We consider a dynamic lot sizing model in which end products to satisfy demands are obtained by remanufacturing m types of cores or manufacturing from raw materials. We consider separate setup costs for manufacturing and remanufacturing in our model. It is conjectured in [21], with reference to [24], that finding an optimal policy to the model when there are separate setup costs for manufacturing and remanufacturing is NP-hard in general. In this paper, we show that an instance of a NP-complete problem can be polynomially reduced to an instance of our model by following [24]. We then show that an optimal policy to our model can be obtained with pseudo-polynomial time complexity for fixed m. To add further to these contributions, we design a polynomial time feasible policy for fixed m for our model. Then we investigate the closeness of this policy to optimality in total system cost. We also provide numerical results in the paper comparing the total system cost under the feasible policy with the optimal cost on instances of the model. Furthermore, we compare numerically the performance of our implementation of the feasible policy with the commercial software package, Gurobi.
Citation
Submitted