The purpose of this thesis is to develop an inventory cost model of fisheries for deteriorating items that might be with a shortage occurring at the supplier involving a supply chain between the producer and buyer. A numerical example of grouper is used to establish the model and demonstrate that integrated choices are more cost-effective compared with independent choices from the supplier, producer or buyer. This research paper is compared by cases with and without shortages. The optimal number of deliveries is derived with the minimal joint total cost from the integrated viewpoint. Finally, the study is through a sensitivity analysis to explore the effect from all the parameters in the supply chain.