A synergic economic order quantity model with trade credit, shortages, imperfect quality and inspection errors

•We consider trade credit, shortage, imperfect quality and inspection errors.•We establish a synergic economic order quantity model.•We show concavity and the closed-form solution of the objective function.•We can derive some existing related EOQ models as special cases.•This paper fills the gap between the EOQ model and reality.

This paper develops a synergic economic order quantity (EOQ) model, in which trade credit, shortages, imperfect quality and inspection errors are taken into consideration simultaneously. We prove that the objective function of annual profit is strictly concave and show the closed-form optimal solution to the model. In special cases, some related EOQ models can be derived from our model, which we illustrate with numerical examples. Managerial implications are also proposed.