A dynamic model for the optimization of decoupling point and production planning in a supply chain

In this paper, we propose a dynamic model to simultaneously determine the optimal position of the decoupling point and production-inventory plan in a supply chain such that the total cost of the deviation from the target production rate and the target inventory level is minimized. Using the optimal control theory, we derive the closed form of the optimal solution when the production smoothing policy and the zero-inventory policy are applied. The result indicates that under the production smoothing policy, the overestimation of demand rate during the pre-decoupling stage guarantees the existence of the optimal decoupling point; meanwhile the optimal decoupling point exists under zero-inventory policy when the demand rate is underestimated. Also we perform mathematical analysis on the behavior of the optimal production rate and the inventory level and the effect of problem parameters such as the length of the product life cycle and the forecast error on the performance.