Replenishment decision for ameliorating inventory with time dependent demand and partial backlogging rate

In contrast to deterioration, amelioration refers to a situation where stocked items incur increased value, quantity, or utility while in stock. It is generally seen in poultry, piggeries, wine industries, etc.; when these items are kept in the farm or the sales counter, they usually incur increase in quantity and value. In this research, we study an inventory model that outlines the optimal replenishment decision for ameliorating items with a partially backlogged time-varying demand rate to raise productivity and understand opportunity cost due to lost sales. Until recently, most of the research in inventory has been focused essentially on deteriorating inventory, giving little or no attention to its ameliorative nature. Therefore, in this research, we developed an EOQ model for such items with time dependent demand and partial backlogging rate. Using differential calculus concept, the various inventory optimising functions, like total cost, number of replenishments, backlogging factors, etc., are computed.