Final answer:
Average on-order inventory in the order-up-to model is not influenced by the variability in demand. In contrast, average on-hand inventory and stockout probability do depend on demand variability due to the need to meet customer needs and the risk of stockouts.
Step-by-step explanation:
In the order-up-to model of inventory management, certain variables are not influenced by the variability in demand. Specifically, the average on-order inventory is determined by the lead time and the order-up-to level and does not depend on the variability of demand. In contrast, both the average on-hand inventory and the stockout probability are affected by the level of demand variability. The average on-hand inventory needs to account for fluctuations in demand to ensure sufficient stock to meet customer needs without incurring excessive holding costs, while the stockout probability is directly influenced by the unpredictability of demand, as more variability increases the risk of running out of stock.