An inventory model for imperfect quality items considering learning effects and partial trade credit policy

The incorporation of payment schemes and imperfect production has received considerable attention in the literature on inventory management; however, researchers have rarely considered these two challenges concurrently. The significance of employing both imperfect production and delay in payment is that both of these challenges affect the profit obtained directly. The total obtained profit can be mitigated by increasing the waste and reducing the number of sold perfect items and delay in payment stimulates the buyers to purchase items and settle their accounts in a specific period. This paper proposes a three-echelon inventory model that (a) Imperfect production is permissible; (b) Inspectors make errors during the inspection process and the errors can be diminished by learning from their previous performance; (c) It is practical to categorize customers into new and old types when old customers are prioritized to receive a full trade credit. As the retailer learns from the experience of screening, the probability of misclassification errors and inspection time decrease for two distinct cases of delay in payment to provide optimal replenishment and promotional decisions. To make a better connection to practical issues, a case study is elaborated. To validate the mathematical model, the impact of the inspector's learning on variables and the total profit is compared in different cases. The analysis shows that it is beneficial for the retailer to make shorter contracts, particularly with new customers to maximize the expected total profit per unit time. Eventually, a numerical experiment is conducted for each subcase to illustrate the impact of learning and determining the optimal policy for the retailer, then some implications for future contributions are outlined.