Optimal acquisition policy in remanufacturing under general core quality distributions

The quality of acquirable used products (cores) is highly variable, which has made production planning and control of remanufacturing systems difficult. This paper studies an acquisition problem in presence of uncertain core quality. In order to derive optimal acquisition policy, the problem is formulated as a non-linear integer programming model in the framework of order statistics. The model is a strictly discrete convex problem with a unique global minimal solution. Then, a single bisection method is developed to obtain the optimal solution under a general continuous quality distribution. Moreover, the expressions of the optimal solution in some frequently used quality distributions are derived. Furthermore, the model is extended to the case of a general remanufacturing cost function, and corresponding results are presented. Finally, numerical experiments are conducted to test the effects of quality distribution, cost relationships of acquirable cores and remanufacturing cost function.