Presenting a Mathematical Model for the Collection and Reproduction of Depreciated Products in a Closed Loop Supply Chain Using the GameTheory

In the real world, remanufacturing depreciated products for the purpose of cost reduction in supply chains, is recognized as a competitive advantage. In this paper, an appropriate approach for collecting and remanufacturing depreciated products in a closed-loop supply chain is considered with the aim of reducing costs using the Stackelberg game theory. To this end, the considered chain members include the manufacturer, the retailer, and the remanufacture contractor (as the third party to the contract). In this research, the four following scenarios are considered and the results are analyzed: 1) Payment by the manufacturer to collect and reproduce the depreciated product; 2) Joint payment of an amount by the retailer and the manufacturer to collect and reproduce the depreciated product; 3) Joint payment of an amount by the manufacturer and the third party to the contract to collect and reproduce the depreciated product; 4) Payment by the manufacturer for collection and non-reproduction of the product. The computational results show that the chain profit will reach its maximum amount with the optimal reproduction rate considering the third scenario, and the chain members will gain more benefits than other scenarios. The findings of this research indicate that when the reproduction process does not take place, the lowest possible profit is made in the chain. The sensitivity analysis performed by increasing the effect of the final product price on customer demand in different periods, shows a decreasing trend in the three decision variables of final product price, selling price to the retailer, and the amount paid to the customer for each consumed product.