A sustainable production-inventory model joint with preventive maintenance and multiple shipments for imperfect quality items

The quality of products, maintenance operations, and transportation policies are primary concerns of managers in inventory and production planning issues. Besides that, environmental concerns and regulations are growing increasingly and attracted much attention to green production concepts such as sustainable production. Previous authors conducted a wide range of research on these problems separately. Regarding the gap of an integrated framework, we formulate a sustainable Economic Production Quantity model by considering preventive maintenance and multiple shipments of items where a portion of produced items are defective. Two different Cases are studied. In Case I, we assumed that the demand in the production period is satisfied by the produced items in the previous cycle. In another state and in Case II, simultaneous production and consumption during the production period is considered and mathematically formulated. An analytical method is presented for solving the models, and a numerical example is discussed for both Cases. Moreover, sensitivity analysis of the models is carried out, and some managerial insight is derived by changing some of the critical parameters of models. Finally, we present some directions for feature researches.