On the Optimality of Inventory and Shipment Decisions in a Joint Three Echelon Inventory Model with Finite Production Rate under Stock Dependent Demand

Abstract

Abstract This paper develops a mathematical model for a joint three-level supply chain with a single manufacturer (may be a supplier) supplying a single kind of product to a single distributor (may be a wholesaler) and then to a single retailer (may be a buyer). The model is developed for finite production rate and the product demand is expressed in terms stock level. In the proposed work, ordering/setup costs, carrying costs and transportation costs are considered for model development. Optimal inventory and shipment decisions are treated as decision variables. The objective of the proposed model is to demonstrate the optimality of decision variables under the novel idea of stock dependent demand. Also aimed at studying the optimal annual net revenue and total relevant costs of the respective entities and the supply chain. Computer programme is written in MATLAB with respect to the optimality criteria derived and the model is solved with the help of case study data. Also the sensitivity analysis is carried out to show the variation in optimality of decision variables and objective function with respect to model parameters. Finally few managerial implications are discussed from the research findings.