Optimal control of decoupling point with deteriorating items
Abstract: 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.
Keywords: decoupling points;
deteriorating items; supply chain; optimal control; “push” and “pull”; supply
chain management
Author: Kuan Yang, Ermei Wang
Journal Code: jptindustrigg140091
