Optimal acquisition and remanufacturing policies for multi-product remanufacturing systems

In order to balance between the environmental and economic benefit, the problem is formulated as a nonlinear programming model in presence of the quality variability of cores and carbon tax scheme, subject to budget and risk constraints. Since the average cost of the remanufactured products is independent of the remanufacturing quantity, the model is then decomposed into two separated sub-problems, namely the remanufacturing problem and the acquisition problem. In the remanufacturing problem, the optimal remanufacturing policies, including the optimal remanufacturing cost thresholds and the optimal remanufacturing rate, are derived. In the acquisition problem, the optimal policies of core portfolio, acquisition quantities, and remanufacturing quantities can be derived. The acquisition problem, viewed as an extended Multi-Product Newsvendor Problem (MPNP), is a convex optimization problem. Furthermore, a two-tier bisection method with polynomial computational complexity can be developed to obtain the optimal policies based on the Karush-Kuhn-Tucker (KKT) conditions. Finally, numerical experiments are provided to show the application of the model and the effect of the quality variability.