Optimization of multi-echelon repairable item inventory systems with fill rate as objective

A sound inventory system for repairable items is the result of cost-efficiency tradeoff between cost and optimal objective. In conventional multi-echelon repairable item inventory models, the operational availability and the waiting time for spares are always the target, but these parameters are rarely used by the designer or customer. This article addresses the issue of how to construct a model of multi-echelon inventory systems with fill rate as the objective. First, an analysis is performed of the spares consumption and replenishment process with multi-echelon inventory positions. Then an optimized model of multi-echelon inventory system is created and the characteristics of objective function are expatiated, which can generate undominated allocations with marginal analysis. The method of using Lagrange multiplier to deal with the problem is also provided. Finally, based on the research conclusion, stock allocation is given in a numerical study and compared with the result generated by a commercial software. The contrastive analysis shows that the algorithm works well and the feasibility and rationality of the analytical method are validated.