The presence of the spare parts stock is a necessity to ensure the continuity of services. The supply of spare parts is a special case of the global supply chain. The main objective of our research is to propose a global spare parts management approach which allows decision makers to determine the essential points in stock management. Thus, it is important for the stock manager to evaluate the system considered from time to time based on performance indicators. Some of these indicators are presented in the form of a dashboard. The presentation of this chapter chronologically traces the progress of our research work. In the first part, we present the work related to the forecast of spare parts needs through parametric and statistical methods as well as a Bayesian modelling of demand forecasting. To measure the appreciation of the supply of spare parts inventory, the second part focuses on work related to the evaluation of the performance of the spare parts system. Thus, we concretize the link between the management of spare parts and maintenance in the third part, more precisely, in the performance evaluation of the joint -management of spare parts and maintenance, in order to visualize the influence of parameters on the system. In the last section of this chapter, we will present the metaheuristic methods and their use in the management of spare parts and maintenance and make an analysis on work done in the literature.

The supply chain of spare parts is the intersection between the supply chain, the after-sales

and the maintenance services. Some authors have tried to define improvement paths in terms

of models to satisfy the performance criteria. In addition, other authors are directed towards

the integration of risk management in the demand forecasting and the stock management

(performance evaluation) through probabilistic models. Among these models, the probabilistic

graphical models are the most used, for example, Bayesian networks and petri nets.

Performance evaluation is done through performance indicators.

To measure the appreciation of the supply of the spare parts stock, this paper focuses on the

performance evaluation of the system by petri nets. This evaluation will be done through

an analytical study. The purpose of this study is to evaluate and analyze the performance of

the system by proposed indicators. First, we present a literature review on Petri nets which

is the essential tool in our modeling. Secondly, we present in the third section the analytical

study of the model based on bath deterministic and stochastic petri networks. Finally, we

present an analysis of the proposed model compared to the existing ones.