An economic production model with imperfect quality components and probabilistic lead times

Purpose: This study investigates a production process that requires N kinds of components for the production of a finished product. The producer orders the various kinds of components from different suppliers and receives the orders in lots at the beginning of each production cycle. Similar to situations often encountered in real life, the lead times are random variables with known probability distributions so that a production cycle starts whenever all N kinds of components become available. Each of the lots received at the start of a production run contains both perfect and imperfect quality components. Once all N kinds of components become available, the producer initiates a screening process to detect the imperfect components. The production of the finished product uses only perfect quality components. The imperfect components are removed from inventory whenever the screening process is completed. The percentage of components of perfect quality present in each lot is a random variable with a known probability distribution. Design/methodology/approach: This production process is described and modeled mathematically and the optimal production/ordering policy is derived based on the mathematical model. Findings: The formulated mathematical model resulted in the determination of the optimal policy consisting of the optimal number of finished items ordered to be produce during each production run, the number of components ordered from each supplier, and the reorder point. The derived closed form expression for the optimal lot size depends on the minimum of the number of perfect quality components in a lot, whereas the reorder point is determined based on the maximum lead time. Practical implications: The modeling approach and results of this study provide practical implications that may be beneficial to both production and supply chain managers as well as researchers. Originality/value: This modeling approach that incorporates decision-making related to the logistics of acquiring the components and accounts for the probabilistic nature of the lead times and quality of components addresses a gap in the logistics/production literature.