weekly planning horizon with the objective of maximizing utilization of the total remaining flying time of fleet. For this purpose, we formulate an integer linear programming (ILP) model by modifying the connection network representation. The proposed model is solved by using branch-and-bound under different priority settings for variables to branch on. A heuristic method based on compressed annealing is applied to the same problem and a comparison of exact and heuristic methods are provided. The model and the heuristic method are extended to incorporate maintenance capacity constraints. Additionally, a rolling horizon based procedure is proposed to update the existing routes when some of the maintenance decisions are already fixed.     

Model-based control strategies for systems with constraints of the program type

The paper presents a model-based tracking control strategy for constrained mechanical systems. Constraints we consider can be material and non-material ones referred to as program constraints. The program constraint equations represent tasks put upon system motions and they can be differential equations of orders higher than one or two, and be non-integrable. The tracking control strategy relies upon two dynamic models: a reference model, which is a dynamic model of a system with arbitrary order differential constraints and a dynamic control model. The reference model serves as a motion planner, which generates inputs to the dynamic control model. It is based upon a generalized program motion equations (GPME) method. The method enables to combine material and program constraints and merge them both into the motion equations. Lagrange’s equations with multipliers are the peculiar case of the GPME, since they can be applied to systems with constraints of first orders. Our tracking strategy referred to as a model reference program motion tracking control strategy enables tracking of any program motion predefined by the program constraints. It extends the “trajectory tracking” to the “program motion tracking”. We also demonstrate that our tracking strategy can be extended to a hybrid program motion/force tracking.     

Consecutive k-out-of-n systems with maintenance

A consective k-out-of-n system consists of n linearly or cycliccally ordered components such that the system fails if and only if at least k consecutive components fail. In this paper we consider a maintained system where each component is repaired independently of the others according to an exponential distribution. Assuming general lifetime distributions for system's components we prove a limit theorem for the time to first failure of both linear and circular systems.     

A new method of digital simulation for an aircraft gas turbine engine control system

An LD-9 aircraft gas turbine engine with its control system is simulated digitally by a new method, called the ‘method of spare parts’. The computer program of simulation possesses the main capabilities of a real engine altitude test facility and is called a ‘digital engine altitude simulator’. The results of simulation show that the capabilities of this new method are much better than that of the ordinary ‘method of block diagram’. The method can be used for modelling and simulating any type of gas turbine engines or industrial process control systems.     

A mathematical model and algorithms for the aircraft hangar maintenance scheduling problem

An aircraft hangar maintenance scheduling problem is studied, motivated by the aircraft heavy maintenance conducted in a hangar operated by an independent maintenance service company. The aircraft hangar maintenance scheduling problem in such context consists of determining a maintenance schedule with minimum penalty costs in fulfilling maintenance requests, and a series of hangar parking plans aligned with the maintenance schedule through the planning period. A mixed-integer linear programming (MILP) mathematical model, integrating the interrelations between the maintenance schedule and aircraft parking layout plans, is presented at first. In the model, the variation of parking capacity of the maintenance hangar and the blocking of the aircraft rolling in and out path are considered. Secondly, the model is enhanced by narrowing down the domain of the time-related decision variables to the possible rolling in and out operations time of each maintenance request. Thirdly, to obtain good quality feasible solutions for large scale instances, a rolling horizon approach incorporating the enhanced mathematical model is presented. The results of computational experiments are reported, showing: (i) the effectiveness of the event-based discrete time MILP model and (ii) the scalability of the rolling horizon approach that is able to provide good feasible solutions for large size instances covering a long planning period.     

The next generation of UK military satellite communication systems

UK military satellite communications systems are currently provided by the Skynet programme. The current generation is collectively known as Skynet 4, and is due to be replaced from 2003 by the next generation. CDA has been asked to conduct an operational research study to review the potential communications requirements of the Ministry of Defence (MoD) in the period 2003–2013, and assess what contribution could be made to them by the proposed future military satellite communications system. This paper discusses some of the political and technical issues surrounding the work carried out. Technically, the study looked at the dynamic loading of five different satellite options in three scenarios set in 2010. Each combination of scenario and satellite was modelled, and the results produced in terms of the chosen measures of effectiveness. The sensitivity of these results to various assumptions was tested to determine the robustness of the results. The scenarios included land, air and maritime operations. In an area where little or no analysis had previously been attempted (at least in the military context) in the UK, this ‘intervention’ succeeded in clarifying the main issues, and setting a course for future work.     

Effect of wing deformation on highlift systems of transport aircraft

An elastic multibody model is developed that combines highlift system models consisting of flap and slat mechanisms with an elastic wing model. It describes the motions and deformations of the highlift systems with airloads applied and, in particular, the effect of wing deformations on the highlift systems. In addition the model contains a flexible wing with the engine and the middle section of the fuselage that is fixed at the symmetry plane of the aircraft. While previously wing deformation was taken into account in static FE simulations only the developed multibody model provides the investigation of the motions and inner loads of the highlift mechanisms with consideration of the wing deformations with dynamical effects. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling preventive maintenance for deteriorating repairable systems

This paper is concerned with practical methods for the analysisand modelling of data for repairable systems which are subjectto preventive maintenance (PM) and still have an increasingrate of occurrence of failures. Aspects of testing for trendand fitting a nonhomogeneous Poission process to data are discussedModels for scheduling preventive maintenance to minimize costor maximize availability are proposed. They show that the optimalPM cycle interval for these systems decreases with increasingequipment age. One-cycle and two-cycle finite-time-zone replacementmodels are also developed to decide the optimal time for replacingthe equipment in current use.     

Preventive maintenance for homogeneous and heterogeneous systems

We consider optimal preventive maintenance for homogeneous and heterogeneous systems with major (critical) and minor (noncritical) failures. A major failure results in a replacement of a failed system, whereas minor failures can be minimally instantaneously repaired. Distinct from the homogeneous case, where the process of minimal repairs is the Poisson process, the process of minimal repairs in the heterogeneous case is the mixed Poisson process that does not possess the memoryless property. This enables considering the number of minimal repairs as the decision parameter for the corresponding optimal preventive maintenance policy. The proposed approach is theoretically justified, and the detailed illustrative numerical examples are presented.     

Dynamic preventive maintenance scheduling of the modules of fighter aircraft based on random effects regression model

Proper maintenance of fighter aircraft is an important issue to control theairpower. Typical maintenance policy applied is based on the constant schedulefor a given module. This kind of maintenance does not take into account varyingcharacteristics of the module over time. In this paper, we utilize the randomeffects Weibull regression model for non-constant MTBF (mean time betweenfailure) and MTTR (mean time to repair) in order to provide a dynamic preventivemaintenance schedule reflecting the module's varying characteristics in atimely manner. Our study is expected to contribute to ROKA (Republic of KoreaAirforce) in terms of improving the level of combat readiness of fighteraircraft.