An optimal inventory control in hybrid manufacturing/remanufacturing system with deteriorating and defective items

An optimal control model in a manufacturing/remanufacturing-inventory system, with defective, deteriorating, returned and disposed items was developed.In this model, the time of deterioration, and the percentages of defective, returned and disposed items were assumed random variables that follow the gamma distribution, beta rectangular, four-parameter generalised beta (FPGB) and Kumaraswamy distributions, respectively.The total of returned items from customers and defective items divided into the remanufacturing and disposed items. An optimality conditions were derived from the dynamic of the manufacturing/remanufacturing inventory level.The explicit solution under continuous-review policy was achieved by using the Pontryagin maximum principle.Also, simulation and sensitivity analysis results were illustrated numerically.The numerical results suggested that the model can help firms to maintain a balance between the manufacturing and remanufacturing rates to hedge demand and inventory levels.Also, the manufacturing rate was positively related to the disposal rate