Scheduling the repair of aircraft components - a case study

In aircraft components maintenance shops, components are distributed amongst repair groups and their respective technicians based on the type of repair, on the technicians skills and workload, and on the customer required dates. This distribution planning is typically done in an empirical manner based on the group leader’s past experience. Such a procedure does not provide any performance guarantees, leading frequently to undesirable delays on the delivery of the aircraft components. Among others, a fundamental challenge faced by the group leaders is to decide how to distribute the components that arrive without customer required dates. This paper addresses the problems of prioritizing the randomly arriving of aircraft components (with or without pre-assigned customer required dates) and of optimally distributing them amongst the technicians of the repair groups. We proposed a formula for prioritizing the list of repairs, pointing out the importance of selecting good estimators for the interarrival times between repair requests, the turn-around-times and the man hours for repair. In addition, a model for the assignment and scheduling problem is designed and a preliminary algorithm along with a numerical illustration is presented.

Temperature-averaged and total free-free Gaunt factors for κ and Maxwellian distributions of electrons

Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by κ-distributions. The free-free spectrum and radiative losses depend on the temperature-averaged (over the electrons distribution) and total Gaunt factors, respectively. Thus, there is a need to calculate and make available these factors to be used by any software that deals with plasma emission. Methods. We recalculated the free-free Gaunt factor for a wide range of energies and frequencies using hypergeometric functions of complex arguments and the Clenshaw recurrence formula technique combined with approximations whenever the difference between the initial and final electron energies is smaller than 10−10 in units of z2Ry. We used double and quadruple precisions. The temperature- averaged and total Gaunt factors calculations make use of the Gauss-Laguerre integration with 128 nodes. Results. The temperature-averaged and total Gaunt factors depend on the κ parameter, which shows increasing deviations (with respect to the results obtained with the use of the Maxwellian distribution) with decreasing κ. Tables of these Gaunt factors are provided.