Although new technologies have been deeply applied in manufacturing systems, manufacturing enterprises are still encountering difficulties in maintaining efficient and flexible production due to the random arrivals of diverse customer requirements. Fast order delivery and low inventory cost are fundamentally contradictory to each other. How to make a suitable production-triggering strategy is a critical issue for an enterprise to maintain a high level of competitiveness in a dynamic environment. In this paper, we focus on production-triggering strategies for manufacturing enterprises to satisfy randomly arriving orders and reduce inventory costs. Unified theoretical models and simulation models of different production strategies are proposed, including time-triggered strategies, event-triggered strategies, and hybrid-triggered strategies. In each model, both part-production-triggering strategies and product-assembly-triggering strategies are considered and implemented. The time-triggered models and hybrid-triggered models also consider the impact of the period on system performance. The results show that hybrid-triggered and time-triggered strategies yield faster order delivery and lower inventory costs than event-triggered strategies if the period is set appropriately.