Allocation of external returns of different quality grades to multiple stages of a closed loop supply chain

A single period multistage closed loop supply chain (CLSC) is presented here considering simultaneous manufacturing of new products and remanufacturing of customer returned used products. The quantity of used products in reverse supply chain considered in the model is a fraction of the new products manufactured in the forward supply chain. Used products of known quantity are pulled from end customers as per quality grades. Products are assumed to be mechanical in nature and remanufacturer has to pay different acquisition prices for different quality grades of return. The groups of graded products based on the acquisition prices are thus sorted and sent to stages of CLSC earmarked for them as per demand for repairing/recycling of raw materials. After repairing/refurbishing and recycling at each stage of reverse supply chain the used parts/products become part of forward supply chain. In this paper, a nonlinear maximizing profitability function for CLSC has been formulated for the system with a price dependent demand for n-stages. The decision variables are selling price of product and percentage return of graded used products entering into different stages. A numerical example for a three stage model illustrates the method followed by managerial insight.