Spare Parts Replacement Policy Based on Chaotic Models

Poisson point processes are widely used to model the consumption of spare parts. However, when the items have very low consumption rates, the historical sample sizes are too small. This paper presents a modelling technique for spare parts policies in the case of items with a low consumption rate. We propose the use of chaotic models derived from the well-known chaotic processes logistic map and Hénon attractor to assess the behaviour of a set of five medium voltage motors supplying four drives in the rolling mill of a steelmaking plant. Supported by the chaotic models, we conclude that the company needs an additional motor to ensure full protection against shortages

Markov-modulated analysis of a spare parts system with random lead times and disruption risks

Spare parts supply chains are highly dependent on the dynamics of their installed bases. A decreasing number of capital products in use increases the nonstationary supply-side risk especially towards the end-of-life of capital products. This supply-side risk appears to present itself through varying lead times coupled with supply disruptions. To model the nonstationary supply-side risk, we consider an exogenous Markov chain that modulates random lead times and disruption probabilities. Assuming that order crossovers do not occur, we prove the optimality of a state-dependent base stock policy. Later, we conduct an impact study to understand the value of considering stochastic lead times and supply disruption risk in spare parts inventory control. Our results indicate that the coupled effect of random lead times and disruptions can be larger than the summation of individual effects even for moderate lead time variances. Also, the effect of nonstationarity on total cost can be as large as the summation of all risk factors combined. In addition to this managerial insight we present a procedure for supply risk mitigation based on an empirical model and our mathematical model. Experiments on a real business case indicate that the procedure is capable of reducing costs while making the inventory system more prepared for disruptions