An inventory model with weibull distribution deteriorating item with exponential declining demand and partial backlogging

In this paper an inventory model developed for Weibull Distribution deteriorating items with exponential declining demand and the shortages are partially backlogged. In (2005) Liang-Yuh Ouyang, Kun-Shan Wu and Mei-Chuan Cheng have presented the paper in inventory model for deteriorating items in which exponential declining demand and partial backlogging. They have used the deterioration rate is constant. In practical cases the deterioration rate increases with time but most of researchers taken into account constant deterioration rate in their own research paper.

This paper is provoked by Ouyang, Wu and Cheng (2005) and expanding their model by using variable deterioration rate. It is assumed that the deterioration rate follows two parameter Weibull Distribution. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Further, we show that the minimized objective cost function is jointly convex and derive the optimal solution. A numerical example is provided to illustrate the problem. Sensitivity analysis of the optimal solution with respect to the changes in the value of the system parameter is also discussed.