Optimization of Spare Parts for Hierarchically Decomposable Systems

Complex technical systems are often hierarchically composed of exchangeable modules, which themselves may be composed of exchangeable submodules. The hierarchy of modules of such systems can be represented by trees.Defective systems are repaired in a supply depot system by exchanging the defective modules from a stock of spare parts. The exchanged defective modules are repaired for resupply. It is assumed that the defective systems arrive following a Poisson process and that the number of repair channels for all the defective modules is infinite. This implies that all the data which are necessary for the computation are the mean values of the input variables, the results being independent of their distribution.Only an infinite stock of spare parts would assure a 100% readiness for the resupply of defective systems. The problem is then to find a good, reasonable compromise between the risk to be out of stock and the cost of spare parts. A dynamic programming algorithm to optimize the allocation of a given budget to all the modules of the system is developed. The optimization criterion is the minimization of the average backlog (i.e. average number of inoperative systems in resupply) of entire systems at the supply depot system. An implementation of the algorithm is described and some illustrative examples are given.