Integrated inventory model for single-vendor single-buyer with imperfect production process

In this paper, we develop an integrated inventory model for a single‐vendor single‐buyer system considering an imperfect production process under stochastic demand and variable lead time. The model takes into account the deterioration of the vendor's production process. The lead time varies linearly with the production lot size. The proposed model jointly determines the optimal safety factor, ordering quantity, production batch, frequency of deliveries, and process quality, simultaneously. An algorithm is suggested to find the solution and a numerical example is presented to illustrate the benefit of a proposed model. The results from this study show that integrating quality improvement into production‐inventory decisions can reduce expected integrated cost significantly.