An order level optimal inventory policy for Weibull distributed deteriorating items varying with generalised demand, shortages and permissible delay in payments

The main purpose of this study is to formulate an optimal ordering policy for deteriorating items with shortages within the economic order quantity (EOQ) framework satisfying the following characteristics: 1) inventory system deals with only one type of item; 2) demand is continuous and quadratic function of time in nature; 3) deterioration rate follows a special type of Weibull distribution function; 4) the complete backlogged shortages are allowed to occur in the proposed model; 5) grace periods in payment are permissible during the inventory cycle. The quadratic demand function justifies the demand pattern of seasonal products as well as newly launched items arriving in the market. Depending upon the positions of the grace period and the shortage time point, the model is derived into two main circumstances: Policy I: grace period is less than or equal to the shortages time point and Policy II: grace period is greater than the shortage time point. Finally, a couple of numerical examples and sensitivity analysis of optimal solutions for illustration are provided.