Deteriorating item inventory model with shortage due to supplier in an integrated supply chain

The aim of this paper is to develop an inventory model for deteriorating items with a shortage occurring at the supplier involving a supply chain between the producer and buyer. A numerical example is used to illustrate the model and demonstrate that integrated decisions are more cost-effective compared with independent decisions from the supplier, producer or buyer. The optimal number of deliveries is derived with the minimal joint total cost from the integrated viewpoint. This study compares cases with and without shortages. A sensitivity analysis is given to explore the effect from a supplier shortage.