A note on an EOQ inventory model with varying time-proportional deterioration, time-dependent demand and shortages under the conditions of permissible delay in payment

The objective of the proposed research is to investigate the effect of trade credit policy with shortages within the Economic Order Quantity (EOQ) framework. The inventory model for a deteriorating item is developed with the following characteristics: (1) delay in payments is permitted; (2) demand is deterministic, time-dependent and quadratic function of time; (3) deteriorating items follow a time-proportional deterioration rate; (4) the grace period is known and fixed and (5) shortages are permitted to occur and are completely backlogged. For settling the account, the formulation of the model is derived under two main circumstances: Case 1 - the grace period is less than the shortages period and Case 2 - the grace period is greater than the shortages period of the system. A couple of numerical examples and sensitivity analysis of the optimal cost with respect to different parameters of the model has been carried out.