DREAM - Dynamic Resource Evaluation and Assembly Model for MRO: Mathematical Formulation and Scalability Analysis

Abstract

Maintenance operations in aviation are inherently dynamic and cannot be planned deterministically in advance. This uncertainty produces significant inefficiencies: resource shortages cause process delays, while excess resources generate economic waste. In this study, a state-based process-assembly and evaluation model ready for implementation for deterministic and discrete-event simulation that has previously been described conceptually is formally mathematically described. The novelty lies in the simultaneous consideration of the parts to be maintained, the resources needed as well as the available process steps: After every process step performed by available resources, the part's state changes thereby generating a new set of feasible follow-up steps at each stage. Because resources are directly tied to the discrete steps performed, the model can only be defined in an emergent fashion: one cannot pre-define processes and then assign resources; instead, resources serve as boundary conditions, and the model must generate the optimal - whether fastest, cheapest, or otherwise - sequence of steps for planning. The scaling behaviour of this model is analyzed on a concise test set, analysing how the number of parts, the number of process steps, the parallel or serial step order, and the traversal algorithm used for generating the process states impact computational performance.