In order-driven inventory decision-making, the arrival of demand orders is often characterized by multiple stochastic superposition, i.e., random arrival of demand orders and random presentation of demand sizes. To solve the common inventory problem in this context, it considers the optimal allocation problem of spare parts inventory under the demand arrival and size conforming to the compound stochastic conditions. Specifically, with the spare parts inventory system as the research object under the cycle check (S, T) ordering strategy, it studies the inventory allocation model for two types of demands with high and low shortage costs based on the backlog demand clearance mechanism of the threshold strategy under the composite stochastic demand conditions to achieve the minimization of inventory costs. For model solving, compared with the enumeration method only used in previous studies, an improved genetic algorithm is applied for the first time, and a simple and efficient heuristic algorithm is designed. The results of numerical experiments show that both the heuristic algorithms are better than the first-come-first-served (FCFS) and stock-piling split (SPS) strategies and indicate that the threshold strategy has a significant advantage over the first-come-first-served (FCFS) and stock-piling split (SPS) strategies. The sensitivity analysis proves that the relative cost advantage of the threshold strategy decreases with the increase of the checking period, the mean value of the arriving demand size, and increases with the increase of the lead time and the cost of the unit stock-piling holding. The results of the project provide decision-making reference for lean inventory management.