An imperfect production inventory model with setup cost reduction and carbon emission for an integrated supply chain

摘要

The present paper develops a sustainable framework under a supply chain environment by considering a vendor and a buyer. The vendor governs the manufacturing process to serve the demand of the buyer. The manufacturing system is imperfect which ends up producing some fraction of defectives. For the sake of maintaining the goodwill of the organization, it is imperative to maintain the quality standards. Thus, the buyer employs the screening process to bifurcate the perfect items from the imperfect ones. The imperfect items secluded after screening are reverted back to the vendor, for which a warranty cost is incurred. Further, in an attempt to achieve sustainability the model considers the carbon-emissions costs during the transportation process. A one-time discrete investment is also considered for minimizing the setup cost of the vendor for subsequent cycles. The models are developed for the case of the individual decision and for the joint verdict of the players under consideration. Moreover, it has been proved that the integrated model performs proficiently over the individual model. The objective is to jointly optimize the costs sustained by the two players. Numerical analysis and sensitivity analysis is done for imparting the validity and robustness of the model.