The present paper focuses on time varying demand and holding cost, taking the same into consideration a finite
horizon inventory problem for a deteriorating item has been developed for study. Deterioration rate is considered as a linearly
time-dependent. The demand rate varies with the time until the shortage occurs, but during the tenure of shortages it becomes
static i.e. constant. Shortages are considered to be a partially backlogged in this study. In the study it is also considered that the
backlogging rate is inversely proportionate to the length of the waiting time for next recovery. The main objective of the study is
to minimize to the total cost of inventory with optimal order quantities of the products in the system. The graphs in the study
show the convexity of the cost function.
