An integrated production–inventory model with imperfect production processes and Weibull distribution deterioration under inflation

This study develops an integrated production and inventory model from the perspectives of both the manufacturer and the retailer. The model assumes a varying rate of deterioration, partial backordering, inflation, imperfect production processes and multiple deliveries. The elapsed time until the production process shift is assumed to be arbitrarily distributed. The discounted cash flow and classical optimization technique are used to derive the optimal solution. A numerical example including the sensitivity analysis is given to validate the results of the production–inventory model. The integrated decision results in lower optimal joint cost compared with an independent decision by the manufacturer and the retailer.