Purpose: The aim of this paper is to develop a dynamic model to simultaneously determine the optimal position of the decoupling point and the optimal path of the production rate as well as the inventory level in a supply chain. With the objective to minimize the total cost of the deviation from the target setting, the closed forms of the optimal solution are derived over a finite planning horizon with deterioration rate under time-varying demand rate.Design/methodology/approach: The Pontryagin's Maximum Principle is employed to explore the optimal position of decoupling point and the optimal production and inventory rate for the proposed dynamic models. The performances of parameters are illustrated through analytical and numerical approaches.Findings: The results denote that the optimal production rate and inventory level are closely related to the target setting which are highly dependent on production policy; meanwhile the optimal decoupling point is exist and unique with the fluctuating of deteriorating rate and product life cycle. The further analyses through both mathematic and numerical approaches indicate that the shorten of product life cycle shifts the optimal decoupling point forward to the end customer meanwhile a backward shifting appears when the deterioration rate increase.Research limitations/implications: There is no shortage allowed and the replacement policy is not taken into account.Practical implications: Solutions derived from this study of the optimal production-inventory plan and decoupling point are instructive for operation decision making. The obtained knowledge about the performance of different parameters is critical to deteriorating supply chains management.Originality/value: Many previous models of the production-inventory problem are only focused on the cost. The paper introduces the decoupling point control into the production and inventory problem such that a critical element-customer demand, can be taken into account. And the problem is solved as dynamic when the production rate, inventory level and the position of the decoupling point are all regarded as decision variables.
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