Inventory Model for Decaying Item with Continuously Variable Holding Cost and Partial Backlogging

Holding costs are determined from the investment in physical stocks and storage facilities for items during a cycle. In most of the research papers, holding cost rate per unit time for perishable inventory is assumed as constant. However, this is not necessarily the case when items in stock are decaying. In this work, paying better attention on the holding cost, we present a deteriorating inventorymodel in which the unit holding cost is continuously based on the deterioration of the inventory with the time the item is in stock. The deterioration rate is assumed as a Weibull distribution function. Declining market demand is considered in this paper. Shortages are allowed and partial backlogged. The partial backlogging rate is a continuous exponentially decreasing function of waiting time in purchasing the item during stock out period. Conditions for uniquely existence of global minimum value of the average total cost per unit time are carried out. Numerical illustration and sensitivity analysis are presented.