A novel mathematical inventory model for growing-mortal items (case study: Rainbow trout)

Abstract

• Developing a novel mathematical inventory model for growing-mortal items. • Studying the proposed model for trout fish production in a two-echelon supply chain (case study). • Applying revenue-sharing contract as well as revenue and cost sharing contract into proposed model. • Proposing a new feeding function for rainbow trout. • Providing managerial insights into trout production in a coordinated supply chain. Unlike the extensive inventory models for both ameliorating and deteriorating items, incorporating some specific features of these products have mostly been neglected. To fill this research gap, providing an appropriate mathematical inventory model for both ameliorating and deteriorating items is of paramount importance. In this regard, this paper proposes a novel mathematical inventory model for products called growing-mortal items in a two-echelon supply chain consisting of one supplier and one farmer. The proposed inventory model is more precise than analogous inventory models due to the fact that the specific growth function for the item is considered as well as mortality rate. As a case study, the model is applied to rainbow trout, which can be used for other types of growing-mortal items. Moreover, a feeding function is first-ever proposed for rainbow trout regarding the case study. The goal of this paper is to study the growth period in the supplier and then in the farmer sites to maximize the profit of the supplier as a leader and farmer as a follower under a Stackelberg game. To demonstrate how to reduce the inventory system costs by two coordination mechanisms, namely revenue-sharing and revenue and cost sharing, the model is solved under centralized and decentralized cases. Finally, sensitivity analysis on key parameters is also conducted to derive some managerial insights.