Production reliability evaluation of quality-differentiated orders with budget constraints under two fulfillment strategies

Stochastic flow production networks (SFPNs) provide a framework for modeling production systems by capturing the stochastic capacities of workstations and associated probabilities. Existing studies have mainly applied this framework to evaluate the production reliability of satisfying a single product demand. Practically, production often yields quality-differentiated products that are generally classified into grades and sold to customers with varying quality requirements. When products are classified into multiple grades, two distinct strategies are available for meeting demand: satisfying demand with the same grade or applying downward substitution (DS), each leading to different costs. This paper extends the SFPN to evaluate production reliability under orders for multiple grades and budget constraints for these two strategies. An algorithm is developed to compute production reliability for either strategy, and sensitivity analysis examines the impact of demand levels, relevant costs and selling prices on system performance. The results provide manufacturer supervisors with actionable insights to support order acceptance decisions based on the expected production reliability and budget of the selected strategy.