An optimal procurement policy for multiple consumable accessories with different lifespan distributions

Abstract

Abstract An unscheduled replacement of the consumable parts may result in the expiration of product life, and the stoppage due to it may incur higher cost. If the lifespans of the parts are different, a proper deadline to replace all such parts may be needed to reduce the potentially higher cost. Thus, an optimal stopping usage time of the consumable parts should be determined to avoid the damages that may be caused due to failure. In this paper, an optimal procurement policy that is applied to such consumable accessories in a supply chain is established. The optimization problem for the maximum allowable usage time and ordering cycle for the accumulators is formulated as a nonlinear programming problem. An algorithm which can directly find optimal solution is proposed to solve the nonlinear model for the consumable accessories. Three kinds of accumulators with different lifespan distributions are presented here to illustrate the algorithm. The results show that the correlation among different cost factors (fixed ordering, penalty, shortage, holding and replacement costs) and the variable (the maximum allowable usage time of accumulators, ordering cycle, the total cost for the supply chain and the total ordering quantities) are prominent.