Optimizing Spare Parts Inventory for Time-Varying Task

As the requirement of task is dynamical, the usage of equipment will change with time and it will result in the fluctuating demand for spare parts all over the time. In order to improve equipment performance, the users need to forecast equipment failure frequency and demand for spare parts within the task period. Demand in a moment of task period is the result of cumulative effect of the failure spare parts during the repairing time. When the failure and repair time is exponential distribution, the current number of using equipment is the cumulative sum of equipment quantity. According to the non-stationary demand for spare parts, the method of inventory optimization based on non-stationary Poisson process is proposed. Considering the influence of dynamical task to spare parts, the function relationship between dynamical requirements for spare parts and time-varying task is founded. Besides analytical method which applies non-homogeneous Poisson process to calculate the required number of spare parts is obtained, and formula for the time-varying backorder number of spare parts is proposed. As to the optimization model the backorder number of spare parts is made as the optimization objective with the cost constraints. Real-time spare parts optimization calculation model for dynamical task demand is established with analysing the convexity of the objective function and the convex optimization methods is introduced. The best spare parts configuration is given in each moment according to the practical example.